Journal of the ICRU Vol 4 No 2 (2004) Report 72 Oxford University Press

DOI: 10.1093/jicru/ndh032

APPENDIX A: COMPILATION OF PHYSICAL DATA A.1

BETA RAYS

Table A.1. Decay data for selected beta-particle-emitting radionuclides. Data from National Nuclear Data Center (2001); photon contamination includes those with energies >10 keV and emission probabilities >0.1 % per disintegration. Radionuclide

32

P Sr---90 Y 90 Y 106 Ru---106 Rh 90

Half-life (d)

14.26 10515 2.67 2.67 373.6 0.000345

Average number per dis.

Maximum energy Emax (MeV)

Average energy hEbi (MeV)

Photon contamination

Method of production

1.0 1.0 1.0 1.0 1.0 1.0

1.71 0.546 2.28 2.28 0.0394 3.54

0.695 0.196 0.934 0.934 0.0100 1.41

-----------

Neutron activation Fission product

------

Neutron activation Fission product

0.926

1.07

0.347

186

3.72

188

69.4 0.709

1.0 1.0

0.349 2.12

0.099 0.764

0.709

1.0

2.12

0.762

Re

W---Re

188

188

Re

ª International Commission on Radiation Units and Measurements 2004

106

Rh---0.512 MeV (20 %) 0.616 MeV (0.8 %) 0.622 MeV (9.9 %) 0.873 MeV (0.4 %) 1.05 MeV (1.6 %) 1.13 MeV (0.4 %) 1.56 MeV (0.2 %) 0.0580 MeV (1.7 %) 0.0593 MeV (3.0 %) 0.0615 MeV (1.2 %) 0.0630 MeV (2.0 %) 0.0714 MeV (0.9 %) 0.137 MeV (9.4 %) 188 W---0.0636 MeV (0.1 %) 0.227 MeV (0.2 %) 0.291 MeV (0.4 %) 188 Re---0.0714 MeV (0.1 %) 0.0615 MeV (1.4 %) 0.0630 MeV (2.4 %) 0.155 MeV (15.1 %) 0.478 MeV (1.0 %) 0.633 MeV (1.3 %) 0.635 MeV (0.1 %) 0.673 MeV (0.1 %) 0.829 MeV (0.4 %)

Neutron activation

Neutron activation

Neutron activation

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

Table A.2. Dimensions of beta-ray sources. Manufacturer (a) 90Sr----90Y planar sources Tracerlab ICN/Tracerlab Atlantic Research Corp Atomchem New England Nuclear Amersham International 3M Isotope Products Laboratory Nuclear Associates Technical Operations Manning Research Model

Diameter (mm)

Model

Physical diameter (mm)

Active diameter (mm)

Active area (mm)2

RA-1 B1 NB-1 SIA.20 6DIA

12.3----13.2 10.2----10.5 10.0 12.0----12.3 11.4 10.3 10.3 10.2

4.3----7.9 7.5----8.9 8.7 7.9 5.0----6.5 8.6 7.5----8.4 8.5

14.7----48.5 43.6----62.4 59.0 49.3 19.9----32.9 57.9 44.6----55.3 57.7

Height (mm)

(b) 90Sr----90Y concave sources manufactured by Amersham International SIA.1 23 5.9 SIA.2 23 5.9 SIA.3 23 5.9 SIA.4 23 5.9 SIA.5 9 · 6b 1.2 SIA.6 15 3.9

Active diameter (mm)

Radius of curvature (mm)

18 18----6a 18 6 7 · 4b 12

15 15 15 15 15 10

(c) 106Ru----106Rh curved sources manufactured by BEBIG GmbH (see www.bebig.de) CCZ 11.6 2.3 9.5 CCY 11.6 2.3 9.5 CCX 11.6 2.3 9.5 CXS 11.6 2.3 7.7 CCA 15.3 3.3 13.0 CCD 17.9 4.3 15.5 CCB 20.2 5.4 17.8 CGD 22.3 6.1 19.9 CCC 24.8 8.0 22.5 COB 19.8 5.2 17.1 COD 25.4 7.5 23.0 COE 19.8 5.2 17.4 COC 25.4 7.5 22.7 CIA 15.3 3.3 13.0 CIB 20.2 5.4 17.8 CIB-2 20.2 5.4 17.8 (a) (b)

6 mm diameter inactive area in center of active area. Rectangular active area.

Manufacturer/marketer

Isotope

Type

(d) Intravascular brachytherapy sources (Waksman and Serruys, 2000) 90 Sr----90Y Seeda Novoste/BEBIG 32 Guidant VI P Wire 90 Boston Scientific Scimed Y Wire (coil) 186,188 Re Wire (coil) CVRT 32 Radiance Medical Systems P Shell 32 Isostent P Stent 188 Progressive Angioplasty Systems Re and others Balloon (liquid-filled) 133 Cook Xe Balloon (gas-filled) (a) (b)

12 12 12 12 12 12 12 13 13 12 14 12 14 12 12 12

For treatments, trains of between 8 and 32 seeds are used. Approximate; final size is lumen-size dependent.

88

Length (mm)

Diameter (mm)

2.5 20 and 27 29 32 20----40 15----25 20----40 30----40

0.6 0.46 0.34 0.85 2.5----3.5b 2.5----3.5b 2----4b 2.5----4b

APPENDIX A: COMPILATION OF PHYSICAL DATA Table A.3. Calculated beta-ray spectra. The values give the number of beta rays/disintegration per unit interval of E/Emax. To get the number per mega electronvolt, these values should be divided by Emax. Spectra for a much larger number of nuclides are given in ICRU Report 56 (ICRU, 1997b). Emax (MeV)

E/Emax 0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 0.325 0.350 0.375 0.400 0.425 0.450 0.475 0.500 0.525 0.550 0.575 0.600 0.625 0.650 0.675 0.700 0.725 0.750 0.775 0.800 0.825 0.850 0.875 0.900 0.925 0.950 0.975 1.000

32

P 1.710

90

Y 2.281

90

106

0.471 0.608 0.750 0.877 0.994 1.101 1.198 1.287 1.365 1.434 1.493 1.541 1.578 1.605 1.620 1.625 1.619 1.602 1.575 1.538 1.491 1.435 1.371 1.299 1.220 1.134 1.044 0.950 0.853 0.754 0.654 0.556 0.461 0.369 0.284 0.206 0.137 0.081 0.037 0.010 0.000

0.761 0.849 0.945 1.031 1.109 1.179 1.239 1.291 1.335 1.372 1.401 1.435 1.443 1.446 1.444 1.438 1.428 1.414 1.395 1.373 1.346 1.315 1.279 1.238 1.191 1.138 1.078 1.012 0.939 0.860 0.775 0.684 0.589 0.492 0.394 0.298 0.207 0.127 0.061 0.017 0.000

7.482 7.213 7.112 6.925 6.581 5.994 5.102 3.923 2.622 1.594 1.401 1.435 1.443 1.446 1.444 1.438 1.428 1.414 1.395 1.373 1.346 1.315 1.279 1.238 1.191 1.138 1.078 1.012 0.939 0.860 0.775 0.684 0.589 0.492 0.394 0.298 0.207 0.127 0.061 0.017 0.000

0.440 0.563 0.693 0.826 0.957 1.084 1.205 1.327 1.421 1.504 1.572 1.627 1.667 1.693 1.703 1.700 1.682 1.652 1.610 1.556 1.491 1.418 1.338 1.252 1.161 1.067 0.972 0.877 0.785 0.690 0.596 0.503 0.414 0.329 0.252 0.183 0.123 0.072 0.033 0.009 0.000

89

Sr----90Y 2.281

Rh 3.540

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01

Energy (MeV)

1.246Eþ02 1.074Eþ02 9.485Eþ01 8.517Eþ01 7.746Eþ01 6.592Eþ01 5.764Eþ01 5.139Eþ01 4.648Eþ01 4.251Eþ01 3.923Eþ01 3.647Eþ01 3.411Eþ01 3.028Eþ01 2.730Eþ01 2.491Eþ01 2.294Eþ01 1.927Eþ01 1.671Eþ01 1.482Eþ01 1.335Eþ01 1.124Eþ01 9.769Eþ00 8.691Eþ00 7.863Eþ00 7.206Eþ00 6.671Eþ00 6.228Eþ00 5.853Eþ00 5.256Eþ00 4.800Eþ00 4.441Eþ00 4.150Eþ00 3.620Eþ00 3.262Eþ00 3.005Eþ00 2.812Eþ00 2.544Eþ00

Collision (MeV cm2 g1)

2.441E03 2.561E03 2.651E03 2.721E03 2.778E03 2.863E03 2.924E03 2.969E03 3.004E03 3.031E03 3.053E03 3.071E03 3.086E03 3.109E03 3.126E03 3.139E03 3.149E03 3.164E03 3.174E03 3.184E03 3.193E03 3.207E03 3.219E03 3.231E03 3.243E03 3.256E03 3.271E03 3.286E03 3.302E03 3.336E03 3.373E03 3.411E03 3.452E03 3.560E03 3.676E03 3.801E03 3.933E03 4.221E03

Radiative (MeV cm2 g1)

Stopping power

1.246Eþ02 1.074Eþ02 9.486Eþ01 8.517Eþ01 7.746Eþ01 6.592Eþ01 5.765Eþ01 5.139Eþ01 4.648Eþ01 4.251Eþ01 3.923Eþ01 3.647Eþ01 3.411Eþ01 3.028Eþ01 2.730Eþ01 2.491Eþ01 2.295Eþ01 1.927Eþ01 1.671Eþ01 1.482Eþ01 1.336Eþ01 1.124Eþ01 9.772Eþ00 8.694Eþ00 7.866Eþ00 7.209Eþ00 6.675Eþ00 6.231Eþ00 5.857Eþ00 5.259Eþ00 4.803Eþ00 4.444Eþ00 4.153Eþ00 3.623Eþ00 3.265Eþ00 3.008Eþ00 2.816Eþ00 2.548Eþ00

Total (MeV cm2 g1) 4.013E06 6.181E06 8.663E06 1.145E05 1.453E05 2.155E05 2.969E05 3.889E05 4.914E05 6.040E05 7.265E05 8.588E05 1.001E04 1.312E04 1.661E04 2.045E04 2.463E04 3.657E04 5.054E04 6.646E04 8.426E04 1.253E03 1.731E03 2.275E03 2.880E03 3.545E03 4.267E03 5.043E03 5.871E03 7.677E03 9.669E03 1.184E02 1.417E02 2.064E02 2.792E02 3.592E02 4.452E02 6.325E02

CSDA range (g cm2)

A-150 Tissue-equivalent plastic

9.797E06 1.218E05 1.447E05 1.668E05 1.883E05 2.300E05 2.702E05 3.091E05 3.470E05 3.839E05 4.201E05 4.556E05 4.904E05 5.584E05 6.244E05 6.886E05 7.514E05 9.028E05 1.047E04 1.187E04 1.322E04 1.583E04 1.832E04 2.071E04 2.302E04 2.526E04 2.745E04 2.958E04 3.166E04 3.570E04 3.959E04 4.336E04 4.702E04 5.577E04 6.405E04 7.197E04 7.960E04 9.423E04

Brems yield

1.263Eþ02 1.089Eþ02 9.617Eþ01 8.634Eþ01 7.852Eþ01 6.682Eþ01 5.843Eþ01 5.208Eþ01 4.710Eþ01 4.308Eþ01 3.976Eþ01 3.696Eþ01 3.456Eþ01 3.068Eþ01 2.766Eþ01 2.524Eþ01 2.325Eþ01 1.953Eþ01 1.693Eþ01 1.501Eþ01 1.353Eþ01 1.138Eþ01 9.897Eþ00 8.805Eþ00 7.966Eþ00 7.300Eþ00 6.758Eþ00 6.309Eþ00 5.930Eþ00 5.324Eþ00 4.863Eþ00 4.498Eþ00 4.204Eþ00 3.667Eþ00 3.304Eþ00 3.044Eþ00 2.848Eþ00 2.577Eþ00

Collision (MeV cm2 g1) 2.491E03 2.616E03 2.710E03 2.784E03 2.843E03 2.933E03 2.996E03 3.043E03 3.079E03 3.107E03 3.129E03 3.147E03 3.162E03 3.185E03 3.201E03 3.212E03 3.221E03 3.234E03 3.241E03 3.248E03 3.253E03 3.265E03 3.275E03 3.285E03 3.296E03 3.308E03 3.321E03 3.336E03 3.352E03 3.385E03 3.421E03 3.460E03 3.500E03 3.609E03 3.727E03 3.853E03 3.987E03 4.278E03

Radiative (MeV cm2 g1)

Stopping power

1.263Eþ02 1.089Eþ02 9.617Eþ01 8.634Eþ01 7.853Eþ01 6.682Eþ01 5.843Eþ01 5.209Eþ01 4.711Eþ01 4.308Eþ01 3.976Eþ01 3.696Eþ01 3.457Eþ01 3.069Eþ01 2.767Eþ01 2.524Eþ01 2.325Eþ01 1.953Eþ01 1.694Eþ01 1.502Eþ01 1.353Eþ01 1.139Eþ01 9.901Eþ00 8.808Eþ00 7.969Eþ00 7.303Eþ00 6.762Eþ00 6.312Eþ00 5.933Eþ00 5.328Eþ00 4.866Eþ00 4.502Eþ00 4.207Eþ00 3.670Eþ00 3.308Eþ00 3.047Eþ00 2.852Eþ00 2.581Eþ00

Total (MeV cm2 g1)

Adipose tissue (ICRU-44)

3.958E06 6.095E06 8.543E06 1.129E05 1.433E05 2.126E05 2.928E05 3.836E05 4.847E05 5.958E05 7.168E05 8.473E05 9.873E05 1.295E04 1.639E04 2.018E04 2.431E04 3.609E04 4.988E04 6.559E04 8.316E04 1.236E03 1.709E03 2.245E03 2.843E03 3.499E03 4.211E03 4.977E03 5.795E03 7.577E03 9.544E03 1.168E02 1.398E02 2.037E02 2.757E02 3.545E02 4.395E02 6.244E02

CSDA range (g cm2)

9.859E06 1.226E05 1.457E05 1.681E05 1.898E05 2.320E05 2.727E05 3.121E05 3.505E05 3.879E05 4.246E05 4.605E05 4.957E05 5.644E05 6.310E05 6.959E05 7.592E05 9.117E05 1.057E04 1.198E04 1.333E04 1.594E04 1.843E04 2.083E04 2.314E04 2.539E04 2.757E04 2.970E04 3.178E04 3.582E04 3.971E04 4.348E04 4.713E04 5.588E04 6.416E04 7.208E04 7.971E04 9.433E04

Brems yield

Table A.4. Values, for monoenergetic electrons (negatrons), of the mass collision stopping power, the mass radiative stopping power, the total mass stopping power, the CSDA range and the bremsstrahlung yield. Results were obtained mainly using the methods and data given in ICRU Report 37 (ICRU, 1984). Values for the mass radiative stopping power are based on the more current work of Seltzer and Berger (1986), and cause small differences in related quantities (CSDA range and bremsstrahlung yield).

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

90

91

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03

Energy (MeV)

3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

1.025Eþ02 8.905Eþ01 7.903Eþ01 7.125Eþ01 6.501Eþ01 5.560Eþ01 4.879Eþ01 4.362Eþ01 3.954Eþ01

Collision (MeV cm2 g1)

2.369Eþ00 2.247Eþ00 2.156Eþ00 2.086Eþ00 2.033Eþ00 1.991Eþ00 1.957Eþ00 1.908Eþ00 1.874Eþ00 1.851Eþ00 1.834Eþ00 1.812Eþ00 1.803Eþ00 1.802Eþ00 1.804Eþ00 1.814Eþ00 1.827Eþ00 1.839Eþ00 1.852Eþ00 1.863Eþ00 1.874Eþ00 1.884Eþ00 1.894Eþ00 1.911Eþ00 1.926Eþ00 1.939Eþ00 1.951Eþ00 1.975Eþ00 1.995Eþ00 2.010Eþ00 2.024Eþ00

2.373Eþ00 2.252Eþ00 2.161Eþ00 2.092Eþ00 2.039Eþ00 1.997Eþ00 1.964Eþ00 1.915Eþ00 1.883Eþ00 1.860Eþ00 1.845Eþ00 1.825Eþ00 1.819Eþ00 1.821Eþ00 1.827Eþ00 1.843Eþ00 1.863Eþ00 1.883Eþ00 1.903Eþ00 1.922Eþ00 1.941Eþ00 1.960Eþ00 1.977Eþ00 2.011Eþ00 2.044Eþ00 2.075Eþ00 2.105Eþ00 2.176Eþ00 2.243Eþ00 2.308Eþ00 2.371Eþ00

2.883E03 3.047E03 3.171E03 3.270E03 3.351E03 3.473E03 3.562E03 3.628E03 3.679E03

Radiative (MeV cm2 g1)

Stopping power

1.025Eþ02 8.905Eþ01 7.904Eþ01 7.125Eþ01 6.502Eþ01 5.560Eþ01 4.879Eþ01 4.362Eþ01 3.954Eþ01

Total (MeV cm2 g1)

Air, dry (near sea level)

4.536E03 4.874E03 5.235E03 5.614E03 6.010E03 6.422E03 6.847E03 7.739E03 8.678E03 9.658E03 1.068E02 1.337E02 1.624E02 1.927E02 2.243E02 2.910E02 3.615E02 4.351E02 5.113E02 5.897E02 6.699E02 7.518E02 8.351E02 1.006E01 1.180E01 1.359E01 1.541E01 2.007E01 2.487E01 2.976E01 3.473E01

4.879E06 7.504E06 1.049E05 1.383E05 1.750E05 2.585E05 3.547E05 4.633E05 5.839E05

CSDA range (g cm2)

8.362E02 1.053E01 1.280E01 1.515E01 1.757E01 2.005E01 2.258E01 2.774E01 3.301E01 3.835E01 4.375E01 5.739E01 7.111E01 8.485E01 9.856E01 1.258Eþ00 1.528Eþ00 1.795Eþ00 2.059Eþ00 2.321Eþ00 2.579Eþ00 2.836Eþ00 3.090Eþ00 3.591Eþ00 4.084Eþ00 4.570Eþ00 5.048Eþ00 6.216Eþ00 7.348Eþ00 8.446Eþ00 9.515Eþ00

1.407E05 1.749E05 2.077E05 2.395E05 2.705E05 3.305E05 3.883E05 4.444E05 4.991E05

Brems yield

1.083E03 1.219E03 1.353E03 1.487E03 1.619E03 1.752E03 1.885E03 2.154E03 2.425E03 2.700E03 2.979E03 3.693E03 4.431E03 5.191E03 5.970E03 7.581E03 9.249E03 1.096E02 1.272E02 1.450E02 1.631E02 1.814E02 1.999E02 2.372E02 2.749E02 3.128E02 3.509E02 4.463E02 5.412E02 6.353E02 7.280E02

1.180Eþ02 1.020Eþ02 9.030Eþ01 8.120Eþ01 7.390Eþ01 6.300Eþ01 5.510Eþ01 4.920Eþ01 4.450Eþ01

Collision (MeV cm2 g1)

2.399Eþ00 2.276Eþ00 2.187Eþ00 2.119Eþ00 2.066Eþ00 2.024Eþ00 1.990Eþ00 1.940Eþ00 1.907Eþ00 1.884Eþ00 1.867Eþ00 1.845Eþ00 1.836Eþ00 1.835Eþ00 1.838Eþ00 1.847Eþ00 1.860Eþ00 1.872Eþ00 1.885Eþ00 1.896Eþ00 1.907Eþ00 1.917Eþ00 1.927Eþ00 1.944Eþ00 1.959Eþ00 1.972Eþ00 1.984Eþ00 2.009Eþ00 2.029Eþ00 2.046Eþ00 2.060Eþ00

2.630E03 2.770E03 2.880E03 2.960E03 3.030E03 3.130E03 3.200E03 3.250E03 3.290E03

Radiative (MeV cm2 g1)

Stopping power

4.598E03 4.942E03 5.307E03 5.692E03 6.095E03 6.513E03 6.945E03 7.851E03 8.804E03 9.800E03 1.083E02 1.356E02 1.648E02 1.956E02 2.277E02 2.954E02 3.671E02 4.418E02 5.193E02 5.989E02 6.805E02 7.636E02 8.482E02 1.021E01 1.199E01 1.381E01 1.566E01 2.040E01 2.527E01 3.024E01 3.529E01

1.180Eþ02 1.020Eþ02 9.030Eþ01 8.120Eþ01 7.390Eþ01 6.300Eþ01 5.520Eþ01 4.920Eþ01 4.450Eþ01

Total (MeV cm2 g1)

Alanine

2.404Eþ00 2.281Eþ00 2.192Eþ00 2.125Eþ00 2.072Eþ00 2.030Eþ00 1.997Eþ00 1.948Eþ00 1.916Eþ00 1.893Eþ00 1.878Eþ00 1.858Eþ00 1.853Eþ00 1.855Eþ00 1.860Eþ00 1.877Eþ00 1.896Eþ00 1.917Eþ00 1.937Eþ00 1.956Eþ00 1.975Eþ00 1.994Eþ00 2.012Eþ00 2.046Eþ00 2.079Eþ00 2.110Eþ00 2.141Eþ00 2.213Eþ00 2.282Eþ00 2.348Eþ00 2.413Eþ00

4.240E06 6.520E06 9.130E06 1.210E05 1.530E05 2.270E05 3.120E05 4.080E05 5.150E05

CSDA range (g cm2)

8.255E02 1.039E01 1.263E01 1.495E01 1.733E01 1.977E01 2.226E01 2.733E01 3.251E01 3.776E01 4.306E01 5.646E01 6.994E01 8.343E01 9.689E01 1.236Eþ00 1.502Eþ00 1.764Eþ00 2.023Eþ00 2.280Eþ00 2.535Eþ00 2.787Eþ00 3.036Eþ00 3.529Eþ00 4.014Eþ00 4.491Eþ00 4.962Eþ00 6.110Eþ00 7.222Eþ00 8.302Eþ00 9.352Eþ00

1.120E05 1.390E05 1.650E05 1.900E05 2.150E05 2.620E05 3.080E05 3.530E05 3.960E05

Brems yield

1.084E03 1.220E03 1.354E03 1.487E03 1.619E03 1.752E03 1.884E03 2.151E03 2.421E03 2.695E03 2.972E03 3.684E03 4.418E03 5.175E03 5.952E03 7.557E03 9.221E03 1.093E02 1.268E02 1.446E02 1.627E02 1.810E02 1.994E02 2.367E02 2.744E02 3.123E02 3.504E02 4.457E02 5.405E02 6.344E02 7.271E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00

Energy (MeV)

3.623Eþ01 3.348Eþ01 3.117Eþ01 2.918Eþ01 2.596Eþ01 2.344Eþ01 2.142Eþ01 1.975Eþ01 1.663Eþ01 1.444Eþ01 1.282Eþ01 1.157Eþ01 9.753Eþ00 8.491Eþ00 7.562Eþ00 6.848Eþ00 6.280Eþ00 5.818Eþ00 5.434Eþ00 5.110Eþ00 4.593Eþ00 4.197Eþ00 3.885Eþ00 3.633Eþ00 3.172Eþ00 2.861Eþ00 2.637Eþ00 2.469Eþ00 2.236Eþ00 2.084Eþ00 1.978Eþ00 1.902Eþ00 1.845Eþ00 1.802Eþ00 1.769Eþ00 1.743Eþ00 1.706Eþ00 1.683Eþ00 1.669Eþ00 1.661Eþ00 1.655Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

3.720E03 3.752E03 3.779E03 3.801E03 3.834E03 3.858E03 3.876E03 3.889E03 3.908E03 3.919E03 3.926E03 3.933E03 3.946E03 3.958E03 3.970E03 3.981E03 3.993E03 4.006E03 4.021E03 4.039E03 4.076E03 4.116E03 4.159E03 4.205E03 4.328E03 4.463E03 4.606E03 4.759E03 5.095E03 5.463E03 5.860E03 6.283E03 6.728E03 7.194E03 7.679E03 8.181E03 9.228E03 1.033E02 1.148E02 1.267E02 1.583E02

Radiative (MeV cm2 g1)

Stopping power

3.623Eþ01 3.349Eþ01 3.117Eþ01 2.919Eþ01 2.596Eþ01 2.345Eþ01 2.142Eþ01 1.976Eþ01 1.663Eþ01 1.445Eþ01 1.283Eþ01 1.158Eþ01 9.757Eþ00 8.495Eþ00 7.566Eþ00 6.852Eþ00 6.284Eþ00 5.822Eþ00 5.438Eþ00 5.114Eþ00 4.597Eþ00 4.201Eþ00 3.890Eþ00 3.637Eþ00 3.176Eþ00 2.865Eþ00 2.642Eþ00 2.474Eþ00 2.241Eþ00 2.089Eþ00 1.984Eþ00 1.908Eþ00 1.852Eþ00 1.809Eþ00 1.776Eþ00 1.751Eþ00 1.715Eþ00 1.694Eþ00 1.681Eþ00 1.674Eþ00 1.671Eþ00

Total (MeV cm2 g1)

Air, dry (near sea level)

7.161E05 8.598E05 1.015E04 1.181E04 1.545E04 1.950E04 2.397E04 2.884E04 4.269E04 5.886E04 7.727E04 9.781E04 1.451E03 2.002E03 2.627E03 3.322E03 4.085E03 4.912E03 5.802E03 6.750E03 8.817E03 1.110E02 1.357E02 1.623E02 2.362E02 3.193E02 4.103E02 5.082E02 7.213E02 9.528E02 1.199E01 1.456E01 1.722E01 1.995E01 2.274E01 2.558E01 3.136E01 3.723E01 4.316E01 4.912E01 6.408E01

CSDA range (g cm2)

5.524E05 6.045E05 6.556E05 7.058E05 8.035E05 8.983E05 9.904E05 1.080E04 1.296E04 1.502E04 1.700E04 1.891E04 2.258E04 2.607E04 2.943E04 3.266E04 3.579E04 3.883E04 4.179E04 4.468E04 5.028E04 5.566E04 6.086E04 6.591E04 7.794E04 8.930E04 1.001E03 1.105E03 1.304E03 1.494E03 1.678E03 1.859E03 2.037E03 2.214E03 2.390E03 2.566E03 2.917E03 3.270E03 3.625E03 3.982E03 4.889E03

Brems yield

4.080Eþ01 3.760Eþ01 3.500Eþ01 3.280Eþ01 2.910Eþ01 2.630Eþ01 2.400Eþ01 2.210Eþ01 1.860Eþ01 1.610Eþ01 1.430Eþ01 1.290Eþ01 1.080Eþ01 9.430Eþ00 8.400Eþ00 7.600Eþ00 6.960Eþ00 6.450Eþ00 6.020Eþ00 5.660Eþ00 5.090Eþ00 4.650Eþ00 4.300Eþ00 4.020Eþ00 3.510Eþ00 3.160Eþ00 2.910Eþ00 2.730Eþ00 2.470Eþ00 2.300Eþ00 2.180Eþ00 2.090Eþ00 2.020Eþ00 1.970Eþ00 1.930Eþ00 1.900Eþ00 1.850Eþ00 1.820Eþ00 1.800Eþ00 1.780Eþ00 1.760Eþ00

Collision (MeV cm2 g1) 3.330E03 3.350E03 3.370E03 3.390E03 3.420E03 3.440E03 3.450E03 3.460E03 3.470E03 3.480E03 3.490E03 3.490E03 3.500E03 3.520E03 3.530E03 3.540E03 3.550E03 3.560E03 3.580E03 3.590E03 3.630E03 3.660E03 3.700E03 3.750E03 3.860E03 3.980E03 4.120E03 4.260E03 4.560E03 4.900E03 5.260E03 5.650E03 6.060E03 6.480E03 6.920E03 7.380E03 8.340E03 9.340E03 1.040E02 1.150E02 1.440E02

Radiative (MeV cm2 g1)

Stopping power

4.080Eþ01 3.760Eþ01 3.500Eþ01 3.280Eþ01 2.910Eþ01 2.630Eþ01 2.400Eþ01 2.210Eþ01 1.860Eþ01 1.610Eþ01 1.430Eþ01 1.290Eþ01 1.090Eþ01 9.440Eþ00 8.400Eþ00 7.600Eþ00 6.970Eþ00 6.450Eþ00 6.030Eþ00 5.660Eþ00 5.090Eþ00 4.650Eþ00 4.300Eþ00 4.020Eþ00 3.510Eþ00 3.160Eþ00 2.920Eþ00 2.730Eþ00 2.470Eþ00 2.300Eþ00 2.190Eþ00 2.100Eþ00 2.030Eþ00 1.980Eþ00 1.940Eþ00 1.910Eþ00 1.860Eþ00 1.830Eþ00 1.810Eþ00 1.790Eþ00 1.770Eþ00

Total (MeV cm2 g1)

Alanine

6.320E05 7.600E05 8.980E05 1.050E04 1.370E04 1.730E04 2.130E04 2.570E04 3.810E04 5.260E04 6.910E04 8.750E04 1.300E03 1.800E03 2.360E03 2.990E03 3.670E03 4.420E03 5.220E03 6.080E03 7.950E03 1.000E02 1.220E02 1.470E02 2.130E02 2.890E02 3.710E02 4.600E02 6.530E02 8.630E02 1.090E01 1.320E01 1.560E01 1.810E01 2.070E01 2.330E01 2.860E01 3.400E01 3.950E01 4.510E01 5.910E01

CSDA range (g cm2)

4.390E05 4.800E05 5.210E05 5.610E05 6.390E05 7.140E05 7.870E05 8.590E05 1.030E04 1.200E04 1.350E04 1.510E04 1.800E04 2.080E04 2.350E04 2.610E04 2.860E04 3.110E04 3.340E04 3.580E04 4.030E04 4.460E04 4.880E04 5.290E04 6.270E04 7.190E04 8.070E04 8.920E04 1.050E03 1.210E03 1.360E03 1.510E03 1.660E03 1.810E03 1.950E03 2.100E03 2.400E03 2.700E03 3.000E03 3.310E03 4.100E03

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

92

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02

Energy (MeV)

1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

93

7.384Eþ01 6.588Eþ01 5.955Eþ01 5.442Eþ01 5.018Eþ01 4.359Eþ01 3.869Eþ01 3.488Eþ01 3.184Eþ01 2.934Eþ01 2.724Eþ01 2.546Eþ01 2.393Eþ01 2.141Eþ01 1.943Eþ01 1.782Eþ01 1.649Eþ01 1.398Eþ01 1.220Eþ01 1.088Eþ01

Collision MeV (cm2 g1)

1.661Eþ00 1.671Eþ00 1.684Eþ00 1.712Eþ00 1.740Eþ00 1.766Eþ00 1.790Eþ00 1.812Eþ00 1.833Eþ00 1.852Eþ00 1.870Eþ00 1.902Eþ00 1.931Eþ00 1.956Eþ00 1.979Eþ00 2.029Eþ00 2.069Eþ00 2.104Eþ00 2.134Eþ00

3.864E03 4.167E03 4.418E03 4.632E03 4.817E03 5.123E03 5.366E03 5.563E03 5.728E03 5.867E03 5.986E03 6.088E03 6.177E03 6.324E03 6.439E03 6.531E03 6.605E03 6.742E03 6.829E03 6.884E03

Radiative (MeV cm2 g1)

Stopping power

1.919E02 2.273E02 2.644E02 3.423E02 4.247E02 5.106E02 5.994E02 6.907E02 7.841E02 8.793E02 9.762E02 1.174E01 1.378E01 1.585E01 1.796E01 2.337E01 2.891E01 3.457E01 4.032E01

7.385Eþ01 6.588Eþ01 5.955Eþ01 5.442Eþ01 5.019Eþ01 4.360Eþ01 3.869Eþ01 3.489Eþ01 3.184Eþ01 2.934Eþ01 2.725Eþ01 2.547Eþ01 2.394Eþ01 2.142Eþ01 1.944Eþ01 1.783Eþ01 1.650Eþ01 1.398Eþ01 1.221Eþ01 1.088Eþ01

Total (MeV cm2 g1)

Aluminum

1.680Eþ00 1.694Eþ00 1.711Eþ00 1.747Eþ00 1.782Eþ00 1.817Eþ00 1.850Eþ00 1.881Eþ00 1.911Eþ00 1.940Eþ00 1.968Eþ00 2.020Eþ00 2.068Eþ00 2.115Eþ00 2.159Eþ00 2.262Eþ00 2.359Eþ00 2.450Eþ00 2.537Eþ00

6.771E06 1.036E05 1.436E05 1.875E05 2.354E05 3.426E05 4.646E05 6.009E05 7.511E05 9.149E05 1.092E04 1.282E04 1.484E04 1.927E04 2.418E04 2.955E04 3.539E04 5.192E04 7.111E04 9.284E04

CSDA range (g cm2)

7.901E01 9.383E01 1.085Eþ00 1.374Eþ00 1.658Eþ00 1.936Eþ00 2.208Eþ00 2.476Eþ00 2.740Eþ00 2.999Eþ00 3.255Eþ00 3.757Eþ00 4.246Eþ00 4.724Eþ00 5.192Eþ00 6.323Eþ00 7.405Eþ00 8.445Eþ00 9.447Eþ00

2.616E05 3.249E05 3.853E05 4.440E05 5.017E05 6.149E05 7.260E05 8.353E05 9.430E05 1.049E04 1.154E04 1.258E04 1.360E04 1.561E04 1.758E04 1.950E04 2.139E04 2.594E04 3.030E04 3.449E04

Brems yield

5.815E03 6.758E03 7.718E03 9.678E03 1.168E02 1.372E02 1.579E02 1.787E02 1.997E02 2.208E02 2.420E02 2.844E02 3.268E02 3.692E02 4.114E02 5.157E02 6.181E02 7.183E02 8.161E02

8.032Eþ01 7.119Eþ01 6.405Eþ01 5.834Eþ01 5.366Eþ01 4.644Eþ01 4.111Eþ01 3.699Eþ01 3.371Eþ01 3.102Eþ01 2.877Eþ01 2.687Eþ01 2.523Eþ01 2.254Eþ01 2.043Eþ01 1.873Eþ01 1.731Eþ01 1.465Eþ01 1.278Eþ01 1.138Eþ01

Collision (MeV cm2 g1)

1.750Eþ00 1.750Eþ00 1.750Eþ00 1.760Eþ00 1.770Eþ00 1.790Eþ00 1.800Eþ00 1.810Eþ00 1.820Eþ00 1.830Eþ00 1.840Eþ00 1.850Eþ00 1.870Eþ00 1.880Eþ00 1.890Eþ00 1.920Eþ00 1.940Eþ00 1.950Eþ00 1.970Eþ00

Radiative (MeV cm2 g1) 3.490E03 3.737E03 3.937E03 4.104E03 4.247E03 4.477E03 4.655E03 4.798E03 4.914E03 5.011E03 5.093E03 5.162E03 5.222E03 5.320E03 5.395E03 5.453E03 5.501E03 5.586E03 5.638E03 5.670E03

1.770Eþ00 1.770Eþ00 1.780Eþ00 1.790Eþ00 1.810Eþ00 1.830Eþ00 1.850Eþ00 1.870Eþ00 1.890Eþ00 1.910Eþ00 1.930Eþ00 1.960Eþ00 2.000Eþ00 2.030Eþ00 2.060Eþ00 2.130Eþ00 2.200Eþ00 2.270Eþ00 2.340Eþ00

8.033Eþ01 7.119Eþ01 6.406Eþ01 5.835Eþ01 5.367Eþ01 4.645Eþ01 4.111Eþ01 3.700Eþ01 3.371Eþ01 3.102Eþ01 2.878Eþ01 2.687Eþ01 2.523Eþ01 2.255Eþ01 2.044Eþ01 1.873Eþ01 1.732Eþ01 1.466Eþ01 1.278Eþ01 1.138Eþ01

Total (MeV cm2 g1)

Aluminum oxide Stopping power

1.740E02 2.070E02 2.410E02 3.120E02 3.880E02 4.660E02 5.480E02 6.320E02 7.170E02 8.050E02 8.940E02 1.080E01 1.260E01 1.450E01 1.650E01 2.150E01 2.660E01 3.180E01 3.710E01

6.225E06 9.537E06 1.325E05 1.734E05 2.181E05 3.186E05 4.332E05 5.617E05 7.034E05 8.582E05 1.026E04 1.206E04 1.398E04 1.818E04 2.284E04 2.796E04 3.351E04 4.927E04 6.758E04 8.835E04

CSDA range (g cm2)

7.330E01 8.740E01 1.020Eþ00 1.300Eþ00 1.570Eþ00 1.850Eþ00 2.120Eþ00 2.390Eþ00 2.650Eþ00 2.920Eþ00 3.180Eþ00 3.690Eþ00 4.200Eþ00 4.690Eþ00 5.180Eþ00 6.380Eþ00 7.530Eþ00 8.650Eþ00 9.730Eþ00

2.172E05 2.697E05 3.197E05 3.682E05 4.156E05 5.081E05 5.981E05 6.863E05 7.727E05 8.576E05 9.411E05 1.023E04 1.104E04 1.263E04 1.418E04 1.569E04 1.716E04 2.072E04 2.412E04 2.739E04

Brems yield

4.910E03 5.750E03 6.610E03 8.380E03 1.020E02 1.210E02 1.400E02 1.600E02 1.800E02 2.000E02 2.200E02 2.610E02 3.020E02 3.440E02 3.850E02 4.890E02 5.920E02 6.940E02 7.940E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00

Energy (MeV)

9.844Eþ00 8.338Eþ00 7.287Eþ00 6.509Eþ00 5.909Eþ00 5.430Eþ00 5.039Eþ00 4.714Eþ00 4.439Eþ00 3.998Eþ00 3.661Eþ00 3.394Eþ00 3.177Eþ00 2.781Eþ00 2.513Eþ00 2.320Eþ00 2.174Eþ00 1.972Eþ00 1.839Eþ00 1.747Eþ00 1.680Eþ00 1.630Eþ00 1.592Eþ00 1.563Eþ00 1.540Eþ00 1.507Eþ00 1.486Eþ00 1.473Eþ00 1.465Eþ00 1.457Eþ00 1.460Eþ00 1.466Eþ00 1.475Eþ00 1.493Eþ00 1.510Eþ00 1.526Eþ00 1.540Eþ00 1.552Eþ00 1.564Eþ00 1.574Eþ00

Collision MeV (cm2 g1)

Table A.4. Continued

6.924E03 6.985E03 7.027E03 7.056E03 7.080E03 7.104E03 7.128E03 7.150E03 7.173E03 7.230E03 7.294E03 7.362E03 7.434E03 7.629E03 7.842E03 8.071E03 8.317E03 8.856E03 9.450E03 1.009E02 1.077E02 1.149E02 1.224E02 1.302E02 1.383E02 1.552E02 1.730E02 1.917E02 2.111E02 2.622E02 3.166E02 3.737E02 4.331E02 5.579E02 6.892E02 8.255E02 9.660E02 1.110E01 1.257E01 1.407E01

Radiative (MeV cm2 g1)

Stopping power

9.851Eþ00 8.345Eþ00 7.294Eþ00 6.516Eþ00 5.916Eþ00 5.437Eþ00 5.046Eþ00 4.721Eþ00 4.446Eþ00 4.005Eþ00 3.668Eþ00 3.401Eþ00 3.185Eþ00 2.789Eþ00 2.521Eþ00 2.328Eþ00 2.183Eþ00 1.981Eþ00 1.849Eþ00 1.757Eþ00 1.691Eþ00 1.642Eþ00 1.604Eþ00 1.576Eþ00 1.553Eþ00 1.522Eþ00 1.503Eþ00 1.492Eþ00 1.486Eþ00 1.484Eþ00 1.491Eþ00 1.504Eþ00 1.518Eþ00 1.549Eþ00 1.579Eþ00 1.609Eþ00 1.637Eþ00 1.663Eþ00 1.689Eþ00 1.714Eþ00

Total (MeV cm2 g1)

Aluminum

1.170E03 1.724E03 2.367E03 3.093E03 3.900E03 4.783E03 5.738E03 6.763E03 7.855E03 1.023E02 1.284E02 1.568E02 1.872E02 2.714E02 3.659E02 4.693E02 5.804E02 8.217E02 1.084E01 1.361E01 1.652E01 1.952E01 2.260E01 2.575E01 2.894E01 3.545E01 4.207E01 4.875E01 5.546E01 7.232E01 8.913E01 1.058Eþ00 1.224Eþ00 1.550Eþ00 1.870Eþ00 2.183Eþ00 2.491Eþ00 2.794Eþ00 3.093Eþ00 3.386Eþ00

CSDA range (g cm2)

3.853E04 4.624E04 5.354E04 6.052E04 6.720E04 7.365E04 7.988E04 8.593E04 9.180E04 1.031E03 1.139E03 1.244E03 1.344E03 1.583E03 1.807E03 2.019E03 2.221E03 2.606E03 2.970E03 3.321E03 3.663E03 3.999E03 4.331E03 4.659E03 4.986E03 5.638E03 6.290E03 6.944E03 7.602E03 9.268E03 1.096E02 1.269E02 1.444E02 1.800E02 2.164E02 2.533E02 2.906E02 3.282E02 3.659E02 4.038E02

Brems yield

1.029Eþ01 8.709Eþ00 7.605Eþ00 6.789Eþ00 6.160Eþ00 5.658Eþ00 5.249Eþ00 4.909Eþ00 4.621Eþ00 4.161Eþ00 3.809Eþ00 3.530Eþ00 3.305Eþ00 2.892Eþ00 2.613Eþ00 2.412Eþ00 2.262Eþ00 2.052Eþ00 1.912Eþ00 1.815Eþ00 1.744Eþ00 1.691Eþ00 1.650Eþ00 1.618Eþ00 1.593Eþ00 1.557Eþ00 1.533Eþ00 1.517Eþ00 1.507Eþ00 1.494Eþ00 1.492Eþ00 1.495Eþ00 1.501Eþ00 1.514Eþ00 1.528Eþ00 1.541Eþ00 1.553Eþ00 1.564Eþ00 1.575Eþ00 1.584Eþ00

Collision (MeV cm2 g1) 5.694E03 5.731E03 5.760E03 5.780E03 5.798E03 5.816E03 5.835E03 5.854E03 5.875E03 5.923E03 5.977E03 6.034E03 6.095E03 6.260E03 6.441E03 6.634E03 6.842E03 7.297E03 7.798E03 8.339E03 8.914E03 9.521E03 1.015E02 1.081E02 1.149E02 1.292E02 1.443E02 1.600E02 1.763E02 2.194E02 2.652E02 3.134E02 3.637E02 4.693E02 5.805E02 6.962E02 8.156E02 9.380E02 1.063E01 1.190E01

Radiative (MeV cm2 g1)

Stopping power

1.030Eþ01 8.715Eþ00 7.611Eþ00 6.795Eþ00 6.165Eþ00 5.664Eþ00 5.255Eþ00 4.915Eþ00 4.627Eþ00 4.167Eþ00 3.815Eþ00 3.536Eþ00 3.311Eþ00 2.898Eþ00 2.619Eþ00 2.419Eþ00 2.269Eþ00 2.059Eþ00 1.920Eþ00 1.823Eþ00 1.753Eþ00 1.700Eþ00 1.660Eþ00 1.629Eþ00 1.605Eþ00 1.570Eþ00 1.547Eþ00 1.533Eþ00 1.524Eþ00 1.516Eþ00 1.519Eþ00 1.527Eþ00 1.537Eþ00 1.561Eþ00 1.586Eþ00 1.611Eþ00 1.635Eþ00 1.658Eþ00 1.681Eþ00 1.703Eþ00

Total (MeV cm2 g1)

Aluminum oxide

1.115E03 1.645E03 2.261E03 2.957E03 3.731E03 4.578E03 5.495E03 6.480E03 7.529E03 9.811E03 1.232E02 1.505E02 1.797E02 2.608E02 3.517E02 4.512E02 5.581E02 7.902E02 1.042E01 1.310E01 1.590E01 1.879E01 2.177E01 2.481E01 2.791E01 3.421E01 4.063E01 4.713E01 5.367E01 7.013E01 8.661E01 1.030Eþ00 1.194Eþ00 1.516Eþ00 1.834Eþ00 2.147Eþ00 2.455Eþ00 2.759Eþ00 3.058Eþ00 3.354Eþ00

CSDA range (g cm2)

3.053E04 3.654E04 4.225E04 4.770E04 5.293E04 5.798E04 6.287E04 6.762E04 7.224E04 8.115E04 8.969E04 9.791E04 1.059E03 1.247E03 1.425E03 1.593E03 1.754E03 2.059E03 2.350E03 2.631E03 2.906E03 3.176E03 3.445E03 3.711E03 3.977E03 4.508E03 5.041E03 5.579E03 6.121E03 7.498E03 8.908E03 1.035E02 1.182E02 1.482E02 1.791E02 2.105E02 2.424E02 2.746E02 3.070E02 3.397E02

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

94

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02

Energy (MeV)

6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

9.533Eþ01 8.306Eþ01 7.385Eþ01 6.667Eþ01 6.090Eþ01 5.217Eþ01 4.583Eþ01 4.101Eþ01 3.720Eþ01 3.411Eþ01 3.154Eþ01 2.937Eþ01 2.752Eþ01 2.449Eþ01 2.213Eþ01 2.023Eþ01 1.866Eþ01 1.572Eþ01 1.366Eþ01 1.214Eþ01 1.095Eþ01 9.238Eþ00 8.047Eþ00 7.169Eþ00 6.493Eþ00 5.957Eþ00 5.520Eþ00 5.156Eþ00 4.850Eþ00 4.360Eþ00

Collision (MeV cm2 g1)

1.583Eþ00 1.599Eþ00 1.613Eþ00 1.625Eþ00 1.635Eþ00 1.658Eþ00 1.676Eþ00 1.691Eþ00 1.704Eþ00

Radiative (MeV cm2 g1)

2.540E03 2.676E03 2.779E03 2.861E03 2.927E03 3.029E03 3.102E03 3.157E03 3.200E03 3.234E03 3.261E03 3.283E03 3.301E03 3.329E03 3.350E03 3.365E03 3.376E03 3.395E03 3.405E03 3.410E03 3.415E03 3.425E03 3.437E03 3.448E03 3.458E03 3.469E03 3.481E03 3.495E03 3.510E03 3.543E03

1.739Eþ00 1.786Eþ00 1.831Eþ00 1.876Eþ00 1.919Eþ00 2.026Eþ00 2.130Eþ00 2.233Eþ00 2.334Eþ00

9.534Eþ01 8.306Eþ01 7.385Eþ01 6.667Eþ01 6.090Eþ01 5.217Eþ01 4.584Eþ01 4.101Eþ01 3.720Eþ01 3.411Eþ01 3.154Eþ01 2.938Eþ01 2.752Eþ01 2.450Eþ01 2.213Eþ01 2.023Eþ01 1.866Eþ01 1.572Eþ01 1.367Eþ01 1.214Eþ01 1.096Eþ01 9.242Eþ00 8.050Eþ00 7.172Eþ00 6.497Eþ00 5.960Eþ00 5.523Eþ00 5.160Eþ00 4.853Eþ00 4.363Eþ00

Total (MeV cm2 g1)

Beryllium oxide

Stopping power

1.559E01 1.869E01 2.187E01 2.510E01 2.839E01 3.678E01 4.538E01 5.414E01 6.302E01

5.245E06 8.062E06 1.126E05 1.483E05 1.876E05 2.766E05 3.791E05 4.946E05 6.228E05 7.633E05 9.159E05 1.080E04 1.256E04 1.642E04 2.072E04 2.545E04 3.061E04 4.526E04 6.237E04 8.182E04 1.035E03 1.534E03 2.116E03 2.775E03 3.509E03 4.313E03 5.186E03 6.123E03 7.123E03 9.300E03

CSDA range (g cm2)

3.676Eþ00 4.243Eþ00 4.796Eþ00 5.336Eþ00 5.863Eþ00 7.130Eþ00 8.334Eþ00 9.480Eþ00 1.057Eþ01

1.332E05 1.655E05 1.961E05 2.256E05 2.543E05 3.096E05 3.628E05 4.144E05 4.645E05 5.133E05 5.611E05 6.079E05 6.538E05 7.432E05 8.299E05 9.142E05 9.964E05 1.194E04 1.383E04 1.564E04 1.739E04 2.074E04 2.393E04 2.700E04 2.996E04 3.282E04 3.560E04 3.831E04 4.095E04 4.607E04

Brems yield

4.417E02 5.174E02 5.928E02 6.676E02 7.418E02 9.233E02 1.099E01 1.267E01 1.429E01

7.459Eþ01 6.655Eþ01 6.015Eþ01 5.497Eþ01 5.069Eþ01 4.403Eþ01 3.908Eþ01 3.524Eþ01 3.216Eþ01 2.964Eþ01 2.752Eþ01 2.572Eþ01 2.417Eþ01 2.163Eþ01 1.963Eþ01 1.800Eþ01 1.666Eþ01 1.412Eþ01 1.233Eþ01 1.099Eþ01 9.945Eþ00 8.424Eþ00 7.363Eþ00 6.577Eþ00 5.970Eþ00 5.487Eþ00 5.093Eþ00 4.764Eþ00 4.486Eþ00 4.041Eþ00

Collision (MeV cm2 g1)

1.593Eþ00 1.609Eþ00 1.622Eþ00 1.634Eþ00 1.645Eþ00 1.667Eþ00 1.685Eþ00 1.700Eþ00 1.713Eþ00

Radiative (MeV cm2 g1) 3.995E03 4.331E03 4.612E03 4.854E03 5.065E03 5.419E03 5.705E03 5.943E03 6.144E03 6.318E03 6.469E03 6.601E03 6.719E03 6.917E03 7.078E03 7.212E03 7.324E03 7.538E03 7.689E03 7.799E03 7.883E03 8.005E03 8.092E03 8.157E03 8.211E03 8.258E03 8.302E03 8.346E03 8.389E03 8.473E03

1.725Eþ00 1.767Eþ00 1.808Eþ00 1.847Eþ00 1.886Eþ00 1.980Eþ00 2.072Eþ00 2.162Eþ00 2.250Eþ00

7.460Eþ01 6.655Eþ01 6.016Eþ01 5.497Eþ01 5.070Eþ01 4.404Eþ01 3.909Eþ01 3.524Eþ01 3.217Eþ01 2.964Eþ01 2.753Eþ01 2.573Eþ01 2.418Eþ01 2.164Eþ01 1.963Eþ01 1.801Eþ01 1.667Eþ01 1.413Eþ01 1.233Eþ01 1.099Eþ01 9.953Eþ00 8.432Eþ00 7.371Eþ00 6.585Eþ00 5.978Eþ00 5.495Eþ00 5.101Eþ00 4.772Eþ00 4.495Eþ00 4.050Eþ00

Total (MeV cm2 g1)

Calcium fluoride Stopping power

1.320E01 1.584E01 1.855E01 2.131E01 2.412E01 3.129E01 3.865E01 4.614E01 5.374E01

6.703E06 1.026E05 1.421E05 1.857E05 2.331E05 3.392E05 4.600E05 5.949E05 7.436E05 9.057E05 1.081E04 1.269E04 1.469E04 1.907E04 2.393E04 2.926E04 3.503E04 5.139E04 7.039E04 9.190E04 1.158E03 1.706E03 2.343E03 3.062E03 3.860E03 4.733E03 5.679E03 6.693E03 7.773E03 1.012E02

CSDA range (g cm2)

3.645Eþ00 4.218Eþ00 4.778Eþ00 5.325Eþ00 5.861Eþ00 7.154Eþ00 8.388Eþ00 9.569Eþ00 1.070Eþ01

2.677E05 3.328E05 3.955E05 4.568E05 5.173E05 6.369E05 7.549E05 8.718E05 9.876E05 1.102E04 1.216E04 1.329E04 1.441E04 1.662E04 1.880E04 2.094E04 2.304E04 2.817E04 3.312E04 3.792E04 4.256E04 5.148E04 5.997E04 6.810E04 7.592E04 8.347E04 9.078E04 9.788E04 1.048E03 1.181E03

Brems yield

3.724E02 4.379E02 5.034E02 5.686E02 6.334E02 7.929E02 9.481E02 1.099E01 1.244E01

APPENDIX A: COMPILATION OF PHYSICAL DATA

95

8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

Energy (MeV)

3.985Eþ00 3.690Eþ00 3.451Eþ00 3.014Eþ00 2.719Eþ00 2.507Eþ00 2.348Eþ00 2.125Eþ00 1.977Eþ00 1.873Eþ00 1.797Eþ00 1.740Eþ00 1.696Eþ00 1.661Eþ00 1.633Eþ00 1.593Eþ00 1.566Eþ00 1.547Eþ00 1.535Eþ00 1.518Eþ00 1.512Eþ00 1.512Eþ00 1.516Eþ00 1.526Eþ00 1.537Eþ00 1.549Eþ00 1.559Eþ00 1.570Eþ00 1.579Eþ00 1.588Eþ00 1.596Eþ00 1.610Eþ00 1.623Eþ00 1.634Eþ00 1.644Eþ00 1.664Eþ00 1.681Eþ00 1.695Eþ00 1.706Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

3.579E03 3.617E03 3.658E03 3.767E03 3.886E03 4.013E03 4.149E03 4.445E03 4.769E03 5.119E03 5.491E03 5.883E03 6.292E03 6.718E03 7.158E03 8.079E03 9.050E03 1.006E02 1.112E02 1.390E02 1.686E02 1.999E02 2.326E02 3.013E02 3.740E02 4.499E02 5.284E02 6.090E02 6.914E02 7.755E02 8.610E02 1.036E01 1.215E01 1.399E01 1.585E01 2.062E01 2.552E01 3.052E01 3.560E01

Radiative (MeV cm2 g1)

Stopping power

3.989Eþ00 3.693Eþ00 3.454Eþ00 3.018Eþ00 2.723Eþ00 2.511Eþ00 2.352Eþ00 2.130Eþ00 1.981Eþ00 1.878Eþ00 1.802Eþ00 1.746Eþ00 1.702Eþ00 1.668Eþ00 1.641Eþ00 1.601Eþ00 1.575Eþ00 1.558Eþ00 1.546Eþ00 1.532Eþ00 1.529Eþ00 1.532Eþ00 1.539Eþ00 1.556Eþ00 1.574Eþ00 1.594Eþ00 1.612Eþ00 1.630Eþ00 1.648Eþ00 1.665Eþ00 1.682Eþ00 1.714Eþ00 1.744Eþ00 1.774Eþ00 1.802Eþ00 1.871Eþ00 1.936Eþ00 2.000Eþ00 2.062Eþ00

Total (MeV cm2 g1)

Beryllium oxide

1.170E02 1.431E02 1.711E02 2.489E02 3.363E02 4.321E02 5.351E02 7.592E02 1.003E01 1.263E01 1.535E01 1.817E01 2.107E01 2.404E01 2.706E01 3.324E01 3.954E01 4.592E01 5.237E01 6.863E01 8.498E01 1.013Eþ00 1.176Eþ00 1.499Eþ00 1.819Eþ00 2.134Eþ00 2.446Eþ00 2.755Eþ00 3.060Eþ00 3.361Eþ00 3.660Eþ00 4.249Eþ00 4.828Eþ00 5.396Eþ00 5.956Eþ00 7.317Eþ00 8.630Eþ00 9.901Eþ00 1.113Eþ01

CSDA range (g cm2)

5.100E04 5.576E04 6.038E04 7.140E04 8.181E04 9.174E04 1.013E03 1.195E03 1.371E03 1.542E03 1.710E03 1.876E03 2.042E03 2.207E03 2.373E03 2.706E03 3.042E03 3.382E03 3.726E03 4.606E03 5.513E03 6.444E03 7.398E03 9.364E03 1.140E02 1.348E02 1.561E02 1.777E02 1.996E02 2.217E02 2.439E02 2.888E02 3.341E02 3.795E02 4.249E02 5.382E02 6.503E02 7.607E02 8.689E02

Brems yield

3.701Eþ00 3.432Eþ00 3.213Eþ00 2.814Eþ00 2.544Eþ00 2.349Eþ00 2.203Eþ00 2.000Eþ00 1.867Eþ00 1.774Eþ00 1.706Eþ00 1.656Eþ00 1.617Eþ00 1.587Eþ00 1.563Eþ00 1.528Eþ00 1.506Eþ00 1.491Eþ00 1.481Eþ00 1.470Eþ00 1.468Eþ00 1.471Eþ00 1.477Eþ00 1.491Eþ00 1.506Eþ00 1.520Eþ00 1.533Eþ00 1.545Eþ00 1.557Eþ00 1.567Eþ00 1.577Eþ00 1.594Eþ00 1.610Eþ00 1.623Eþ00 1.635Eþ00 1.659Eþ00 1.679Eþ00 1.695Eþ00 1.709Eþ00

Collision (MeV cm2 g1) 8.558E03 8.646E03 8.737E03 8.975E03 9.228E03 9.495E03 9.779E03 1.040E02 1.108E02 1.182E02 1.260E02 1.342E02 1.428E02 1.517E02 1.610E02 1.803E02 2.006E02 2.219E02 2.441E02 3.025E02 3.645E02 4.297E02 4.974E02 6.395E02 7.885E02 9.432E02 1.103E01 1.266E01 1.432E01 1.602E01 1.775E01 2.126E01 2.484E01 2.849E01 3.220E01 4.167E01 5.136E01 6.123E01 7.124E01

Radiative (MeV cm2 g1)

Stopping power

3.709Eþ00 3.440Eþ00 3.222Eþ00 2.823Eþ00 2.553Eþ00 2.359Eþ00 2.213Eþ00 2.011Eþ00 1.878Eþ00 1.786Eþ00 1.719Eþ00 1.669Eþ00 1.631Eþ00 1.602Eþ00 1.579Eþ00 1.546Eþ00 1.526Eþ00 1.513Eþ00 1.505Eþ00 1.500Eþ00 1.505Eþ00 1.514Eþ00 1.527Eþ00 1.555Eþ00 1.584Eþ00 1.614Eþ00 1.643Eþ00 1.672Eþ00 1.700Eþ00 1.727Eþ00 1.754Eþ00 1.807Eþ00 1.858Eþ00 1.908Eþ00 1.957Eþ00 2.076Eþ00 2.193Eþ00 2.307Eþ00 2.421Eþ00

Total (MeV cm2 g1)

Calcium fluoride

1.271E02 1.551E02 1.851E02 2.684E02 3.617E02 4.638E02 5.733E02 8.112E02 1.069E01 1.342E01 1.628E01 1.923E01 2.226E01 2.536E01 2.850E01 3.491E01 4.142E01 4.800E01 5.463E01 7.128E01 8.793E01 1.045Eþ00 1.209Eþ00 1.534Eþ00 1.853Eþ00 2.165Eþ00 2.472Eþ00 2.774Eþ00 3.070Eþ00 3.362Eþ00 3.649Eþ00 4.211Eþ00 4.757Eþ00 5.288Eþ00 5.805Eþ00 7.045Eþ00 8.217Eþ00 9.328Eþ00 1.039Eþ01

CSDA range (g cm2)

1.308E03 1.431E03 1.549E03 1.829E03 2.091E03 2.338E03 2.574E03 3.019E03 3.439E03 3.842E03 4.233E03 4.617E03 4.995E03 5.369E03 5.741E03 6.482E03 7.222E03 7.964E03 8.712E03 1.061E02 1.254E02 1.450E02 1.650E02 2.057E02 2.471E02 2.891E02 3.314E02 3.739E02 4.165E02 4.591E02 5.017E02 5.863E02 6.702E02 7.530E02 8.347E02 1.033E01 1.224E01 1.406E01 1.580E01

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

96

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01

Energy (MeV)

7.994Eþ01 7.101Eþ01 6.399Eþ01 5.835Eþ01 5.372Eþ01 4.655Eþ01 4.124Eþ01 3.714Eþ01 3.386Eþ01 3.117Eþ01 2.893Eþ01 2.702Eþ01 2.538Eþ01 2.269Eþ01 2.057Eþ01 1.886Eþ01 1.744Eþ01 1.477Eþ01 1.288Eþ01 1.148Eþ01 1.039Eþ01 8.791Eþ00 7.679Eþ00 6.856Eþ00 6.222Eþ00 5.716Eþ00 5.304Eþ00 4.961Eþ00 4.670Eþ00 4.206Eþ00 3.850Eþ00 3.569Eþ00 3.342Eþ00 2.925Eþ00 2.643Eþ00 2.441Eþ00 2.289Eþ00 2.077Eþ00 1.937Eþ00 1.839Eþ00 1.767Eþ00 1.714Eþ00 1.673Eþ00

Collision (MeV cm2 g1)

3.896E03 4.209E03 4.468E03 4.690E03 4.882E03 5.202E03 5.459E03 5.671E03 5.850E03 6.003E03 6.135E03 6.251E03 6.353E03 6.525E03 6.664E03 6.777E03 6.872E03 7.053E03 7.178E03 7.269E03 7.337E03 7.435E03 7.504E03 7.559E03 7.604E03 7.643E03 7.680E03 7.717E03 7.754E03 7.829E03 7.906E03 7.986E03 8.069E03 8.288E03 8.523E03 8.772E03 9.037E03 9.618E03 1.026E02 1.095E02 1.168E02 1.245E02 1.325E02

Radiative (MeV cm2 g1)

Stopping power

7.994Eþ01 7.101Eþ01 6.399Eþ01 5.836Eþ01 5.372Eþ01 4.655Eþ01 4.125Eþ01 3.714Eþ01 3.386Eþ01 3.118Eþ01 2.894Eþ01 2.703Eþ01 2.539Eþ01 2.270Eþ01 2.058Eþ01 1.887Eþ01 1.745Eþ01 1.478Eþ01 1.289Eþ01 1.149Eþ01 1.039Eþ01 8.798Eþ00 7.686Eþ00 6.864Eþ00 6.229Eþ00 5.724Eþ00 5.312Eþ00 4.968Eþ00 4.678Eþ00 4.214Eþ00 3.858Eþ00 3.577Eþ00 3.350Eþ00 2.933Eþ00 2.652Eþ00 2.449Eþ00 2.298Eþ00 2.087Eþ00 1.947Eþ00 1.850Eþ00 1.779Eþ00 1.726Eþ00 1.686Eþ00

Total (MeV cm2 g1)

Calcium sulfate

6.255E06 9.579E06 1.329E05 1.739E05 2.186E05 3.189E05 4.332E05 5.612E05 7.023E05 8.564E05 1.023E04 1.202E04 1.393E04 1.810E04 2.274E04 2.782E04 3.333E04 4.897E04 6.713E04 8.772E04 1.106E03 1.632E03 2.241E03 2.931E03 3.697E03 4.535E03 5.443E03 6.417E03 7.455E03 9.712E03 1.220E02 1.489E02 1.778E02 2.579E02 3.478E02 4.460E02 5.515E02 7.806E02 1.029E01 1.293E01 1.569E01 1.854E01 2.148E01

CSDA range (g cm2)

2.437E05 3.029E05 3.600E05 4.159E05 4.709E05 5.794E05 6.863E05 7.919E05 8.963E05 9.997E05 1.102E04 1.203E04 1.304E04 1.502E04 1.696E04 1.887E04 2.075E04 2.532E04 2.972E04 3.398E04 3.810E04 4.601E04 5.353E04 6.073E04 6.765E04 7.434E04 8.082E04 8.710E04 9.323E04 1.050E03 1.163E03 1.272E03 1.377E03 1.625E03 1.858E03 2.078E03 2.288E03 2.685E03 3.061E03 3.423E03 3.775E03 4.121E03 4.462E03

Brems yield

1.062Eþ02 9.207Eþ01 8.155Eþ01 7.342Eþ01 6.691Eþ01 5.712Eþ01 5.006Eþ01 4.471Eþ01 4.049Eþ01 3.708Eþ01 3.425Eþ01 3.187Eþ01 2.983Eþ01 2.651Eþ01 2.393Eþ01 2.185Eþ01 2.014Eþ01 1.694Eþ01 1.471Eþ01 1.305Eþ01 1.177Eþ01 9.911Eþ00 8.624Eþ00 7.677Eþ00 6.948Eþ00 6.370Eþ00 5.899Eþ00 5.508Eþ00 5.177Eþ00 4.650Eþ00 4.247Eþ00 3.929Eþ00 3.671Eþ00 3.201Eþ00 2.883Eþ00 2.654Eþ00 2.482Eþ00 2.241Eþ00 2.083Eþ00 1.972Eþ00 1.891Eþ00 1.830Eþ00 1.782Eþ00

Collision (MeV cm2 g1) 2.507E03 2.626E03 2.714E03 2.782E03 2.836E03 2.914E03 2.969E03 3.008E03 3.037E03 3.059E03 3.077E03 3.090E03 3.101E03 3.117E03 3.128E03 3.136E03 3.142E03 3.148E03 3.151E03 3.157E03 3.163E03 3.173E03 3.181E03 3.190E03 3.200E03 3.213E03 3.227E03 3.241E03 3.256E03 3.289E03 3.324E03 3.361E03 3.400E03 3.505E03 3.619E03 3.741E03 3.870E03 4.153E03 4.462E03 4.795E03 5.148E03 5.521E03 5.910E03

Radiative (MeV cm2 g1)

Stopping power

1.062Eþ02 9.207Eþ01 8.156Eþ01 7.342Eþ01 6.691Eþ01 5.712Eþ01 5.006Eþ01 4.471Eþ01 4.049Eþ01 3.708Eþ01 3.425Eþ01 3.187Eþ01 2.983Eþ01 2.651Eþ01 2.393Eþ01 2.185Eþ01 2.014Eþ01 1.694Eþ01 1.471Eþ01 1.305Eþ01 1.177Eþ01 9.915Eþ00 8.628Eþ00 7.680Eþ00 6.951Eþ00 6.373Eþ00 5.902Eþ00 5.511Eþ00 5.181Eþ00 4.653Eþ00 4.250Eþ00 3.932Eþ00 3.675Eþ00 3.205Eþ00 2.887Eþ00 2.658Eþ00 2.486Eþ00 2.245Eþ00 2.087Eþ00 1.977Eþ00 1.896Eþ00 1.835Eþ00 1.788Eþ00

Total (MeV cm2 g1)

Carbon, graphite

4.706E06 7.241E06 1.013E05 1.337E05 1.694E05 2.506E05 3.443E05 4.502E05 5.679E05 6.971E05 8.375E05 9.889E05 1.151E04 1.508E04 1.905E04 2.343E04 2.820E04 4.179E04 5.768E04 7.576E04 9.596E04 1.424E03 1.967E03 2.582E03 3.268E03 4.020E03 4.836E03 5.713E03 6.650E03 8.691E03 1.094E02 1.339E02 1.603E02 2.334E02 3.158E02 4.062E02 5.036E02 7.160E02 9.475E02 1.194E01 1.452E01 1.721E01 1.997E01

CSDA range (g cm2)

1.180E05 1.465E05 1.736E05 1.997E05 2.249E05 2.734E05 3.198E05 3.646E05 4.079E05 4.501E05 4.913E05 5.315E05 5.710E05 6.477E05 7.220E05 7.941E05 8.645E05 1.034E04 1.195E04 1.350E04 1.501E04 1.790E04 2.066E04 2.331E04 2.587E04 2.836E04 3.077E04 3.314E04 3.545E04 3.992E04 4.424E04 4.842E04 5.248E04 6.219E04 7.140E04 8.022E04 8.872E04 1.051E03 1.208E03 1.361E03 1.512E03 1.662E03 1.812E03

Brems yield

APPENDIX A: COMPILATION OF PHYSICAL DATA

97

98

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03

Energy (MeV)

5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

Energy (MeV)

1.185Eþ02 1.025Eþ02 9.073Eþ01 8.161Eþ01 7.434Eþ01

Collision (MeV cm2 g1)

1.641Eþ00 1.615Eþ00 1.579Eþ00 1.554Eþ00 1.538Eþ00 1.528Eþ00 1.515Eþ00 1.514Eþ00 1.517Eþ00 1.523Eþ00 1.537Eþ00 1.552Eþ00 1.567Eþ00 1.581Eþ00 1.594Eþ00 1.605Eþ00 1.616Eþ00 1.626Eþ00 1.644Eþ00 1.659Eþ00 1.673Eþ00 1.685Eþ00 1.710Eþ00 1.730Eþ00 1.746Eþ00 1.759Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

Radiative (MeV cm2 g1)

2.746E03 2.900E03 3.018E03 3.112E03 3.189E03

1.655Eþ00 1.630Eþ00 1.595Eþ00 1.573Eþ00 1.559Eþ00 1.551Eþ00 1.544Eþ00 1.548Eþ00 1.557Eþ00 1.569Eþ00 1.597Eþ00 1.626Eþ00 1.655Eþ00 1.684Eþ00 1.712Eþ00 1.740Eþ00 1.766Eþ00 1.793Eþ00 1.843Eþ00 1.893Eþ00 1.941Eþ00 1.988Eþ00 2.102Eþ00 2.213Eþ00 2.322Eþ00 2.430Eþ00

Total (MeV cm2 g1)

1.185Eþ02 1.025Eþ02 9.073Eþ01 8.162Eþ01 7.434Eþ01

Total (MeV cm2 g1)

Eye lens (ICRU-44)

Stopping power

1.408E02 1.495E02 1.676E02 1.866E02 2.066E02 2.273E02 2.819E02 3.400E02 4.010E02 4.646E02 5.977E02 7.377E02 8.831E02 1.033E01 1.186E01 1.343E01 1.502E01 1.665E01 1.995E01 2.333E01 2.676E01 3.026E01 3.918E01 4.832E01 5.762E01 6.706E01

Radiative (MeV cm2 g1)

Stopping power

Calcium sulfate

4.221E06 6.496E06 9.094E06 1.200E05 1.522E05

CSDA range (g cm2)

2.447E01 2.752E01 3.372E01 4.004E01 4.642E01 5.286E01 6.903E01 8.521E01 1.013Eþ00 1.173Eþ00 1.489Eþ00 1.799Eþ00 2.104Eþ00 2.404Eþ00 2.698Eþ00 2.988Eþ00 3.273Eþ00 3.554Eþ00 4.104Eþ00 4.639Eþ00 5.161Eþ00 5.670Eþ00 6.893Eþ00 8.052Eþ00 9.155Eþ00 1.021Eþ01

CSDA range (g cm2)

1.159E05 1.442E05 1.715E05 1.980E05 2.239E05

Brems yield

4.800E03 5.137E03 5.808E03 6.480E03 7.155E03 7.834E03 9.557E03 1.132E02 1.311E02 1.493E02 1.864E02 2.244E02 2.628E02 3.016E02 3.407E02 3.798E02 4.191E02 4.583E02 5.365E02 6.141E02 6.910E02 7.670E02 9.527E02 1.132E01 1.303E01 1.468E01

Brems yield

1.220Eþ02 1.053Eþ02 9.305Eþ01 8.358Eþ01 7.605Eþ01

Collision (MeV cm2 g1)

1.745Eþ00 1.716Eþ00 1.672Eþ00 1.643Eþ00 1.623Eþ00 1.609Eþ00 1.590Eþ00 1.584Eþ00 1.584Eþ00 1.587Eþ00 1.598Eþ00 1.611Eþ00 1.623Eþ00 1.636Eþ00 1.647Eþ00 1.658Eþ00 1.667Eþ00 1.676Eþ00 1.693Eþ00 1.707Eþ00 1.719Eþ00 1.730Eþ00 1.753Eþ00 1.770Eþ00 1.785Eþ00 1.797Eþ00

Collision (MeV cm2 g1)

Radiative (MeV cm2 g1) 2.508E03 2.633E03 2.727E03 2.800E03 2.859E03

1.752Eþ00 1.722Eþ00 1.680Eþ00 1.651Eþ00 1.632Eþ00 1.619Eþ00 1.603Eþ00 1.600Eþ00 1.603Eþ00 1.609Eþ00 1.627Eþ00 1.646Eþ00 1.666Eþ00 1.686Eþ00 1.705Eþ00 1.723Eþ00 1.741Eþ00 1.758Eþ00 1.791Eþ00 1.823Eþ00 1.853Eþ00 1.882Eþ00 1.950Eþ00 2.015Eþ00 2.077Eþ00 2.138Eþ00

Total (MeV cm2 g1)

1.221Eþ02 1.053Eþ02 9.305Eþ01 8.359Eþ01 7.605Eþ01

Total (MeV cm2 g1)

GAFchromic sensor Stopping power

6.315E03 6.734E03 7.610E03 8.533E03 9.497E03 1.050E02 1.314E02 1.596E02 1.894E02 2.204E02 2.860E02 3.552E02 4.274E02 5.023E02 5.793E02 6.582E02 7.385E02 8.203E02 9.877E02 1.160E01 1.335E01 1.514E01 1.971E01 2.442E01 2.922E01 3.410E01

Radiative (MeV cm2 g1)

Stopping power

Carbon, graphite

4.097E06 6.308E06 8.839E06 1.168E05 1.482E05

CSDA range (g cm2)

2.280E01 2.567E01 3.156E01 3.757E01 4.366E01 4.981E01 6.534E01 8.096E01 9.657E01 1.121Eþ00 1.431Eþ00 1.736Eþ00 2.038Eþ00 2.336Eþ00 2.631Eþ00 2.923Eþ00 3.212Eþ00 3.497Eþ00 4.061Eþ00 4.614Eþ00 5.158Eþ00 5.694Eþ00 6.999Eþ00 8.260Eþ00 9.482Eþ00 1.067Eþ01

CSDA range (g cm2)

1.027E05 1.277E05 1.517E05 1.749E05 1.975E05

Brems yield

1.961E03 2.111E03 2.412E03 2.716E03 3.025E03 3.337E03 4.136E03 4.961E03 5.808E03 6.676E03 8.466E03 1.032E02 1.222E02 1.415E02 1.612E02 1.812E02 2.014E02 2.217E02 2.627E02 3.041E02 3.457E02 3.874E02 4.916E02 5.950E02 6.971E02 7.977E02

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00

6.340Eþ01 5.554Eþ01 4.957Eþ01 4.488Eþ01 4.108Eþ01 3.794Eþ01 3.529Eþ01 3.303Eþ01 2.935Eþ01 2.648Eþ01 2.417Eþ01 2.228Eþ01 1.873Eþ01 1.626Eþ01 1.442Eþ01 1.301Eþ01 1.095Eþ01 9.529Eþ00 8.482Eþ00 7.677Eþ00 7.038Eþ00 6.518Eþ00 6.086Eþ00 5.721Eþ00 5.139Eþ00 4.695Eþ00 4.345Eþ00 4.061Eþ00 3.544Eþ00 3.195Eþ00 2.944Eþ00 2.756Eþ00 2.495Eþ00 2.324Eþ00 2.205Eþ00 2.119Eþ00 2.056Eþ00 2.006Eþ00 1.966Eþ00 1.934Eþ00 1.887Eþ00 1.856Eþ00 1.834Eþ00 1.819Eþ00 1.798Eþ00 1.791Eþ00 1.790Eþ00 1.793Eþ00 1.803Eþ00 1.815Eþ00 1.828Eþ00

3.306E03 3.392E03 3.456E03 3.506E03 3.546E03 3.578E03 3.604E03 3.625E03 3.659E03 3.683E03 3.700E03 3.714E03 3.735E03 3.747E03 3.753E03 3.759E03 3.771E03 3.784E03 3.795E03 3.806E03 3.817E03 3.831E03 3.846E03 3.863E03 3.899E03 3.938E03 3.981E03 4.025E03 4.145E03 4.276E03 4.416E03 4.565E03 4.891E03 5.249E03 5.634E03 6.044E03 6.476E03 6.927E03 7.396E03 7.882E03 8.898E03 9.967E03 1.108E02 1.224E02 1.530E02 1.857E02 2.201E02 2.561E02 3.319E02 4.119E02 4.956E02

6.341Eþ01 5.554Eþ01 4.958Eþ01 4.488Eþ01 4.109Eþ01 3.794Eþ01 3.530Eþ01 3.303Eþ01 2.935Eþ01 2.648Eþ01 2.418Eþ01 2.228Eþ01 1.874Eþ01 1.626Eþ01 1.443Eþ01 1.301Eþ01 1.096Eþ01 9.533Eþ00 8.485Eþ00 7.680Eþ00 7.041Eþ00 6.521Eþ00 6.090Eþ00 5.725Eþ00 5.143Eþ00 4.699Eþ00 4.349Eþ00 4.065Eþ00 3.548Eþ00 3.199Eþ00 2.949Eþ00 2.761Eþ00 2.500Eþ00 2.329Eþ00 2.211Eþ00 2.125Eþ00 2.062Eþ00 2.013Eþ00 1.973Eþ00 1.942Eþ00 1.896Eþ00 1.866Eþ00 1.845Eþ00 1.831Eþ00 1.814Eþ00 1.810Eþ00 1.812Eþ00 1.819Eþ00 1.836Eþ00 1.857Eþ00 1.877Eþ00

2.253E05 3.097E05 4.052E05 5.114E05 6.279E05 7.547E05 8.914E05 1.038E04 1.360E04 1.719E04 2.115E04 2.546E04 3.775E04 5.211E04 6.847E04 8.675E04 1.288E03 1.779E03 2.336E03 2.956E03 3.637E03 4.376E03 5.170E03 6.017E03 7.864E03 9.901E03 1.212E02 1.450E02 2.111E02 2.854E02 3.670E02 4.547E02 6.457E02 8.534E02 1.074E01 1.305E01 1.544E01 1.789E01 2.040E01 2.296E01 2.817E01 3.349E01 3.888E01 4.433E01 5.806E01 7.186E01 8.567E01 9.944E01 1.268Eþ00 1.539Eþ00 1.807Eþ00

2.742E05 3.229E05 3.702E05 4.164E05 4.615E05 5.056E05 5.489E05 5.915E05 6.745E05 7.551E05 8.335E05 9.100E05 1.094E04 1.270E04 1.439E04 1.603E04 1.916E04 2.214E04 2.501E04 2.778E04 3.046E04 3.306E04 3.560E04 3.808E04 4.287E04 4.749E04 5.196E04 5.629E04 6.664E04 7.642E04 8.575E04 9.473E04 1.119E03 1.283E03 1.443E03 1.600E03 1.754E03 1.908E03 2.061E03 2.215E03 2.523E03 2.835E03 3.150E03 3.470E03 4.287E03 5.130E03 5.997E03 6.886E03 8.722E03 1.062E02 1.257E02

6.475Eþ01 5.664Eþ01 5.051Eþ01 4.570Eþ01 4.180Eþ01 3.858Eþ01 3.587Eþ01 3.356Eþ01 2.980Eþ01 2.687Eþ01 2.452Eþ01 2.259Eþ01 1.898Eþ01 1.646Eþ01 1.460Eþ01 1.316Eþ01 1.107Eþ01 9.628Eþ00 8.566Eþ00 7.751Eþ00 7.104Eþ00 6.577Eþ00 6.140Eþ00 5.771Eþ00 5.183Eþ00 4.734Eþ00 4.379Eþ00 4.093Eþ00 3.570Eþ00 3.218Eþ00 2.964Eþ00 2.774Eþ00 2.510Eþ00 2.338Eþ00 2.217Eþ00 2.126Eþ00 2.058Eþ00 2.004Eþ00 1.963Eþ00 1.929Eþ00 1.880Eþ00 1.847Eþ00 1.824Eþ00 1.807Eþ00 1.785Eþ00 1.776Eþ00 1.775Eþ00 1.777Eþ00 1.787Eþ00 1.799Eþ00 1.812Eþ00

2.947E03 3.009E03 3.055E03 3.089E03 3.117E03 3.138E03 3.155E03 3.169E03 3.190E03 3.205E03 3.216E03 3.224E03 3.235E03 3.242E03 3.248E03 3.253E03 3.264E03 3.274E03 3.284E03 3.295E03 3.307E03 3.320E03 3.335E03 3.350E03 3.384E03 3.420E03 3.458E03 3.498E03 3.607E03 3.724E03 3.849E03 3.983E03 4.274E03 4.593E03 4.936E03 5.301E03 5.685E03 6.087E03 6.504E03 6.936E03 7.840E03 8.791E03 9.784E03 1.082E02 1.354E02 1.645E02 1.952E02 2.273E02 2.948E02 3.663E02 4.409E02

6.475Eþ01 5.665Eþ01 5.052Eþ01 4.570Eþ01 4.181Eþ01 3.859Eþ01 3.588Eþ01 3.356Eþ01 2.980Eþ01 2.687Eþ01 2.452Eþ01 2.259Eþ01 1.898Eþ01 1.646Eþ01 1.460Eþ01 1.316Eþ01 1.107Eþ01 9.631Eþ00 8.569Eþ00 7.754Eþ00 7.107Eþ00 6.580Eþ00 6.144Eþ00 5.775Eþ00 5.186Eþ00 4.737Eþ00 4.383Eþ00 4.096Eþ00 3.574Eþ00 3.221Eþ00 2.968Eþ00 2.778Eþ00 2.515Eþ00 2.342Eþ00 2.222Eþ00 2.131Eþ00 2.063Eþ00 2.011Eþ00 1.969Eþ00 1.936Eþ00 1.888Eþ00 1.856Eþ00 1.833Eþ00 1.818Eþ00 1.798Eþ00 1.793Eþ00 1.795Eþ00 1.800Eþ00 1.817Eþ00 1.836Eþ00 1.856Eþ00

2.197E05 3.025E05 3.961E05 5.003E05 6.149E05 7.395E05 8.740E05 1.018E04 1.335E04 1.689E04 2.079E04 2.504E04 3.717E04 5.136E04 6.752E04 8.558E04 1.272E03 1.758E03 2.309E03 2.924E03 3.598E03 4.330E03 5.117E03 5.957E03 7.788E03 9.809E03 1.201E02 1.437E02 2.093E02 2.832E02 3.642E02 4.513E02 6.411E02 8.476E02 1.067E01 1.297E01 1.536E01 1.781E01 2.033E01 2.289E01 2.812E01 3.347E01 3.889E01 4.437E01 5.821E01 7.214E01 8.608E01 9.999E01 1.276Eþ00 1.550Eþ00 1.821Eþ00

2.411E05 2.832E05 3.239E05 3.635E05 4.021E05 4.398E05 4.768E05 5.131E05 5.837E05 6.523E05 7.190E05 7.841E05 9.407E05 1.090E04 1.234E04 1.373E04 1.641E04 1.897E04 2.143E04 2.380E04 2.610E04 2.834E04 3.053E04 3.266E04 3.680E04 4.080E04 4.466E04 4.841E04 5.737E04 6.586E04 7.398E04 8.180E04 9.679E04 1.112E03 1.252E03 1.389E03 1.526E03 1.663E03 1.799E03 1.936E03 2.212E03 2.491E03 2.774E03 3.061E03 3.795E03 4.554E03 5.335E03 6.136E03 7.792E03 9.508E03 1.127E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

99

100

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02

Energy (MeV)

4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

Energy (MeV)

1.082Eþ02 9.384Eþ01 8.316Eþ01 7.488Eþ01 6.826Eþ01 5.830Eþ01 5.111Eþ01 4.565Eþ01 4.135Eþ01 3.787Eþ01 3.499Eþ01 3.256Eþ01 3.048Eþ01 2.709Eþ01 2.446Eþ01 2.234Eþ01 2.059Eþ01 1.732Eþ01

Collision (MeV cm2 g1)

1.840Eþ00 1.851Eþ00 1.862Eþ00 1.872Eþ00 1.881Eþ00 1.898Eþ00 1.913Eþ00 1.926Eþ00 1.938Eþ00 1.963Eþ00 1.983Eþ00 2.000Eþ00 2.014Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

1.898Eþ00 1.918Eþ00 1.938Eþ00 1.957Eþ00 1.976Eþ00 2.012Eþ00 2.047Eþ00 2.080Eþ00 2.113Eþ00 2.190Eþ00 2.265Eþ00 2.337Eþ00 2.407Eþ00

Total (MeV cm2 g1)

2.605E03 2.737E03 2.837E03 2.914E03 2.976E03 3.069E03 3.134E03 3.183E03 3.219E03 3.247E03 3.270E03 3.288E03 3.302E03 3.324E03 3.340E03 3.351E03 3.359E03 3.370E03

Radiative (MeV cm2 g1)

Stopping power

1.082Eþ02 9.384Eþ01 8.316Eþ01 7.489Eþ01 6.827Eþ01 5.830Eþ01 5.111Eþ01 4.565Eþ01 4.136Eþ01 3.788Eþ01 3.499Eþ01 3.256Eþ01 3.048Eþ01 2.710Eþ01 2.446Eþ01 2.234Eþ01 2.059Eþ01 1.733Eþ01

Total (MeV cm2 g1)

‘‘Kapton’’ polyimide film

5.821E02 6.709E02 7.617E02 8.544E02 9.487E02 1.142E01 1.340E01 1.542E01 1.747E01 2.274E01 2.815E01 3.367E01 3.927E01

Radiative (MeV cm2 g1)

Stopping power

Eye lens (ICRU-44)

4.620E06 7.108E06 9.944E06 1.312E05 1.662E05 2.457E05 3.376E05 4.413E05 5.565E05 6.830E05 8.204E05 9.687E05 1.127E04 1.476E04 1.865E04 2.293E04 2.760E04 4.089E04

CSDA range (g cm2)

2.072Eþ00 2.334Eþ00 2.593Eþ00 2.850Eþ00 3.104Eþ00 3.605Eþ00 4.098Eþ00 4.583Eþ00 5.060Eþ00 6.222Eþ00 7.344Eþ00 8.431Eþ00 9.485Eþ00

CSDA range (g cm2)

1.203E05 1.495E05 1.774E05 2.042E05 2.303E05 2.805E05 3.288E05 3.755E05 4.208E05 4.649E05 5.080E05 5.502E05 5.916E05 6.722E05 7.502E05 8.261E05 9.001E05 1.078E04

Brems yield

1.457E02 1.660E02 1.865E02 2.072E02 2.282E02 2.704E02 3.130E02 3.557E02 3.986E02 5.055E02 6.114E02 7.159E02 8.185E02

Brems yield

9.160Eþ01 7.983Eþ01 7.100Eþ01 6.410Eþ01 5.856Eþ01 5.017Eþ01 4.409Eþ01 3.945Eþ01 3.579Eþ01 3.282Eþ01 3.035Eþ01 2.826Eþ01 2.648Eþ01 2.357Eþ01 2.130Eþ01 1.947Eþ01 1.796Eþ01 1.513Eþ01

Collision (MeV cm2 g1)

1.824Eþ00 1.835Eþ00 1.846Eþ00 1.856Eþ00 1.865Eþ00 1.882Eþ00 1.896Eþ00 1.909Eþ00 1.921Eþ00 1.945Eþ00 1.964Eþ00 1.980Eþ00 1.994Eþ00

Collision (MeV cm2 g1)

Radiative (MeV cm2 g1) 2.612E03 2.767E03 2.889E03 2.987E03 3.069E03 3.197E03 3.292E03 3.365E03 3.423E03 3.470E03 3.508E03 3.540E03 3.567E03 3.609E03 3.640E03 3.663E03 3.681E03 3.712E03

1.875Eþ00 1.895Eþ00 1.914Eþ00 1.932Eþ00 1.950Eþ00 1.984Eþ00 2.016Eþ00 2.047Eþ00 2.077Eþ00 2.149Eþ00 2.216Eþ00 2.282Eþ00 2.346Eþ00

Total (MeV cm2 g1)

9.161Eþ01 7.983Eþ01 7.100Eþ01 6.411Eþ01 5.857Eþ01 5.017Eþ01 4.409Eþ01 3.946Eþ01 3.579Eþ01 3.282Eþ01 3.035Eþ01 2.827Eþ01 2.648Eþ01 2.357Eþ01 2.130Eþ01 1.947Eþ01 1.796Eþ01 1.514Eþ01

Total (MeV cm2 g1)

Lithium fluoride Stopping power

5.181E02 5.976E02 6.789E02 7.619E02 8.463E02 1.019E01 1.197E01 1.378E01 1.562E01 2.035E01 2.521E01 3.016E01 3.520E01

Radiative (MeV cm2 g1)

Stopping power

GAFchromic sensor

5.458E06 8.390E06 1.172E05 1.543E05 1.951E05 2.877E05 3.943E05 5.144E05 6.476E05 7.936E05 9.522E05 1.123E04 1.306E04 1.707E04 2.154E04 2.646E04 3.181E04 4.704E04

CSDA range (g cm2)

2.089Eþ00 2.354Eþ00 2.617Eþ00 2.877Eþ00 3.135Eþ00 3.643Eþ00 4.143Eþ00 4.635Eþ00 5.120Eþ00 6.303Eþ00 7.449Eþ00 8.560Eþ00 9.641Eþ00

CSDA range (g cm2)

1.426E05 1.773E05 2.105E05 2.428E05 2.743E05 3.356E05 3.951E05 4.529E05 5.094E05 5.647E05 6.189E05 6.721E05 7.244E05 8.265E05 9.258E05 1.022E04 1.117E04 1.344E04

Brems yield

1.307E02 1.491E02 1.677E02 1.865E02 2.055E02 2.438E02 2.825E02 3.215E02 3.606E02 4.585E02 5.558E02 6.521E02 7.471E02

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

1.504Eþ01 1.335Eþ01 1.204Eþ01 1.014Eþ01 8.828Eþ00 7.860Eþ00 7.116Eþ00 6.525Eþ00 6.044Eþ00 5.644Eþ00 5.307Eþ00 4.768Eþ00 4.357Eþ00 4.032Eþ00 3.770Eþ00 3.290Eþ00 2.967Eþ00 2.735Eþ00 2.560Eþ00 2.318Eþ00 2.159Eþ00 2.049Eþ00 1.969Eþ00 1.906Eþ00 1.859Eþ00 1.821Eþ00 1.791Eþ00 1.747Eþ00 1.717Eþ00 1.696Eþ00 1.682Eþ00 1.663Eþ00 1.657Eþ00 1.657Eþ00 1.660Eþ00 1.670Eþ00 1.683Eþ00 1.696Eþ00 1.708Eþ00 1.719Eþ00 1.730Eþ00 1.740Eþ00 1.749Eþ00 1.765Eþ00 1.780Eþ00 1.793Eþ00 1.804Eþ00 1.828Eþ00 1.847Eþ00 1.862Eþ00 1.875Eþ00

3.376E03 3.382E03 3.388E03 3.398E03 3.408E03 3.417E03 3.428E03 3.440E03 3.453E03 3.468E03 3.484E03 3.518E03 3.554E03 3.593E03 3.635E03 3.745E03 3.865E03 3.994E03 4.130E03 4.429E03 4.756E03 5.108E03 5.483E03 5.878E03 6.290E03 6.719E03 7.162E03 8.091E03 9.068E03 1.009E02 1.115E02 1.395E02 1.693E02 2.008E02 2.337E02 3.030E02 3.763E02 4.527E02 5.319E02 6.133E02 6.966E02 7.815E02 8.679E02 1.045E01 1.226E01 1.412E01 1.600E01 2.084E01 2.580E01 3.087E01 3.602E01

1.504Eþ01 1.335Eþ01 1.204Eþ01 1.015Eþ01 8.832Eþ00 7.864Eþ00 7.119Eþ00 6.528Eþ00 6.047Eþ00 5.647Eþ00 5.310Eþ00 4.772Eþ00 4.360Eþ00 4.036Eþ00 3.773Eþ00 3.294Eþ00 2.971Eþ00 2.739Eþ00 2.564Eþ00 2.322Eþ00 2.164Eþ00 2.055Eþ00 1.974Eþ00 1.912Eþ00 1.865Eþ00 1.828Eþ00 1.798Eþ00 1.755Eþ00 1.726Eþ00 1.707Eþ00 1.693Eþ00 1.677Eþ00 1.674Eþ00 1.677Eþ00 1.683Eþ00 1.701Eþ00 1.720Eþ00 1.741Eþ00 1.761Eþ00 1.780Eþ00 1.799Eþ00 1.818Eþ00 1.836Eþ00 1.870Eþ00 1.903Eþ00 1.934Eþ00 1.964Eþ00 2.036Eþ00 2.105Eþ00 2.171Eþ00 2.235Eþ00

5.642E04 7.410E04 9.385E04 1.393E03 1.923E03 2.524E03 3.193E03 3.928E03 4.724E03 5.580E03 6.494E03 8.485E03 1.068E02 1.307E02 1.563E02 2.275E02 3.076E02 3.955E02 4.899E02 6.955E02 9.190E02 1.156E01 1.405E01 1.662E01 1.927E01 2.198E01 2.474E01 3.038E01 3.613E01 4.195E01 4.784E01 6.269E01 7.761E01 9.254E01 1.074Eþ00 1.370Eþ00 1.662Eþ00 1.951Eþ00 2.237Eþ00 2.519Eþ00 2.798Eþ00 3.075Eþ00 3.349Eþ00 3.888Eþ00 4.418Eþ00 4.940Eþ00 5.453Eþ00 6.702Eþ00 7.910Eþ00 9.079Eþ00 1.021Eþ01

1.248E04 1.411E04 1.568E04 1.871E04 2.161E04 2.438E04 2.706E04 2.966E04 3.218E04 3.465E04 3.705E04 4.171E04 4.621E04 5.055E04 5.476E04 6.483E04 7.435E04 8.345E04 9.220E04 1.090E03 1.250E03 1.406E03 1.559E03 1.711E03 1.862E03 2.013E03 2.165E03 2.469E03 2.777E03 3.088E03 3.404E03 4.212E03 5.045E03 5.902E03 6.780E03 8.592E03 1.047E02 1.239E02 1.435E02 1.635E02 1.837E02 2.042E02 2.248E02 2.663E02 3.083E02 3.504E02 3.926E02 4.980E02 6.025E02 7.056E02 8.071E02

1.315Eþ01 1.168Eþ01 1.055Eþ01 8.894Eþ00 7.748Eþ00 6.902Eþ00 6.252Eþ00 5.736Eþ00 5.315Eþ00 4.965Eþ00 4.670Eþ00 4.198Eþ00 3.838Eþ00 3.553Eþ00 3.323Eþ00 2.903Eþ00 2.619Eþ00 2.415Eþ00 2.261Eþ00 2.048Eþ00 1.907Eþ00 1.809Eþ00 1.737Eþ00 1.683Eþ00 1.642Eþ00 1.609Eþ00 1.583Eþ00 1.546Eþ00 1.521Eþ00 1.503Eþ00 1.491Eþ00 1.476Eþ00 1.471Eþ00 1.471Eþ00 1.474Eþ00 1.483Eþ00 1.493Eþ00 1.503Eþ00 1.513Eþ00 1.523Eþ00 1.531Eþ00 1.539Eþ00 1.547Eþ00 1.560Eþ00 1.572Eþ00 1.583Eþ00 1.592Eþ00 1.612Eþ00 1.629Eþ00 1.642Eþ00 1.654Eþ00

3.729E03 3.738E03 3.745E03 3.759E03 3.772E03 3.783E03 3.793E03 3.804E03 3.816E03 3.830E03 3.846E03 3.880E03 3.917E03 3.958E03 4.001E03 4.116E03 4.241E03 4.376E03 4.520E03 4.835E03 5.182E03 5.556E03 5.953E03 6.373E03 6.811E03 7.267E03 7.738E03 8.725E03 9.763E03 1.085E02 1.197E02 1.495E02 1.812E02 2.146E02 2.494E02 3.228E02 4.003E02 4.811E02 5.646E02 6.505E02 7.384E02 8.279E02 9.188E02 1.105E01 1.295E01 1.490E01 1.688E01 2.194E01 2.713E01 3.242E01 3.779E01

1.316Eþ01 1.169Eþ01 1.055Eþ01 8.898Eþ00 7.751Eþ00 6.906Eþ00 6.256Eþ00 5.739Eþ00 5.319Eþ00 4.969Eþ00 4.674Eþ00 4.202Eþ00 3.842Eþ00 3.557Eþ00 3.327Eþ00 2.907Eþ00 2.623Eþ00 2.419Eþ00 2.266Eþ00 2.053Eþ00 1.912Eþ00 1.814Eþ00 1.743Eþ00 1.690Eþ00 1.649Eþ00 1.617Eþ00 1.591Eþ00 1.554Eþ00 1.530Eþ00 1.514Eþ00 1.503Eþ00 1.491Eþ00 1.489Eþ00 1.493Eþ00 1.499Eþ00 1.515Eþ00 1.533Eþ00 1.552Eþ00 1.570Eþ00 1.588Eþ00 1.605Eþ00 1.622Eþ00 1.639Eþ00 1.671Eþ00 1.702Eþ00 1.732Eþ00 1.761Eþ00 1.832Eþ00 1.900Eþ00 1.966Eþ00 2.032Eþ00

6.480E04 8.501E04 1.076E03 1.594E03 2.198E03 2.883E03 3.645E03 4.480E03 5.386E03 6.359E03 7.397E03 9.659E03 1.215E02 1.486E02 1.777E02 2.584E02 3.492E02 4.486E02 5.555E02 7.881E02 1.041E01 1.310E01 1.591E01 1.883E01 2.183E01 2.489E01 2.801E01 3.437E01 4.086E01 4.743E01 5.406E01 7.077E01 8.756E01 1.043Eþ00 1.211Eþ00 1.542Eþ00 1.870Eþ00 2.195Eþ00 2.515Eþ00 2.832Eþ00 3.145Eþ00 3.455Eþ00 3.762Eþ00 4.366Eþ00 4.959Eþ00 5.541Eþ00 6.114Eþ00 7.506Eþ00 8.846Eþ00 1.014Eþ01 1.139Eþ01

1.561E04 1.769E04 1.970E04 2.354E04 2.719E04 3.070E04 3.408E04 3.734E04 4.051E04 4.359E04 4.660E04 5.242E04 5.802E04 6.342E04 6.865E04 8.113E04 9.290E04 1.041E03 1.149E03 1.354E03 1.551E03 1.741E03 1.929E03 2.114E03 2.297E03 2.481E03 2.664E03 3.031E03 3.402E03 3.776E03 4.155E03 5.122E03 6.117E03 7.138E03 8.184E03 1.034E02 1.257E02 1.485E02 1.718E02 1.954E02 2.194E02 2.436E02 2.679E02 3.169E02 3.662E02 4.156E02 4.650E02 5.878E02 7.087E02 8.273E02 9.433E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

101

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01

Energy (MeV)

9.576Eþ01 8.347Eþ01 7.424Eþ01 6.705Eþ01 6.126Eþ01 5.249Eþ01 4.612Eþ01 4.128Eþ01 3.745Eþ01 3.434Eþ01 3.176Eþ01 2.958Eþ01 2.771Eþ01 2.467Eþ01 2.229Eþ01 2.038Eþ01 1.880Eþ01 1.584Eþ01 1.377Eþ01 1.223Eþ01 1.104Eþ01 9.311Eþ00 8.111Eþ00 7.227Eþ00 6.546Eþ00 6.005Eþ00 5.565Eþ00 5.199Eþ00 4.890Eþ00 4.396Eþ00 4.019Eþ00 3.721Eþ00 3.480Eþ00 3.040Eþ00 2.742Eþ00 2.528Eþ00 2.368Eþ00 2.145Eþ00 1.999Eþ00 1.895Eþ00

Collision MeV (cm2 g1)

Table A.4. Continued

2.646E03 2.790E03 2.901E03 2.988E03 3.060E03 3.168E03 3.247E03 3.306E03 3.352E03 3.388E03 3.417E03 3.440E03 3.460E03 3.490E03 3.511E03 3.527E03 3.539E03 3.558E03 3.569E03 3.574E03 3.578E03 3.589E03 3.601E03 3.611E03 3.622E03 3.633E03 3.645E03 3.659E03 3.675E03 3.709E03 3.746E03 3.786E03 3.828E03 3.942E03 4.065E03 4.197E03 4.338E03 4.646E03 4.985E03 5.349E03

Radiative (MeV cm2 g1)

Stopping power

9.576Eþ01 8.347Eþ01 7.425Eþ01 6.705Eþ01 6.126Eþ01 5.249Eþ01 4.613Eþ01 4.128Eþ01 3.745Eþ01 3.434Eþ01 3.176Eþ01 2.958Eþ01 2.771Eþ01 2.467Eþ01 2.229Eþ01 2.038Eþ01 1.880Eþ01 1.584Eþ01 1.377Eþ01 1.223Eþ01 1.104Eþ01 9.315Eþ00 8.115Eþ00 7.230Eþ00 6.550Eþ00 6.009Eþ00 5.568Eþ00 5.203Eþ00 4.893Eþ00 4.400Eþ00 4.022Eþ00 3.725Eþ00 3.483Eþ00 3.043Eþ00 2.746Eþ00 2.533Eþ00 2.373Eþ00 2.150Eþ00 2.004Eþ00 1.900Eþ00

Total (MeV cm2 g1)

Lithium tetraborate

5.221E06 8.025E06 1.121E05 1.476E05 1.866E05 2.751E05 3.770E05 4.918E05 6.191E05 7.587E05 9.102E05 1.073E04 1.248E04 1.631E04 2.058E04 2.528E04 3.040E04 4.494E04 6.192E04 8.122E04 1.028E03 1.523E03 2.100E03 2.754E03 3.482E03 4.280E03 5.145E03 6.074E03 7.066E03 9.226E03 1.161E02 1.419E02 1.697E02 2.468E02 3.335E02 4.285E02 5.306E02 7.527E02 9.941E02 1.251E01

CSDA range (g cm2)

1.381E05 1.716E05 2.034E05 2.341E05 2.639E05 3.215E05 3.770E05 4.306E05 4.828E05 5.337E05 5.835E05 6.322E05 6.800E05 7.731E05 8.634E05 9.512E05 1.037E04 1.243E04 1.439E04 1.627E04 1.809E04 2.157E04 2.489E04 2.807E04 3.114E04 3.412E04 3.700E04 3.981E04 4.255E04 4.787E04 5.298E04 5.792E04 6.270E04 7.413E04 8.492E04 9.520E04 1.051E03 1.240E03 1.421E03 1.597E03

Brems yield

9.159Eþ01 8.020Eþ01 7.157Eþ01 6.479Eþ01 5.931Eþ01 5.096Eþ01 4.488Eþ01 4.023Eþ01 3.654Eþ01 3.354Eþ01 3.105Eþ01 2.894Eþ01 2.713Eþ01 2.418Eþ01 2.187Eþ01 2.000Eþ01 1.847Eþ01 1.558Eþ01 1.356Eþ01 1.205Eþ01 1.088Eþ01 9.189Eþ00 8.011Eþ00 7.141Eþ00 6.472Eþ00 5.940Eþ00 5.506Eþ00 5.145Eþ00 4.841Eþ00 4.354Eþ00 3.982Eþ00 3.688Eþ00 3.450Eþ00 3.015Eþ00 2.721Eþ00 2.510Eþ00 2.352Eþ00 2.132Eþ00 1.988Eþ00 1.887Eþ00

Collision (MeV cm2 g1) 2.915E03 3.088E03 3.223E03 3.332E03 3.422E03 3.561E03 3.665E03 3.744E03 3.807E03 3.857E03 3.898E03 3.932E03 3.961E03 4.006E03 4.039E03 4.064E03 4.083E03 4.116E03 4.135E03 4.146E03 4.153E03 4.169E03 4.183E03 4.196E03 4.208E03 4.221E03 4.234E03 4.250E03 4.267E03 4.305E03 4.346E03 4.391E03 4.438E03 4.566E03 4.705E03 4.854E03 5.013E03 5.362E03 5.745E03 6.158E03

Radiative (MeV cm2 g1)

Stopping power

9.159Eþ01 8.021Eþ01 7.157Eþ01 6.479Eþ01 5.931Eþ01 5.096Eþ01 4.488Eþ01 4.023Eþ01 3.654Eþ01 3.355Eþ01 3.105Eþ01 2.894Eþ01 2.713Eþ01 2.418Eþ01 2.187Eþ01 2.001Eþ01 1.847Eþ01 1.558Eþ01 1.356Eþ01 1.206Eþ01 1.089Eþ01 9.193Eþ00 8.015Eþ00 7.145Eþ00 6.476Eþ00 5.944Eþ00 5.510Eþ00 5.150Eþ00 4.845Eþ00 4.358Eþ00 3.986Eþ00 3.692Eþ00 3.454Eþ00 3.020Eþ00 2.726Eþ00 2.515Eþ00 2.357Eþ00 2.137Eþ00 1.993Eþ00 1.893Eþ00

Total (MeV cm2 g1)

Magnesium tetraborate

5.459E06 8.383E06 1.169E05 1.537E05 1.940E05 2.853E05 3.901E05 5.080E05 6.385E05 7.815E05 9.366E05 1.103E04 1.282E04 1.673E04 2.109E04 2.587E04 3.108E04 4.588E04 6.313E04 8.272E04 1.046E03 1.548E03 2.132E03 2.794E03 3.530E03 4.337E03 5.212E03 6.151E03 7.153E03 9.334E03 1.174E02 1.435E02 1.715E02 2.492E02 3.366E02 4.322E02 5.350E02 7.586E02 1.001E01 1.259E01

CSDA range (g cm2)

1.591E05 1.977E05 2.344E05 2.698E05 3.043E05 3.711E05 4.356E05 4.982E05 5.592E05 6.188E05 6.772E05 7.345E05 7.907E05 9.005E05 1.007E04 1.111E04 1.212E04 1.455E04 1.687E04 1.910E04 2.124E04 2.535E04 2.926E04 3.300E04 3.661E04 4.010E04 4.349E04 4.678E04 4.999E04 5.620E04 6.217E04 6.793E04 7.351E04 8.680E04 9.933E04 1.113E03 1.227E03 1.446E03 1.654E03 1.856E03

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

102

103

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03

Energy (MeV)

4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

1.189Eþ02 1.029Eþ02 9.108Eþ01 8.194Eþ01 7.464Eþ01 6.366Eþ01 5.577Eþ01 4.978Eþ01 4.507Eþ01 4.126Eþ01

Collision (MeV cm2 g1)

1.819Eþ00 1.762Eþ00 1.717Eþ00 1.683Eþ00 1.655Eþ00 1.615Eþ00 1.588Eþ00 1.569Eþ00 1.557Eþ00 1.540Eþ00 1.534Eþ00 1.535Eþ00 1.538Eþ00 1.548Eþ00 1.560Eþ00 1.572Eþ00 1.583Eþ00 1.593Eþ00 1.603Eþ00 1.612Eþ00 1.621Eþ00 1.636Eþ00 1.649Eþ00 1.661Eþ00 1.671Eþ00 1.693Eþ00 1.710Eþ00 1.725Eþ00 1.737Eþ00

1.824Eþ00 1.768Eþ00 1.724Eþ00 1.690Eþ00 1.663Eþ00 1.623Eþ00 1.597Eþ00 1.580Eþ00 1.568Eþ00 1.554Eþ00 1.552Eþ00 1.555Eþ00 1.562Eþ00 1.579Eþ00 1.599Eþ00 1.619Eþ00 1.638Eþ00 1.657Eþ00 1.675Eþ00 1.693Eþ00 1.710Eþ00 1.744Eþ00 1.776Eþ00 1.806Eþ00 1.836Eþ00 1.908Eþ00 1.976Eþ00 2.043Eþ00 2.108Eþ00

2.776E03 2.934E03 3.056E03 3.153E03 3.233E03 3.355E03 3.445E03 3.512E03 3.565E03 3.607E03

Radiative (MeV cm2 g1)

Stopping power

1.189Eþ02 1.029Eþ02 9.108Eþ01 8.194Eþ01 7.464Eþ01 6.367Eþ01 5.577Eþ01 4.978Eþ01 4.507Eþ01 4.126Eþ01

Total (MeV cm2 g1)

Muscle, skeletal (ICRU-44)

5.737E03 6.145E03 6.572E03 7.016E03 7.475E03 8.436E03 9.448E03 1.050E02 1.160E02 1.450E02 1.758E02 2.084E02 2.424E02 3.141E02 3.898E02 4.688E02 5.506E02 6.345E02 7.203E02 8.078E02 8.969E02 1.079E01 1.266E01 1.457E01 1.651E01 2.147E01 2.657E01 3.178E01 3.706E01

4.205E06 6.472E06 9.060E06 1.196E05 1.516E05 2.244E05 3.085E05 4.036E05 5.093E05 6.254E05

CSDA range (g cm2)

1.520E01 1.798E01 2.085E01 2.378E01 2.676E01 3.285E01 3.907E01 4.536E01 5.172E01 6.775E01 8.385E01 9.995E01 1.160Eþ00 1.478Eþ00 1.793Eþ00 2.104Eþ00 2.411Eþ00 2.714Eþ00 3.014Eþ00 3.311Eþ00 3.605Eþ00 4.184Eþ00 4.752Eþ00 5.311Eþ00 5.860Eþ00 7.195Eþ00 8.483Eþ00 9.727Eþ00 1.093Eþ01

1.167E05 1.453E05 1.728E05 1.996E05 2.257E05 2.767E05 3.260E05 3.740E05 4.208E05 4.665E05

Brems yield

1.769E03 1.941E03 2.111E03 2.281E03 2.451E03 2.793E03 3.138E03 3.487E03 3.841E03 4.744E03 5.674E03 6.629E03 7.607E03 9.624E03 1.171E02 1.384E02 1.602E02 1.824E02 2.048E02 2.274E02 2.502E02 2.961E02 3.423E02 3.887E02 4.351E02 5.507E02 6.649E02 7.772E02 8.872E02

1.251Eþ02 1.079Eþ02 9.519Eþ01 8.545Eþ01 7.770Eþ01 6.611Eþ01 5.779Eþ01 5.151Eþ01 4.658Eþ01 4.260Eþ01

Collision (MeV cm2 g1)

1.812Eþ00 1.756Eþ00 1.713Eþ00 1.679Eþ00 1.652Eþ00 1.613Eþ00 1.587Eþ00 1.569Eþ00 1.557Eþ00 1.541Eþ00 1.537Eþ00 1.538Eþ00 1.542Eþ00 1.553Eþ00 1.566Eþ00 1.578Eþ00 1.590Eþ00 1.601Eþ00 1.611Eþ00 1.620Eþ00 1.629Eþ00 1.645Eþ00 1.658Eþ00 1.671Eþ00 1.681Eþ00 1.704Eþ00 1.722Eþ00 1.737Eþ00 1.749Eþ00

1.819Eþ00 1.763Eþ00 1.720Eþ00 1.687Eþ00 1.660Eþ00 1.622Eþ00 1.597Eþ00 1.581Eþ00 1.570Eþ00 1.558Eþ00 1.557Eþ00 1.562Eþ00 1.569Eþ00 1.589Eþ00 1.610Eþ00 1.631Eþ00 1.652Eþ00 1.673Eþ00 1.693Eþ00 1.712Eþ00 1.731Eþ00 1.767Eþ00 1.801Eþ00 1.835Eþ00 1.868Eþ00 1.946Eþ00 2.021Eþ00 2.095Eþ00 2.167Eþ00

2.470E03 2.591E03 2.681E03 2.752E03 2.808E03 2.893E03 2.952E03 2.996E03 3.029E03 3.055E03

Radiative (MeV cm2 g1)

Stopping power

1.251Eþ02 1.079Eþ02 9.520Eþ01 8.545Eþ01 7.771Eþ01 6.611Eþ01 5.780Eþ01 5.152Eþ01 4.659Eþ01 4.261Eþ01

Total (MeV cm2 g1)

Nylon, type 6 and type 6/6

6.597E03 7.061E03 7.545E03 8.049E03 8.570E03 9.660E03 1.081E02 1.201E02 1.325E02 1.654E02 2.004E02 2.373E02 2.758E02 3.568E02 4.424E02 5.316E02 6.239E02 7.185E02 8.153E02 9.139E02 1.014E01 1.219E01 1.430E01 1.644E01 1.863E01 2.421E01 2.994E01 3.579E01 4.172E01

3.996E06 6.154E06 8.627E06 1.140E05 1.448E05 2.148E05 2.959E05 3.877E05 4.899E05 6.023E05

CSDA range (g cm2)

1.529E01 1.808E01 2.095E01 2.389E01 2.688E01 3.298E01 3.919E01 4.549E01 5.184E01 6.784E01 8.390E01 9.994E01 1.159Eþ00 1.476Eþ00 1.788Eþ00 2.097Eþ00 2.402Eþ00 2.702Eþ00 2.999Eþ00 3.293Eþ00 3.584Eþ00 4.155Eþ00 4.716Eþ00 5.266Eþ00 5.806Eþ00 7.117Eþ00 8.378Eþ00 9.592Eþ00 1.077Eþ01

9.868E06 1.227E05 1.458E05 1.681E05 1.898E05 2.318E05 2.722E05 3.114E05 3.495E05 3.866E05

Brems yield

2.054E03 2.250E03 2.444E03 2.638E03 2.832E03 3.221E03 3.614E03 4.010E03 4.411E03 5.433E03 6.484E03 7.561E03 8.663E03 1.093E02 1.327E02 1.566E02 1.810E02 2.057E02 2.307E02 2.559E02 2.813E02 3.322E02 3.835E02 4.348E02 4.860E02 6.131E02 7.382E02 8.607E02 9.804E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00

Energy (MeV)

3.810Eþ01 3.544Eþ01 3.317Eþ01 2.947Eþ01 2.659Eþ01 2.428Eþ01 2.238Eþ01 1.882Eþ01 1.633Eþ01 1.449Eþ01 1.307Eþ01 1.100Eþ01 9.573Eþ00 8.521Eþ00 7.712Eþ00 7.070Eþ00 6.548Eþ00 6.114Eþ00 5.748Eþ00 5.163Eþ00 4.717Eþ00 4.365Eþ00 4.081Eþ00 3.561Eþ00 3.210Eþ00 2.958Eþ00 2.769Eþ00 2.507Eþ00 2.335Eþ00 2.216Eþ00 2.130Eþ00 2.065Eþ00 2.016Eþ00 1.976Eþ00 1.944Eþ00 1.898Eþ00 1.866Eþ00 1.844Eþ00 1.829Eþ00 1.809Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

3.641E03 3.669E03 3.692E03 3.728E03 3.754E03 3.774E03 3.788E03 3.812E03 3.826E03 3.833E03 3.839E03 3.853E03 3.866E03 3.877E03 3.889E03 3.900E03 3.914E03 3.929E03 3.947E03 3.983E03 4.023E03 4.066E03 4.112E03 4.234E03 4.367E03 4.509E03 4.661E03 4.993E03 5.357E03 5.749E03 6.166E03 6.606E03 7.066E03 7.543E03 8.037E03 9.071E03 1.016E02 1.130E02 1.248E02 1.559E02

Radiative (MeV cm2 g1)

Stopping power

3.811Eþ01 3.545Eþ01 3.317Eþ01 2.948Eþ01 2.660Eþ01 2.428Eþ01 2.238Eþ01 1.882Eþ01 1.634Eþ01 1.449Eþ01 1.307Eþ01 1.101Eþ01 9.577Eþ00 8.524Eþ00 7.716Eþ00 7.074Eþ00 6.552Eþ00 6.118Eþ00 5.752Eþ00 5.167Eþ00 4.721Eþ00 4.369Eþ00 4.085Eþ00 3.565Eþ00 3.215Eþ00 2.963Eþ00 2.774Eþ00 2.512Eþ00 2.340Eþ00 2.221Eþ00 2.136Eþ00 2.072Eþ00 2.023Eþ00 1.984Eþ00 1.952Eþ00 1.907Eþ00 1.876Eþ00 1.856Eþ00 1.842Eþ00 1.824Eþ00

Total (MeV cm2 g1)

Muscle, skeletal (ICRU-44)

7.516E05 8.877E05 1.034E04 1.354E04 1.712E04 2.106E04 2.535E04 3.759E04 5.189E04 6.817E04 8.636E04 1.282E03 1.771E03 2.326E03 2.943E03 3.621E03 4.356E03 5.146E03 5.990E03 7.828E03 9.855E03 1.206E02 1.443E02 2.101E02 2.841E02 3.653E02 4.526E02 6.427E02 8.493E02 1.069E01 1.299E01 1.537E01 1.781E01 2.031E01 2.285E01 2.803E01 3.332E01 3.868E01 4.410E01 5.775E01

CSDA range (g cm2)

5.114E05 5.554E05 5.986E05 6.830E05 7.650E05 8.447E05 9.226E05 1.110E04 1.289E04 1.462E04 1.628E04 1.947E04 2.251E04 2.543E04 2.824E04 3.097E04 3.362E04 3.620E04 3.872E04 4.360E04 4.829E04 5.284E04 5.724E04 6.775E04 7.769E04 8.718E04 9.630E04 1.137E03 1.304E03 1.466E03 1.625E03 1.782E03 1.938E03 2.093E03 2.249E03 2.561E03 2.877E03 3.196E03 3.519E03 4.346E03

Brems yield

3.931Eþ01 3.654Eþ01 3.417Eþ01 3.033Eþ01 2.735Eþ01 2.495Eþ01 2.298Eþ01 1.930Eþ01 1.673Eþ01 1.483Eþ01 1.337Eþ01 1.125Eþ01 9.778Eþ00 8.698Eþ00 7.869Eþ00 7.211Eþ00 6.676Eþ00 6.232Eþ00 5.857Eþ00 5.259Eþ00 4.803Eþ00 4.443Eþ00 4.152Eþ00 3.621Eþ00 3.263Eþ00 3.006Eþ00 2.813Eþ00 2.544Eþ00 2.369Eþ00 2.247Eþ00 2.156Eþ00 2.086Eþ00 2.032Eþ00 1.990Eþ00 1.956Eþ00 1.906Eþ00 1.872Eþ00 1.849Eþ00 1.832Eþ00 1.809Eþ00

Collision (MeV cm2 g1) 3.075E03 3.091E03 3.104E03 3.124E03 3.138E03 3.148E03 3.156E03 3.166E03 3.172E03 3.178E03 3.184E03 3.194E03 3.204E03 3.214E03 3.225E03 3.237E03 3.250E03 3.265E03 3.280E03 3.313E03 3.349E03 3.386E03 3.426E03 3.533E03 3.649E03 3.772E03 3.904E03 4.191E03 4.504E03 4.842E03 5.201E03 5.579E03 5.974E03 6.385E03 6.809E03 7.698E03 8.634E03 9.611E03 1.063E02 1.331E02

Radiative (MeV cm2 g1)

Stopping power

3.931Eþ01 3.654Eþ01 3.418Eþ01 3.034Eþ01 2.735Eþ01 2.495Eþ01 2.298Eþ01 1.930Eþ01 1.674Eþ01 1.484Eþ01 1.337Eþ01 1.125Eþ01 9.781Eþ00 8.701Eþ00 7.872Eþ00 7.214Eþ00 6.679Eþ00 6.235Eþ00 5.860Eþ00 5.262Eþ00 4.806Eþ00 4.446Eþ00 4.155Eþ00 3.624Eþ00 3.266Eþ00 3.009Eþ00 2.817Eþ00 2.549Eþ00 2.374Eþ00 2.252Eþ00 2.161Eþ00 2.092Eþ00 2.038Eþ00 1.996Eþ00 1.963Eþ00 1.914Eþ00 1.881Eþ00 1.859Eþ00 1.843Eþ00 1.823Eþ00

Total (MeV cm2 g1)

Nylon, type 6 and type 6/6

7.245E05 8.566E05 9.981E05 1.309E04 1.657E04 2.040E04 2.458E04 3.651E04 5.046E04 6.636E04 8.414E04 1.251E03 1.729E03 2.272E03 2.877E03 3.542E03 4.263E03 5.038E03 5.866E03 7.670E03 9.662E03 1.183E02 1.416E02 2.063E02 2.791E02 3.590E02 4.450E02 6.322E02 8.359E02 1.052E01 1.279E01 1.515E01 1.757E01 2.005E01 2.258E01 2.774E01 3.301E01 3.836E01 4.377E01 5.742E01

CSDA range (g cm2)

4.229E05 4.585E05 4.934E05 5.614E05 6.273E05 6.915E05 7.541E05 9.049E05 1.049E04 1.187E04 1.322E04 1.580E04 1.826E04 2.064E04 2.293E04 2.515E04 2.731E04 2.942E04 3.148E04 3.548E04 3.934E04 4.307E04 4.670E04 5.537E04 6.358E04 7.144E04 7.901E04 9.352E04 1.075E03 1.210E03 1.344E03 1.476E03 1.608E03 1.741E03 1.874E03 2.141E03 2.411E03 2.686E03 2.964E03 3.677E03

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

104

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02

Energy (MeV)

1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

105

1.231Eþ02 1.062Eþ02 9.370Eþ01 8.413Eþ01 7.651Eþ01 6.510Eþ01 5.693Eþ01 5.075Eþ01 4.589Eþ01 4.197Eþ01 3.873Eþ01 3.601Eþ01 3.368Eþ01 2.989Eþ01 2.695Eþ01 2.459Eþ01 2.265Eþ01 1.902Eþ01 1.650Eþ01 1.463Eþ01

Collision (MeV cm2 g1)

1.801Eþ00 1.801Eþ00 1.803Eþ00 1.814Eþ00 1.826Eþ00 1.838Eþ00 1.850Eþ00 1.862Eþ00 1.872Eþ00 1.882Eþ00 1.892Eþ00 1.908Eþ00 1.923Eþ00 1.936Eþ00 1.948Eþ00 1.974Eþ00 1.994Eþ00 2.011Eþ00 2.025Eþ00

1.820Eþ00 1.823Eþ00 1.830Eþ00 1.847Eþ00 1.868Eþ00 1.889Eþ00 1.910Eþ00 1.930Eþ00 1.950Eþ00 1.969Eþ00 1.988Eþ00 2.025Eþ00 2.060Eþ00 2.093Eþ00 2.126Eþ00 2.205Eþ00 2.280Eþ00 2.353Eþ00 2.425Eþ00

7.147E01 8.520E01 9.889E01 1.261Eþ00 1.530Eþ00 1.796Eþ00 2.060Eþ00 2.320Eþ00 2.578Eþ00 2.833Eþ00 3.086Eþ00 3.584Eþ00 4.074Eþ00 4.555Eþ00 5.029Eþ00 6.184Eþ00 7.299Eþ00 8.378Eþ00 9.424Eþ00

2.374E03 2.483E03 2.563E03 2.625E03 2.674E03 2.746E03 2.796E03 2.832E03 2.859E03 2.880E03 2.896E03 2.908E03 2.918E03 2.933E03 2.944E03 2.952E03 2.957E03 2.963E03 2.967E03 2.973E03

Radiative (MeV cm2 g1)

Stopping power

1.231Eþ02 1.062Eþ02 9.370Eþ01 8.413Eþ01 7.651Eþ01 6.511Eþ01 5.693Eþ01 5.075Eþ01 4.590Eþ01 4.198Eþ01 3.874Eþ01 3.601Eþ01 3.368Eþ01 2.990Eþ01 2.695Eþ01 2.459Eþ01 2.265Eþ01 1.903Eþ01 1.650Eþ01 1.463Eþ01

Total (MeV cm2 g1) 4.062E06 6.256E06 8.768E06 1.159E05 1.471E05 2.182E05 3.005E05 3.937E05 4.975E05 6.115E05 7.357E05 8.696E05 1.013E04 1.329E04 1.682E04 2.071E04 2.495E04 3.704E04 5.120E04 6.732E04

CSDA range (g cm2)

Plastic scintillator (vinyltoluene)

1.892E02 2.242E02 2.608E02 3.379E02 4.194E02 5.045E02 5.925E02 6.828E02 7.752E02 8.694E02 9.654E02 1.162E01 1.363E01 1.568E01 1.777E01 2.313E01 2.863E01 3.423E01 3.993E01

9.641E06 1.198E05 1.422E05 1.637E05 1.846E05 2.249E05 2.635E05 3.008E05 3.371E05 3.724E05 4.068E05 4.405E05 4.736E05 5.379E05 6.003E05 6.610E05 7.202E05 8.626E05 9.986E05 1.130E04

Brems yield

5.199E03 6.077E03 6.977E03 8.834E03 1.076E02 1.273E02 1.475E02 1.680E02 1.887E02 2.097E02 2.309E02 2.736E02 3.166E02 3.598E02 4.031E02 5.111E02 6.180E02 7.234E02 8.269E02

1.148Eþ02 9.927Eþ01 8.782Eþ01 7.898Eþ01 7.193Eþ01 6.133Eþ01 5.371Eþ01 4.794Eþ01 4.339Eþ01 3.972Eþ01 3.668Eþ01 3.411Eþ01 3.192Eþ01 2.836Eþ01 2.559Eþ01 2.336Eþ01 2.153Eþ01 1.810Eþ01 1.571Eþ01 1.393Eþ01

Collision (MeV cm2 g1)

1.801Eþ00 1.799Eþ00 1.802Eþ00 1.811Eþ00 1.823Eþ00 1.836Eþ00 1.848Eþ00 1.859Eþ00 1.870Eþ00 1.880Eþ00 1.889Eþ00 1.906Eþ00 1.921Eþ00 1.934Eþ00 1.946Eþ00 1.970Eþ00 1.990Eþ00 2.006Eþ00 2.019Eþ00

1.817Eþ00 1.819Eþ00 1.824Eþ00 1.840Eþ00 1.859Eþ00 1.879Eþ00 1.899Eþ00 1.918Eþ00 1.937Eþ00 1.955Eþ00 1.973Eþ00 2.007Eþ00 2.039Eþ00 2.070Eþ00 2.100Eþ00 2.171Eþ00 2.238Eþ00 2.303Eþ00 2.366Eþ00

7.116E01 8.492E01 9.865E01 1.259Eþ00 1.530Eþ00 1.797Eþ00 2.062Eþ00 2.324Eþ00 2.583Eþ00 2.840Eþ00 3.095Eþ00 3.597Eþ00 4.092Eþ00 4.579Eþ00 5.058Eþ00 6.229Eþ00 7.363Eþ00 8.464Eþ00 9.535Eþ00

2.526E03 2.651E03 2.745E03 2.818E03 2.876E03 2.963E03 3.024E03 3.068E03 3.102E03 3.129E03 3.149E03 3.166E03 3.180E03 3.200E03 3.214E03 3.224E03 3.232E03 3.242E03 3.248E03 3.254E03

Radiative (MeV cm2 g1)

Stopping power

1.148Eþ02 9.927Eþ01 8.782Eþ01 7.899Eþ01 7.193Eþ01 6.134Eþ01 5.371Eþ01 4.794Eþ01 4.340Eþ01 3.972Eþ01 3.668Eþ01 3.412Eþ01 3.192Eþ01 2.836Eþ01 2.559Eþ01 2.336Eþ01 2.153Eþ01 1.810Eþ01 1.571Eþ01 1.394Eþ01

Total (MeV cm2 g1)

4.357E06 6.706E06 9.390E06 1.240E05 1.572E05 2.327E05 3.201E05 4.188E05 5.286E05 6.491E05 7.802E05 9.217E05 1.073E04 1.406E04 1.778E04 2.188E04 2.634E04 3.906E04 5.393E04 7.086E04

CSDA range (g cm2)

Polycarbonate, ‘‘makrolon’’, ‘‘lexan’’

1.617E02 1.919E02 2.234E02 2.900E02 3.603E02 4.337E02 5.098E02 5.880E02 6.681E02 7.498E02 8.330E02 1.003E01 1.178E01 1.356E01 1.538E01 2.004E01 2.483E01 2.971E01 3.468E01

1.101E05 1.368E05 1.623E05 1.869E05 2.109E05 2.570E05 3.014E05 3.443E05 3.860E05 4.266E05 4.662E05 5.051E05 5.432E05 6.173E05 6.892E05 7.591E05 8.273E05 9.913E05 1.148E04 1.298E04

Brems yield

4.413E03 5.171E03 5.950E03 7.558E03 9.225E03 1.094E02 1.269E02 1.448E02 1.629E02 1.812E02 1.996E02 2.370E02 2.747E02 3.127E02 3.508E02 4.463E02 5.414E02 6.355E02 7.284E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00

Energy (MeV)

1.318Eþ01 1.109Eþ01 9.642Eþ00 8.578Eþ00 7.760Eþ00 7.112Eþ00 6.584Eþ00 6.146Eþ00 5.777Eþ00 5.187Eþ00 4.737Eþ00 4.382Eþ00 4.095Eþ00 3.572Eþ00 3.219Eþ00 2.965Eþ00 2.775Eþ00 2.510Eþ00 2.337Eþ00 2.217Eþ00 2.129Eþ00 2.061Eþ00 2.009Eþ00 1.967Eþ00 1.934Eþ00 1.886Eþ00 1.853Eþ00 1.830Eþ00 1.814Eþ00 1.792Eþ00 1.784Eþ00 1.783Eþ00 1.785Eþ00 1.796Eþ00 1.808Eþ00 1.821Eþ00 1.833Eþ00 1.845Eþ00 1.856Eþ00 1.866Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

2.979E03 2.989E03 2.998E03 3.007E03 3.018E03 3.030E03 3.044E03 3.058E03 3.073E03 3.105E03 3.139E03 3.175E03 3.214E03 3.316E03 3.426E03 3.543E03 3.668E03 3.941E03 4.238E03 4.558E03 4.899E03 5.257E03 5.632E03 6.020E03 6.423E03 7.265E03 8.153E03 9.079E03 1.004E02 1.258E02 1.530E02 1.816E02 2.116E02 2.747E02 3.415E02 4.111E02 4.833E02 5.577E02 6.338E02 7.115E02

Radiative (MeV cm2 g1)

Stopping power

1.318Eþ01 1.109Eþ01 9.645Eþ00 8.581Eþ00 7.763Eþ00 7.115Eþ00 6.587Eþ00 6.150Eþ00 5.780Eþ00 5.190Eþ00 4.740Eþ00 4.386Eþ00 4.099Eþ00 3.575Eþ00 3.222Eþ00 2.969Eþ00 2.779Eþ00 2.514Eþ00 2.342Eþ00 2.222Eþ00 2.134Eþ00 2.066Eþ00 2.014Eþ00 1.973Eþ00 1.941Eþ00 1.893Eþ00 1.861Eþ00 1.839Eþ00 1.824Eþ00 1.804Eþ00 1.799Eþ00 1.801Eþ00 1.807Eþ00 1.823Eþ00 1.842Eþ00 1.862Eþ00 1.882Eþ00 1.901Eþ00 1.919Eþ00 1.937Eþ00

Total (MeV cm2 g1) 8.535E04 1.269E03 1.754E03 2.305E03 2.918E03 3.592E03 4.323E03 5.109E03 5.948E03 7.778E03 9.797E03 1.199E02 1.435E02 2.091E02 2.830E02 3.639E02 4.511E02 6.409E02 8.474E02 1.067E01 1.297E01 1.535E01 1.780E01 2.031E01 2.287E01 2.809E01 3.342E01 3.883E01 4.429E01 5.808E01 7.197E01 8.586E01 9.972E01 1.273Eþ00 1.546Eþ00 1.816Eþ00 2.083Eþ00 2.347Eþ00 2.609Eþ00 2.868Eþ00

CSDA range (g cm2)

Plastic scintillator (vinyltoluene)

1.257E04 1.501E04 1.735E04 1.960E04 2.177E04 2.388E04 2.593E04 2.793E04 2.989E04 3.370E04 3.737E04 4.092E04 4.437E04 5.262E04 6.045E04 6.794E04 7.516E04 8.901E04 1.023E03 1.153E03 1.280E03 1.407E03 1.533E03 1.660E03 1.786E03 2.042E03 2.300E03 2.562E03 2.828E03 3.509E03 4.213E03 4.939E03 5.683E03 7.222E03 8.818E03 1.046E02 1.214E02 1.384E02 1.558E02 1.733E02

Brems yield

1.256Eþ01 1.058Eþ01 9.202Eþ00 8.190Eþ00 7.412Eþ00 6.795Eþ00 6.293Eþ00 5.876Eþ00 5.524Eþ00 4.962Eþ00 4.533Eþ00 4.194Eþ00 3.920Eþ00 3.421Eþ00 3.084Eþ00 2.842Eþ00 2.660Eþ00 2.407Eþ00 2.242Eþ00 2.128Eþ00 2.044Eþ00 1.980Eþ00 1.930Eþ00 1.891Eþ00 1.859Eþ00 1.813Eþ00 1.782Eþ00 1.761Eþ00 1.746Eþ00 1.726Eþ00 1.719Eþ00 1.718Eþ00 1.721Eþ00 1.731Eþ00 1.744Eþ00 1.757Eþ00 1.769Eþ00 1.780Eþ00 1.791Eþ00 1.801Eþ00

Collision (MeV cm2 g1) 3.260E03 3.270E03 3.279E03 3.289E03 3.299E03 3.312E03 3.325E03 3.340E03 3.355E03 3.389E03 3.424E03 3.463E03 3.503E03 3.611E03 3.728E03 3.853E03 3.987E03 4.277E03 4.595E03 4.938E03 5.302E03 5.686E03 6.086E03 6.503E03 6.934E03 7.836E03 8.786E03 9.778E03 1.081E02 1.353E02 1.643E02 1.950E02 2.269E02 2.944E02 3.657E02 4.401E02 5.172E02 5.964E02 6.776E02 7.603E02

Radiative (MeV cm2 g1)

Stopping power

1.257Eþ01 1.058Eþ01 9.205Eþ00 8.193Eþ00 7.416Eþ00 6.798Eþ00 6.296Eþ00 5.879Eþ00 5.527Eþ00 4.965Eþ00 4.536Eþ00 4.198Eþ00 3.924Eþ00 3.425Eþ00 3.088Eþ00 2.846Eþ00 2.664Eþ00 2.412Eþ00 2.247Eþ00 2.133Eþ00 2.050Eþ00 1.986Eþ00 1.936Eþ00 1.897Eþ00 1.866Eþ00 1.821Eþ00 1.791Eþ00 1.771Eþ00 1.757Eþ00 1.739Eþ00 1.735Eþ00 1.738Eþ00 1.744Eþ00 1.761Eþ00 1.781Eþ00 1.801Eþ00 1.821Eþ00 1.840Eþ00 1.859Eþ00 1.877Eþ00

Total (MeV cm2 g1) 8.978E04 1.333E03 1.842E03 2.419E03 3.061E03 3.766E03 4.531E03 5.354E03 6.231E03 8.144E03 1.025E02 1.255E02 1.502E02 2.186E02 2.957E02 3.802E02 4.711E02 6.691E02 8.843E02 1.113E01 1.352E01 1.600E01 1.856E01 2.116E01 2.382E01 2.925E01 3.479E01 4.041E01 4.608E01 6.040E01 7.479E01 8.920E01 1.036Eþ00 1.321Eþ00 1.603Eþ00 1.883Eþ00 2.159Eþ00 2.432Eþ00 2.702Eþ00 2.970Eþ00

CSDA range (g cm2)

Polycarbonate, ‘‘makrolon’’, ‘‘lexan’’

1.444E04 1.724E04 1.992E04 2.249E04 2.497E04 2.737E04 2.971E04 3.199E04 3.423E04 3.855E04 4.272E04 4.675E04 5.067E04 6.002E04 6.888E04 7.734E04 8.549E04 1.011E03 1.161E03 1.306E03 1.449E03 1.591E03 1.732E03 1.874E03 2.015E03 2.300E03 2.588E03 2.879E03 3.175E03 3.932E03 4.713E03 5.517E03 6.342E03 8.045E03 9.807E03 1.162E02 1.347E02 1.535E02 1.726E02 1.919E02

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

106

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02

Energy (MeV)

6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

1.103Eþ02 9.563Eþ01 8.472Eþ01 7.628Eþ01 6.953Eþ01 5.936Eþ01 5.203Eþ01 4.647Eþ01 4.210Eþ01 3.855Eþ01 3.561Eþ01 3.313Eþ01 3.102Eþ01 2.757Eþ01 2.488Eþ01 2.273Eþ01 2.095Eþ01 1.762Eþ01 1.530Eþ01 1.358Eþ01 1.225Eþ01 1.032Eþ01 8.978Eþ00 7.993Eþ00 7.236Eþ00 6.635Eþ00 6.145Eþ00 5.739Eþ00 5.396Eþ00 4.848Eþ00

Collision (MeV cm2 g1)

1.875Eþ00 1.892Eþ00 1.907Eþ00 1.921Eþ00 1.932Eþ00 1.957Eþ00 1.976Eþ00 1.992Eþ00 2.005Eþ00

1.954Eþ00 1.988Eþ00 2.019Eþ00 2.049Eþ00 2.078Eþ00 2.147Eþ00 2.212Eþ00 2.274Eþ00 2.335Eþ00

3.125Eþ00 3.632Eþ00 4.132Eþ00 4.623Eþ00 5.108Eþ00 6.291Eþ00 7.438Eþ00 8.552Eþ00 9.637Eþ00

2.628E03 2.765E03 2.867E03 2.948E03 3.013E03 3.110E03 3.179E03 3.230E03 3.270E03 3.300E03 3.324E03 3.344E03 3.360E03 3.384E03 3.401E03 3.413E03 3.422E03 3.435E03 3.443E03 3.449E03 3.454E03 3.465E03 3.475E03 3.485E03 3.495E03 3.507E03 3.521E03 3.536E03 3.552E03 3.586E03

Radiative (MeV cm2 g1)

Stopping power

1.103Eþ02 9.563Eþ01 8.473Eþ01 7.628Eþ01 6.953Eþ01 5.937Eþ01 5.204Eþ01 4.648Eþ01 4.210Eþ01 3.855Eþ01 3.561Eþ01 3.314Eþ01 3.102Eþ01 2.757Eþ01 2.489Eþ01 2.273Eþ01 2.095Eþ01 1.763Eþ01 1.530Eþ01 1.358Eþ01 1.225Eþ01 1.032Eþ01 8.982Eþ00 7.997Eþ00 7.239Eþ00 6.638Eþ00 6.149Eþ00 5.742Eþ00 5.399Eþ00 4.851Eþ00

Total (MeV cm2 g1) 4.532E06 6.973E06 9.756E06 1.287E05 1.631E05 2.412E05 3.314E05 4.332E05 5.464E05 6.707E05 8.058E05 9.514E05 1.107E04 1.450E04 1.832E04 2.253E04 2.712E04 4.019E04 5.545E04 7.283E04 9.224E04 1.369E03 1.890E03 2.481E03 3.139E03 3.862E03 4.645E03 5.487E03 6.386E03 8.344E03

CSDA range (g cm2)

Polyethylene terephthalate, ‘‘mylar’’

7.905E02 9.522E02 1.118E01 1.288E01 1.461E01 1.904E01 2.359E01 2.825E01 3.298E01

1.191E05 1.480E05 1.757E05 2.024E05 2.283E05 2.784E05 3.266E05 3.733E05 4.186E05 4.628E05 5.060E05 5.483E05 5.898E05 6.706E05 7.490E05 8.251E05 8.994E05 1.078E04 1.248E04 1.412E04 1.571E04 1.875E04 2.165E04 2.443E04 2.712E04 2.973E04 3.226E04 3.473E04 3.714E04 4.182E04

Brems yield

1.910E02 2.269E02 2.631E02 2.995E02 3.361E02 4.279E02 5.195E02 6.102E02 6.999E02

1.190Eþ02 1.030Eþ02 9.116Eþ01 8.202Eþ01 7.473Eþ01 6.375Eþ01 5.585Eþ01 4.986Eþ01 4.515Eþ01 4.133Eþ01 3.817Eþ01 3.551Eþ01 3.323Eþ01 2.953Eþ01 2.665Eþ01 2.433Eþ01 2.242Eþ01 1.886Eþ01 1.637Eþ01 1.452Eþ01 1.310Eþ01 1.103Eþ01 9.596Eþ00 8.542Eþ00 7.731Eþ00 7.088Eþ00 6.565Eþ00 6.130Eþ00 5.763Eþ00 5.177Eþ00

Collision (MeV cm2 g1)

1.811Eþ00 1.827Eþ00 1.842Eþ00 1.855Eþ00 1.867Eþ00 1.891Eþ00 1.910Eþ00 1.926Eþ00 1.939Eþ00

Radiative (MeV cm2 g1) 2.809E03 2.971E03 3.095E03 3.195E03 3.277E03 3.403E03 3.495E03 3.564E03 3.619E03 3.662E03 3.696E03 3.725E03 3.748E03 3.785E03 3.811E03 3.830E03 3.845E03 3.869E03 3.882E03 3.888E03 3.893E03 3.905E03 3.918E03 3.929E03 3.940E03 3.952E03 3.965E03 3.980E03 3.997E03 4.034E03

1.895Eþ00 1.929Eþ00 1.962Eþ00 1.993Eþ00 2.023Eþ00 2.094Eþ00 2.162Eþ00 2.227Eþ00 2.290Eþ00

1.190Eþ02 1.030Eþ02 9.117Eþ01 8.203Eþ01 7.473Eþ01 6.375Eþ01 5.585Eþ01 4.986Eþ01 4.515Eþ01 4.133Eþ01 3.817Eþ01 3.551Eþ01 3.324Eþ01 2.954Eþ01 2.665Eþ01 2.433Eþ01 2.243Eþ01 1.886Eþ01 1.637Eþ01 1.453Eþ01 1.310Eþ01 1.103Eþ01 9.600Eþ00 8.546Eþ00 7.735Eþ00 7.092Eþ00 6.568Eþ00 6.134Eþ00 5.767Eþ00 5.181Eþ00

Total (MeV cm2 g1)

Polymer gel, ‘‘bang-2’’ Stopping power

8.445E02 1.017E01 1.194E01 1.374E01 1.558E01 2.029E01 2.514E01 3.008E01 3.510E01

4.203E06 6.469E06 9.054E06 1.195E05 1.515E05 2.242E05 3.082E05 4.031E05 5.086E05 6.245E05 7.505E05 8.864E05 1.032E04 1.352E04 1.709E04 2.102E04 2.530E04 3.751E04 5.178E04 6.803E04 8.618E04 1.280E03 1.767E03 2.320E03 2.936E03 3.612E03 4.345E03 5.134E03 5.975E03 7.808E03

CSDA range (g cm2)

3.235Eþ00 3.758Eþ00 4.272Eþ00 4.778Eþ00 5.276Eþ00 6.490Eþ00 7.665Eþ00 8.805Eþ00 9.912Eþ00

1.181E05 1.469E05 1.748E05 2.019E05 2.284E05 2.800E05 3.300E05 3.787E05 4.261E05 4.725E05 5.180E05 5.626E05 6.064E05 6.920E05 7.750E05 8.558E05 9.347E05 1.125E04 1.306E04 1.480E04 1.648E04 1.970E04 2.277E04 2.572E04 2.857E04 3.132E04 3.399E04 3.660E04 3.914E04 4.406E04

Brems yield

2.113E02 2.506E02 2.903E02 3.301E02 3.701E02 4.702E02 5.695E02 6.678E02 7.646E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

107

8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

Energy (MeV)

4.430Eþ00 4.100Eþ00 3.832Eþ00 3.345Eþ00 3.016Eþ00 2.780Eþ00 2.603Eþ00 2.356Eþ00 2.195Eþ00 2.083Eþ00 2.002Eþ00 1.939Eþ00 1.890Eþ00 1.852Eþ00 1.821Eþ00 1.776Eþ00 1.746Eþ00 1.725Eþ00 1.711Eþ00 1.691Eþ00 1.684Eþ00 1.684Eþ00 1.687Eþ00 1.698Eþ00 1.710Eþ00 1.723Eþ00 1.735Eþ00 1.746Eþ00 1.757Eþ00 1.767Eþ00 1.776Eþ00 1.793Eþ00 1.807Eþ00 1.820Eþ00 1.832Eþ00 1.856Eþ00 1.875Eþ00 1.890Eþ00 1.904Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

3.623E03 3.663E03 3.704E03 3.817E03 3.939E03 4.069E03 4.208E03 4.512E03 4.844E03 5.203E03 5.583E03 5.985E03 6.405E03 6.840E03 7.291E03 8.236E03 9.230E03 1.027E02 1.134E02 1.419E02 1.723E02 2.043E02 2.378E02 3.083E02 3.827E02 4.605E02 5.410E02 6.237E02 7.084E02 7.948E02 8.826E02 1.062E01 1.247E01 1.435E01 1.627E01 2.118E01 2.623E01 3.138E01 3.661E01

Radiative (MeV cm2 g1)

Stopping power

4.433Eþ00 4.103Eþ00 3.836Eþ00 3.349Eþ00 3.020Eþ00 2.784Eþ00 2.607Eþ00 2.361Eþ00 2.200Eþ00 2.088Eþ00 2.007Eþ00 1.945Eþ00 1.896Eþ00 1.858Eþ00 1.828Eþ00 1.784Eþ00 1.755Eþ00 1.735Eþ00 1.722Eþ00 1.705Eþ00 1.702Eþ00 1.705Eþ00 1.711Eþ00 1.728Eþ00 1.748Eþ00 1.769Eþ00 1.789Eþ00 1.808Eþ00 1.828Eþ00 1.846Eþ00 1.864Eþ00 1.899Eþ00 1.932Eþ00 1.964Eþ00 1.994Eþ00 2.067Eþ00 2.137Eþ00 2.204Eþ00 2.270Eþ00

Total (MeV cm2 g1) 1.050E02 1.285E02 1.537E02 2.238E02 3.026E02 3.890E02 4.819E02 6.841E02 9.040E02 1.138E01 1.382E01 1.635E01 1.896E01 2.162E01 2.434E01 2.988E01 3.553E01 4.126E01 4.705E01 6.165E01 7.633E01 9.102E01 1.057Eþ00 1.347Eþ00 1.635Eþ00 1.919Eþ00 2.200Eþ00 2.478Eþ00 2.753Eþ00 3.026Eþ00 3.295Eþ00 3.827Eþ00 4.349Eþ00 4.862Eþ00 5.367Eþ00 6.598Eþ00 7.788Eþ00 8.939Eþ00 1.006Eþ01

CSDA range (g cm2)

Polyethylene terephthalate, ‘‘mylar’’

4.632E04 5.068E04 5.490E04 6.499E04 7.454E04 8.365E04 9.243E04 1.092E03 1.253E03 1.409E03 1.563E03 1.714E03 1.866E03 2.017E03 2.168E03 2.473E03 2.781E03 3.092E03 3.408E03 4.217E03 5.050E03 5.907E03 6.786E03 8.600E03 1.048E02 1.240E02 1.437E02 1.637E02 1.839E02 2.044E02 2.250E02 2.667E02 3.086E02 3.508E02 3.931E02 4.986E02 6.033E02 7.065E02 8.080E02

Brems yield

4.730Eþ00 4.377Eþ00 4.091Eþ00 3.571Eþ00 3.219Eþ00 2.966Eþ00 2.777Eþ00 2.514Eþ00 2.341Eþ00 2.222Eþ00 2.136Eþ00 2.071Eþ00 2.023Eþ00 1.983Eþ00 1.952Eþ00 1.905Eþ00 1.874Eþ00 1.852Eþ00 1.837Eþ00 1.817Eþ00 1.810Eþ00 1.809Eþ00 1.812Eþ00 1.822Eþ00 1.834Eþ00 1.847Eþ00 1.859Eþ00 1.870Eþ00 1.881Eþ00 1.890Eþ00 1.900Eþ00 1.916Eþ00 1.931Eþ00 1.944Eþ00 1.956Eþ00 1.982Eþ00 2.002Eþ00 2.019Eþ00 2.034Eþ00

Collision (MeV cm2 g1) 4.074E03 4.117E03 4.163E03 4.286E03 4.421E03 4.564E03 4.718E03 5.053E03 5.421E03 5.818E03 6.240E03 6.685E03 7.150E03 7.633E03 8.133E03 9.179E03 1.028E02 1.143E02 1.262E02 1.578E02 1.914E02 2.269E02 2.639E02 3.419E02 4.243E02 5.104E02 5.994E02 6.907E02 7.842E02 8.795E02 9.765E02 1.175E01 1.379E01 1.586E01 1.798E01 2.339E01 2.895E01 3.463E01 4.039E01

Radiative (MeV cm2 g1)

Stopping power

4.734Eþ00 4.381Eþ00 4.096Eþ00 3.575Eþ00 3.223Eþ00 2.971Eþ00 2.782Eþ00 2.519Eþ00 2.347Eþ00 2.228Eþ00 2.142Eþ00 2.078Eþ00 2.030Eþ00 1.991Eþ00 1.960Eþ00 1.914Eþ00 1.884Eþ00 1.864Eþ00 1.850Eþ00 1.833Eþ00 1.829Eþ00 1.832Eþ00 1.838Eþ00 1.856Eþ00 1.877Eþ00 1.898Eþ00 1.919Eþ00 1.939Eþ00 1.959Eþ00 1.978Eþ00 1.997Eþ00 2.034Eþ00 2.069Eþ00 2.103Eþ00 2.136Eþ00 2.216Eþ00 2.292Eþ00 2.365Eþ00 2.438Eþ00

Total (MeV cm2 g1)

Polymer gel, ‘‘bang-2’’

9.831E03 1.203E02 1.439E02 2.095E02 2.834E02 3.643E02 4.514E02 6.409E02 8.470E02 1.066E01 1.295E01 1.532E01 1.776E01 2.025E01 2.278E01 2.795E01 3.321E01 3.855E01 4.394E01 5.753E01 7.119E01 8.485E01 9.847E01 1.255Eþ00 1.523Eþ00 1.788Eþ00 2.050Eþ00 2.310Eþ00 2.566Eþ00 2.820Eþ00 3.072Eþ00 3.568Eþ00 4.055Eþ00 4.534Eþ00 5.006Eþ00 6.155Eþ00 7.265Eþ00 8.338Eþ00 9.379Eþ00

CSDA range (g cm2)

4.880E04 5.339E04 5.783E04 6.844E04 7.847E04 8.803E04 9.723E04 1.148E03 1.317E03 1.480E03 1.640E03 1.799E03 1.956E03 2.112E03 2.269E03 2.583E03 2.901E03 3.222E03 3.548E03 4.380E03 5.239E03 6.121E03 7.027E03 8.896E03 1.083E02 1.282E02 1.485E02 1.691E02 1.900E02 2.112E02 2.325E02 2.754E02 3.188E02 3.623E02 4.058E02 5.145E02 6.222E02 7.282E02 8.323E02

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

108

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01

Energy (MeV)

1.170Eþ02 1.012Eþ02 8.955Eþ01 8.055Eþ01 7.337Eþ01 6.257Eþ01 5.481Eþ01 4.892Eþ01 4.429Eþ01 4.054Eþ01 3.744Eþ01 3.482Eþ01 3.259Eþ01 2.896Eþ01 2.613Eþ01 2.385Eþ01 2.198Eþ01 1.848Eþ01 1.604Eþ01 1.423Eþ01 1.283Eþ01 1.080Eþ01 9.400Eþ00 8.367Eþ00 7.573Eþ00 6.942Eþ00 6.429Eþ00 6.003Eþ00 5.644Eþ00 5.070Eþ00 4.631Eþ00 4.286Eþ00 4.006Eþ00 3.496Eþ00 3.152Eþ00 2.904Eþ00 2.719Eþ00 2.461Eþ00 2.292Eþ00 2.175Eþ00 2.090Eþ00 2.026Eþ00 1.975Eþ00 1.935Eþ00

Collision (MeV cm2 g1)

2.560E03 2.691E03 2.789E03 2.867E03 2.929E03 3.023E03 3.089E03 3.138E03 3.176E03 3.205E03 3.228E03 3.247E03 3.263E03 3.286E03 3.303E03 3.315E03 3.323E03 3.336E03 3.344E03 3.350E03 3.356E03 3.366E03 3.376E03 3.386E03 3.397E03 3.409E03 3.422E03 3.437E03 3.453E03 3.487E03 3.523E03 3.563E03 3.604E03 3.714E03 3.834E03 3.962E03 4.099E03 4.397E03 4.723E03 5.074E03 5.448E03 5.841E03 6.253E03 6.680E03

Radiative (MeV cm2 g1)

Stopping power

1.170Eþ02 1.012Eþ02 8.956Eþ01 8.056Eþ01 7.337Eþ01 6.258Eþ01 5.481Eþ01 4.892Eþ01 4.429Eþ01 4.054Eþ01 3.744Eþ01 3.483Eþ01 3.259Eþ01 2.896Eþ01 2.613Eþ01 2.385Eþ01 2.198Eþ01 1.849Eþ01 1.604Eþ01 1.423Eþ01 1.284Eþ01 1.081Eþ01 9.404Eþ00 8.370Eþ00 7.576Eþ00 6.946Eþ00 6.433Eþ00 6.007Eþ00 5.647Eþ00 5.073Eþ00 4.635Eþ00 4.289Eþ00 4.010Eþ00 3.500Eþ00 3.155Eþ00 2.908Eþ00 2.723Eþ00 2.465Eþ00 2.297Eþ00 2.180Eþ00 2.096Eþ00 2.032Eþ00 1.981Eþ00 1.942Eþ00

Total (MeV cm2 g1)/c> 4.275E06 6.580E06 9.212E06 1.216E05 1.542E05 2.282E05 3.138E05 4.106E05 5.181E05 6.363E05 7.647E05 9.033E05 1.052E04 1.378E04 1.742E04 2.143E04 2.580E04 3.826E04 5.282E04 6.940E04 8.792E04 1.306E03 1.803E03 2.368E03 2.997E03 3.687E03 4.436E03 5.241E03 6.100E03 7.972E03 1.004E02 1.228E02 1.470E02 2.140E02 2.894E02 3.721E02 4.610E02 6.547E02 8.653E02 1.089E01 1.323E01 1.566E01 1.815E01 2.070E01

CSDA range (g cm2)

Polymethyl Methacrylate, ‘‘lucite’’, ‘‘perspex’’

1.095E05 1.361E05 1.615E05 1.861E05 2.101E05 2.563E05 3.009E05 3.440E05 3.859E05 4.268E05 4.668E05 5.059E05 5.444E05 6.192E05 6.918E05 7.624E05 8.312E05 9.969E05 1.155E04 1.307E04 1.454E04 1.737E04 2.006E04 2.265E04 2.516E04 2.758E04 2.994E04 3.223E04 3.448E04 3.884E04 4.303E04 4.709E04 5.103E04 6.044E04 6.935E04 7.786E04 8.606E04 1.018E03 1.168E03 1.314E03 1.458E03 1.600E03 1.742E03 1.883E03

Brems yield

1.197Eþ02 1.034Eþ02 9.137Eþ01 8.210Eþ01 7.472Eþ01 6.364Eþ01 5.569Eþ01 4.967Eþ01 4.494Eþ01 4.112Eþ01 3.796Eþ01 3.529Eþ01 3.302Eþ01 2.932Eþ01 2.644Eþ01 2.413Eþ01 2.223Eþ01 1.868Eþ01 1.621Eþ01 1.437Eþ01 1.296Eþ01 1.091Eþ01 9.485Eþ00 8.440Eþ00 7.637Eþ00 7.000Eþ00 6.481Eþ00 6.051Eþ00 5.688Eþ00 5.108Eþ00 4.666Eþ00 4.317Eþ00 4.034Eþ00 3.520Eþ00 3.172Eþ00 2.923Eþ00 2.735Eþ00 2.475Eþ00 2.305Eþ00 2.187Eþ00 2.101Eþ00 2.035Eþ00 1.984Eþ00 1.943Eþ00

Collision (MeV cm2 g1) 2.386E03 2.496E03 2.577E03 2.639E03 2.689E03 2.761E03 2.812E03 2.848E03 2.875E03 2.896E03 2.912E03 2.924E03 2.935E03 2.950E03 2.960E03 2.968E03 2.973E03 2.979E03 2.984E03 2.990E03 2.996E03 3.006E03 3.015E03 3.024E03 3.034E03 3.047E03 3.060E03 3.075E03 3.089E03 3.121E03 3.156E03 3.192E03 3.230E03 3.332E03 3.443E03 3.561E03 3.686E03 3.959E03 4.258E03 4.580E03 4.921E03 5.281E03 5.656E03 6.047E03

Radiative (MeV cm2 g1)

Stopping power

1.197Eþ02 1.034Eþ02 9.137Eþ01 8.211Eþ01 7.472Eþ01 6.364Eþ01 5.569Eþ01 4.967Eþ01 4.495Eþ01 4.112Eþ01 3.796Eþ01 3.530Eþ01 3.302Eþ01 2.933Eþ01 2.645Eþ01 2.414Eþ01 2.224Eþ01 1.869Eþ01 1.621Eþ01 1.438Eþ01 1.296Eþ01 1.091Eþ01 9.488Eþ00 8.443Eþ00 7.640Eþ00 7.003Eþ00 6.484Eþ00 6.054Eþ00 5.691Eþ00 5.111Eþ00 4.669Eþ00 4.320Eþ00 4.038Eþ00 3.523Eþ00 3.176Eþ00 2.926Eþ00 2.739Eþ00 2.479Eþ00 2.309Eþ00 2.192Eþ00 2.106Eþ00 2.040Eþ00 1.989Eþ00 1.950Eþ00

Total (MeV cm2 g1)

Polystyrene

4.176E06 6.430E06 9.007E06 1.190E05 1.509E05 2.237E05 3.079E05 4.032E05 5.091E05 6.256E05 7.523E05 8.890E05 1.036E04 1.358E04 1.717E04 2.113E04 2.545E04 3.777E04 5.218E04 6.859E04 8.694E04 1.292E03 1.785E03 2.345E03 2.968E03 3.653E03 4.395E03 5.194E03 6.047E03 7.905E03 9.955E03 1.218E02 1.458E02 2.124E02 2.873E02 3.695E02 4.579E02 6.504E02 8.598E02 1.082E01 1.315E01 1.557E01 1.805E01 2.059E01

CSDA range (g cm2)

9.962E06 1.238E05 1.468E05 1.689E05 1.904E05 2.318E05 2.714E05 3.097E05 3.468E05 3.829E05 4.182E05 4.527E05 4.866E05 5.524E05 6.162E05 6.783E05 7.388E05 8.844E05 1.023E04 1.157E04 1.287E04 1.537E04 1.775E04 2.005E04 2.226E04 2.441E04 2.651E04 2.855E04 3.055E04 3.443E04 3.817E04 4.179E04 4.531E04 5.372E04 6.169E04 6.932E04 7.668E04 9.078E04 1.043E03 1.175E03 1.305E03 1.433E03 1.562E03 1.690E03

Brems yield

APPENDIX A: COMPILATION OF PHYSICAL DATA

109

110

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03

Energy (MeV)

6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

Energy (MeV)

9.304Eþ01 8.122Eþ01 7.232Eþ01 6.536Eþ01 5.975Eþ01

Collision (MeV cm2 g1)

1.903Eþ00 1.856Eþ00 1.825Eþ00 1.803Eþ00 1.788Eþ00 1.767Eþ00 1.760Eþ00 1.759Eþ00 1.762Eþ00 1.772Eþ00 1.784Eþ00 1.797Eþ00 1.809Eþ00 1.821Eþ00 1.832Eþ00 1.842Eþ00 1.851Eþ00 1.868Eþ00 1.883Eþ00 1.896Eþ00 1.908Eþ00 1.932Eþ00 1.952Eþ00 1.968Eþ00 1.982Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

1.910Eþ00 1.864Eþ00 1.834Eþ00 1.813Eþ00 1.799Eþ00 1.781Eþ00 1.776Eþ00 1.779Eþ00 1.785Eþ00 1.802Eþ00 1.822Eþ00 1.842Eþ00 1.862Eþ00 1.882Eþ00 1.901Eþ00 1.920Eþ00 1.938Eþ00 1.972Eþ00 2.005Eþ00 2.037Eþ00 2.068Eþ00 2.141Eþ00 2.210Eþ00 2.277Eþ00 2.342Eþ00

Total (MeV cm2 g1)

2.979E03 3.162E03 3.305E03 3.420E03 3.516E03

Radiative (MeV cm2 g1)

Stopping power

9.304Eþ01 8.122Eþ01 7.232Eþ01 6.536Eþ01 5.976Eþ01

Total (MeV cm2 g1)

2.330E01 2.860E01 3.401E01 3.950E01 4.504E01 5.902E01 7.308E01 8.715E01 1.012Eþ00 1.291Eþ00 1.567Eþ00 1.840Eþ00 2.109Eþ00 2.377Eþ00 2.641Eþ00 2.903Eþ00 3.162Eþ00 3.673Eþ00 4.176Eþ00 4.671Eþ00 5.158Eþ00 6.346Eþ00 7.496Eþ00 8.610Eþ00 9.693Eþ00

CSDA range (g cm2)

5.374E06 8.258E06 1.153E05 1.517E05 1.917E05

CSDA range (g cm2)

Polytetrafluoroethylene, ‘‘teflon’’

7.122E03 8.047E03 9.021E03 1.004E02 1.109E02 1.389E02 1.686E02 2.001E02 2.329E02 3.020E02 3.751E02 4.515E02 5.305E02 6.117E02 6.949E02 7.797E02 8.660E02 1.043E01 1.224E01 1.409E01 1.597E01 2.080E01 2.576E01 3.083E01 3.597E01

Radiative (MeV cm2 g1)

Stopping power

Polymethyl Methacrylate, ‘‘lucite’’, ‘‘perspex’’

1.601E05 1.990E05 2.364E05 2.727E05 3.081E05

Brems yield

2.025E03 2.310E03 2.598E03 2.890E03 3.187E03 3.945E03 4.727E03 5.533E03 6.359E03 8.065E03 9.832E03 1.165E02 1.350E02 1.539E02 1.730E02 1.924E02 2.119E02 2.513E02 2.911E02 3.311E02 3.712E02 4.715E02 5.711E02 6.696E02 7.666E02

Brems yield

1.192Eþ02 1.032Eþ02 9.128Eþ01 8.210Eþ01 7.478Eþ01

Collision (MeV cm2 g1)

1.911Eþ00 1.864Eþ00 1.832Eþ00 1.810Eþ00 1.794Eþ00 1.773Eþ00 1.766Eþ00 1.765Eþ00 1.768Eþ00 1.778Eþ00 1.791Eþ00 1.804Eþ00 1.816Eþ00 1.828Eþ00 1.839Eþ00 1.849Eþ00 1.859Eþ00 1.876Eþ00 1.891Eþ00 1.904Eþ00 1.916Eþ00 1.940Eþ00 1.960Eþ00 1.975Eþ00 1.989Eþ00

Collision (MeV cm2 g1)

2.740E03 2.893E03 3.011E03 3.105E03 3.182E03

Radiative (MeV cm2 g1)

1.918Eþ00 1.871Eþ00 1.840Eþ00 1.819Eþ00 1.804Eþ00 1.786Eþ00 1.781Eþ00 1.783Eþ00 1.789Eþ00 1.806Eþ00 1.825Eþ00 1.845Eþ00 1.865Eþ00 1.884Eþ00 1.902Eþ00 1.920Eþ00 1.938Eþ00 1.971Eþ00 2.003Eþ00 2.033Eþ00 2.062Eþ00 2.131Eþ00 2.196Eþ00 2.259Eþ00 2.320Eþ00

Total (MeV cm2 g1)

1.192Eþ02 1.032Eþ02 9.129Eþ01 8.211Eþ01 7.478Eþ01

Total (MeV cm2 g1)

Skin (ICRU-44) Stopping power

6.450E03 7.296E03 8.187E03 9.116E03 1.008E02 1.263E02 1.536E02 1.823E02 2.124E02 2.757E02 3.427E02 4.126E02 4.850E02 5.596E02 6.360E02 7.139E02 7.931E02 9.554E02 1.122E01 1.292E01 1.466E01 1.910E01 2.367E01 2.833E01 3.308E01

Radiative (MeV cm2 g1)

Stopping power

Polystyrene

4.193E06 6.454E06 9.036E06 1.193E05 1.512E05

CSDA range (g cm2)

2.318E01 2.846E01 3.385E01 3.932E01 4.484E01 5.878E01 7.281E01 8.684E01 1.008Eþ00 1.287Eþ00 1.562Eþ00 1.835Eþ00 2.104Eþ00 2.371Eþ00 2.635Eþ00 2.897Eþ00 3.156Eþ00 3.667Eþ00 4.171Eþ00 4.666Eþ00 5.155Eþ00 6.347Eþ00 7.502Eþ00 8.624Eþ00 9.717Eþ00

CSDA range (g cm2)

1.149E05 1.430E05 1.700E05 1.963E05 2.220E05

Brems yield

1.818E03 2.077E03 2.339E03 2.605E03 2.874E03 3.565E03 4.278E03 5.013E03 5.767E03 7.325E03 8.940E03 1.060E02 1.230E02 1.403E02 1.578E02 1.756E02 1.935E02 2.297E02 2.663E02 3.031E02 3.401E02 4.329E02 5.253E02 6.169E02 7.073E02

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00

5.125Eþ01 4.507Eþ01 4.035Eþ01 3.663Eþ01 3.360Eþ01 3.108Eþ01 2.895Eþ01 2.713Eþ01 2.416Eþ01 2.184Eþ01 1.997Eþ01 1.843Eþ01 1.553Eþ01 1.351Eþ01 1.200Eþ01 1.084Eþ01 9.141Eþ00 7.965Eþ00 7.098Eþ00 6.430Eþ00 5.900Eþ00 5.468Eþ00 5.109Eþ00 4.806Eþ00 4.321Eþ00 3.951Eþ00 3.658Eþ00 3.421Eþ00 2.989Eþ00 2.697Eþ00 2.487Eþ00 2.330Eþ00 2.111Eþ00 1.968Eþ00 1.869Eþ00 1.797Eþ00 1.741Eþ00 1.698Eþ00 1.665Eþ00 1.638Eþ00 1.599Eþ00 1.573Eþ00 1.555Eþ00 1.542Eþ00 1.526Eþ00 1.521Eþ00 1.521Eþ00 1.524Eþ00 1.534Eþ00 1.545Eþ00 1.557Eþ00

3.664E03 3.774E03 3.858E03 3.924E03 3.978E03 4.021E03 4.057E03 4.087E03 4.134E03 4.168E03 4.194E03 4.213E03 4.245E03 4.262E03 4.272E03 4.279E03 4.294E03 4.307E03 4.318E03 4.328E03 4.340E03 4.353E03 4.369E03 4.386E03 4.424E03 4.466E03 4.511E03 4.560E03 4.689E03 4.830E03 4.982E03 5.144E03 5.499E03 5.891E03 6.313E03 6.762E03 7.236E03 7.731E03 8.246E03 8.779E03 9.894E03 1.107E02 1.229E02 1.357E02 1.692E02 2.051E02 2.427E02 2.821E02 3.649E02 4.523E02 5.434E02

5.125Eþ01 4.507Eþ01 4.036Eþ01 3.663Eþ01 3.360Eþ01 3.108Eþ01 2.896Eþ01 2.713Eþ01 2.417Eþ01 2.184Eþ01 1.997Eþ01 1.843Eþ01 1.554Eþ01 1.351Eþ01 1.201Eþ01 1.084Eþ01 9.146Eþ00 7.970Eþ00 7.102Eþ00 6.435Eþ00 5.904Eþ00 5.472Eþ00 5.113Eþ00 4.810Eþ00 4.325Eþ00 3.955Eþ00 3.663Eþ00 3.426Eþ00 2.994Eþ00 2.702Eþ00 2.492Eþ00 2.335Eþ00 2.116Eþ00 1.974Eþ00 1.875Eþ00 1.803Eþ00 1.748Eþ00 1.706Eþ00 1.673Eþ00 1.647Eþ00 1.609Eþ00 1.584Eþ00 1.567Eþ00 1.556Eþ00 1.543Eþ00 1.541Eþ00 1.545Eþ00 1.552Eþ00 1.570Eþ00 1.590Eþ00 1.611Eþ00

2.824E05 3.867E05 5.041E05 6.343E05 7.770E05 9.319E05 1.099E04 1.277E04 1.668E04 2.104E04 2.584E04 3.105E04 4.589E04 6.320E04 8.287E04 1.048E03 1.553E03 2.140E03 2.806E03 3.547E03 4.359E03 5.239E03 6.185E03 7.194E03 9.391E03 1.181E02 1.444E02 1.727E02 2.511E02 3.392E02 4.357E02 5.395E02 7.651E02 1.010E01 1.271E01 1.543E01 1.824E01 2.114E01 2.410E01 2.711E01 3.326E01 3.953E01 4.588E01 5.229E01 6.844E01 8.466E01 1.009Eþ00 1.170Eþ00 1.490Eþ00 1.807Eþ00 2.119Eþ00

3.769E05 4.435E05 5.083E05 5.715E05 6.333E05 6.938E05 7.533E05 8.116E05 9.256E05 1.036E04 1.144E04 1.249E04 1.501E04 1.742E04 1.973E04 2.195E04 2.621E04 3.026E04 3.415E04 3.788E04 4.150E04 4.500E04 4.841E04 5.174E04 5.817E04 6.435E04 7.032E04 7.611E04 8.988E04 1.029E03 1.152E03 1.271E03 1.497E03 1.713E03 1.922E03 2.126E03 2.328E03 2.529E03 2.729E03 2.929E03 3.330E03 3.735E03 4.144E03 4.558E03 5.614E03 6.700E03 7.815E03 8.955E03 1.130E02 1.372E02 1.620E02

6.377Eþ01 5.585Eþ01 4.985Eþ01 4.513Eþ01 4.131Eþ01 3.815Eþ01 3.548Eþ01 3.320Eþ01 2.950Eþ01 2.662Eþ01 2.430Eþ01 2.239Eþ01 1.883Eþ01 1.634Eþ01 1.450Eþ01 1.307Eþ01 1.101Eþ01 9.575Eþ00 8.522Eþ00 7.713Eþ00 7.071Eþ00 6.549Eþ00 6.115Eþ00 5.748Eþ00 5.164Eþ00 4.717Eþ00 4.365Eþ00 4.080Eþ00 3.561Eþ00 3.210Eþ00 2.958Eþ00 2.769Eþ00 2.506Eþ00 2.334Eþ00 2.215Eþ00 2.129Eþ00 2.065Eþ00 2.014Eþ00 1.974Eþ00 1.942Eþ00 1.895Eþ00 1.863Eþ00 1.841Eþ00 1.825Eþ00 1.804Eþ00 1.797Eþ00 1.796Eþ00 1.799Eþ00 1.809Eþ00 1.821Eþ00 1.833Eþ00

3.299E03 3.385E03 3.450E03 3.500E03 3.540E03 3.572E03 3.598E03 3.620E03 3.654E03 3.678E03 3.696E03 3.709E03 3.731E03 3.743E03 3.751E03 3.756E03 3.769E03 3.782E03 3.793E03 3.804E03 3.816E03 3.829E03 3.844E03 3.861E03 3.898E03 3.937E03 3.979E03 4.024E03 4.144E03 4.275E03 4.415E03 4.564E03 4.890E03 5.247E03 5.633E03 6.042E03 6.474E03 6.925E03 7.394E03 7.880E03 8.895E03 9.964E03 1.108E02 1.224E02 1.530E02 1.857E02 2.201E02 2.561E02 3.318E02 4.118E02 4.954E02

6.377Eþ01 5.585Eþ01 4.985Eþ01 4.513Eþ01 4.131Eþ01 3.815Eþ01 3.549Eþ01 3.321Eþ01 2.950Eþ01 2.662Eþ01 2.430Eþ01 2.240Eþ01 1.883Eþ01 1.634Eþ01 1.450Eþ01 1.307Eþ01 1.101Eþ01 9.579Eþ00 8.526Eþ00 7.717Eþ00 7.075Eþ00 6.552Eþ00 6.118Eþ00 5.752Eþ00 5.167Eþ00 4.721Eþ00 4.369Eþ00 4.084Eþ00 3.565Eþ00 3.214Eþ00 2.962Eþ00 2.773Eþ00 2.511Eþ00 2.339Eþ00 2.221Eþ00 2.135Eþ00 2.071Eþ00 2.021Eþ00 1.981Eþ00 1.950Eþ00 1.903Eþ00 1.873Eþ00 1.852Eþ00 1.838Eþ00 1.820Eþ00 1.815Eþ00 1.818Eþ00 1.824Eþ00 1.842Eþ00 1.862Eþ00 1.883Eþ00

2.239E05 3.079E05 4.028E05 5.084E05 6.243E05 7.504E05 8.864E05 1.032E04 1.352E04 1.710E04 2.103E04 2.532E04 3.755E04 5.184E04 6.812E04 8.630E04 1.282E03 1.770E03 2.325E03 2.942E03 3.619E03 4.355E03 5.145E03 5.988E03 7.826E03 9.854E03 1.206E02 1.443E02 2.101E02 2.841E02 3.653E02 4.526E02 6.428E02 8.495E02 1.069E01 1.299E01 1.537E01 1.782E01 2.031E01 2.286E01 2.805E01 3.335E01 3.873E01 4.415E01 5.783E01 7.159E01 8.536E01 9.908E01 1.264Eþ00 1.534Eþ00 1.801Eþ00

2.719E05 3.203E05 3.673E05 4.131E05 4.579E05 5.018E05 5.448E05 5.871E05 6.696E05 7.497E05 8.277E05 9.038E05 1.087E04 1.262E04 1.430E04 1.593E04 1.904E04 2.202E04 2.487E04 2.762E04 3.029E04 3.288E04 3.541E04 3.787E04 4.265E04 4.725E04 5.169E04 5.600E04 6.630E04 7.603E04 8.533E04 9.426E04 1.114E03 1.277E03 1.436E03 1.592E03 1.746E03 1.899E03 2.052E03 2.205E03 2.512E03 2.822E03 3.137E03 3.455E03 4.270E03 5.110E03 5.975E03 6.861E03 8.691E03 1.059E02 1.253E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

111

112

1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02

Energy (MeV)

4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

Energy (MeV)

7.478Eþ01 6.686Eþ01 6.052Eþ01 5.537Eþ01 5.110Eþ01 4.445Eþ01 3.948Eþ01 3.562Eþ01 3.253Eþ01 2.999Eþ01 2.786Eþ01 2.605Eþ01 2.448Eþ01 2.192Eþ01 1.989Eþ01 1.825Eþ01 1.689Eþ01

Collision (MeV cm2 g1)

1.568Eþ00 1.578Eþ00 1.588Eþ00 1.597Eþ00 1.605Eþ00 1.620Eþ00 1.633Eþ00 1.645Eþ00 1.656Eþ00 1.678Eþ00 1.695Eþ00 1.710Eþ00 1.723Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

4.138E03 4.474E03 4.754E03 4.995E03 5.204E03 5.553E03 5.832E03 6.061E03 6.254E03 6.417E03 6.558E03 6.680E03 6.787E03 6.965E03 7.105E03 7.219E03 7.312E03

Radiative (MeV cm2 g1)

Stopping power

6.376E02 7.346E02 8.337E02 9.345E02 1.037E01 1.247E01 1.462E01 1.681E01 1.904E01 2.474E01 3.059E01 3.655E01 4.260E01

Radiative (MeV cm2 g1)

Stopping power

7.478Eþ01 6.686Eþ01 6.053Eþ01 5.537Eþ01 5.111Eþ01 4.445Eþ01 3.949Eþ01 3.563Eþ01 3.253Eþ01 2.999Eþ01 2.786Eþ01 2.605Eþ01 2.449Eþ01 2.192Eþ01 1.990Eþ01 1.826Eþ01 1.690Eþ01

Total (MeV cm2 g1)

Silicon

1.631Eþ00 1.651Eþ00 1.671Eþ00 1.690Eþ00 1.709Eþ00 1.745Eþ00 1.779Eþ00 1.813Eþ00 1.846Eþ00 1.925Eþ00 2.001Eþ00 2.076Eþ00 2.149Eþ00

Total (MeV cm2 g1)

6.686E06 1.023E05 1.416E05 1.849E05 2.319E05 3.371E05 4.567E05 5.902E05 7.372E05 8.975E05 1.071E04 1.256E04 1.454E04 1.887E04 2.366E04 2.891E04 3.461E04

CSDA range (g cm2)

2.428Eþ00 2.732Eþ00 3.033Eþ00 3.331Eþ00 3.625Eþ00 4.204Eþ00 4.772Eþ00 5.328Eþ00 5.875Eþ00 7.201Eþ00 8.474Eþ00 9.701Eþ00 1.088Eþ01

CSDA range (g cm2)

Polytetrafluoroethylene, ‘‘teflon’’

2.767E05 3.436E05 4.076E05 4.699E05 5.312E05 6.517E05 7.703E05 8.873E05 1.003E04 1.117E04 1.230E04 1.342E04 1.452E04 1.670E04 1.883E04 2.092E04 2.297E04

Brems yield

1.873E02 2.129E02 2.388E02 2.649E02 2.912E02 3.440E02 3.970E02 4.500E02 5.029E02 6.342E02 7.631E02 8.892E02 1.012E01

Brems yield

1.187Eþ02 1.027Eþ02 9.093Eþ01 8.181Eþ01 7.452Eþ01 6.357Eþ01 5.569Eþ01 4.971Eþ01 4.501Eþ01 4.120Eþ01 3.805Eþ01 3.540Eþ01 3.313Eþ01 2.944Eþ01 2.656Eþ01 2.425Eþ01 2.235Eþ01

Collision (MeV cm2 g1)

1.845Eþ00 1.857Eþ00 1.867Eþ00 1.877Eþ00 1.887Eþ00 1.903Eþ00 1.918Eþ00 1.932Eþ00 1.943Eþ00 1.968Eþ00 1.989Eþ00 2.006Eþ00 2.020Eþ00

Collision (MeV cm2 g1) 1.904Eþ00 1.924Eþ00 1.944Eþ00 1.963Eþ00 1.981Eþ00 2.018Eþ00 2.052Eþ00 2.086Eþ00 2.118Eþ00 2.196Eþ00 2.270Eþ00 2.342Eþ00 2.412Eþ00

Total (MeV cm2 g1) 2.065Eþ00 2.326Eþ00 2.585Eþ00 2.841Eþ00 3.094Eþ00 3.594Eþ00 4.086Eþ00 4.569Eþ00 5.045Eþ00 6.204Eþ00 7.323Eþ00 8.407Eþ00 9.459Eþ00

CSDA range (g cm2)

2.784E03 2.942E03 3.064E03 3.161E03 3.241E03 3.363E03 3.452E03 3.519E03 3.571E03 3.612E03 3.645E03 3.673E03 3.695E03 3.730E03 3.755E03 3.773E03 3.787E03

Radiative (MeV cm2 g1)

Stopping power

1.187Eþ02 1.027Eþ02 9.093Eþ01 8.181Eþ01 7.452Eþ01 6.357Eþ01 5.569Eþ01 4.971Eþ01 4.501Eþ01 4.121Eþ01 3.806Eþ01 3.540Eþ01 3.313Eþ01 2.944Eþ01 2.657Eþ01 2.425Eþ01 2.235Eþ01

Total (MeV cm2 g1)

4.213E06 6.484E06 9.076E06 1.198E05 1.519E05 2.248E05 3.090E05 4.042E05 5.101E05 6.263E05 7.527E05 8.890E05 1.035E04 1.356E04 1.714E04 2.109E04 2.538E04

CSDA range (g cm2)

Tissue, soft (ICRU four component)

5.819E02 6.707E02 7.615E02 8.542E02 9.484E02 1.141E01 1.339E01 1.541E01 1.747E01 2.273E01 2.814E01 3.366E01 3.926E01

Radiative (MeV cm2 g1)

Stopping power

Skin (ICRU-44)

1.173E05 1.459E05 1.736E05 2.005E05 2.267E05 2.778E05 3.273E05 3.754E05 4.223E05 4.682E05 5.131E05 5.572E05 6.005E05 6.849E05 7.669E05 8.467E05 9.245E05

Brems yield

1.452E02 1.654E02 1.859E02 2.066E02 2.274E02 2.695E02 3.120E02 3.546E02 3.974E02 5.040E02 6.097E02 7.139E02 8.162E02

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01 4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

1.432Eþ01 1.251Eþ01 1.115Eþ01 1.010Eþ01 8.556Eþ00 7.480Eþ00 6.682Eþ00 6.067Eþ00 5.576Eþ00 5.175Eþ00 4.842Eþ00 4.560Eþ00 4.107Eþ00 3.761Eþ00 3.487Eþ00 3.265Eþ00 2.859Eþ00 2.583Eþ00 2.385Eþ00 2.236Eþ00 2.028Eþ00 1.892Eþ00 1.797Eþ00 1.729Eþ00 1.677Eþ00 1.638Eþ00 1.608Eþ00 1.585Eþ00 1.551Eþ00 1.529Eþ00 1.516Eþ00 1.507Eþ00 1.500Eþ00 1.502Eþ00 1.509Eþ00 1.518Eþ00 1.538Eþ00 1.558Eþ00 1.575Eþ00 1.591Eþ00 1.605Eþ00 1.618Eþ00 1.629Eþ00 1.639Eþ00 1.657Eþ00 1.672Eþ00 1.685Eþ00 1.697Eþ00 1.721Eþ00 1.740Eþ00 1.756Eþ00 1.769Eþ00

7.484E03 7.596E03 7.671E03 7.724E03 7.799E03 7.852E03 7.894E03 7.930E03 7.961E03 7.988E03 8.015E03 8.043E03 8.108E03 8.180E03 8.257E03 8.337E03 8.557E03 8.794E03 9.047E03 9.318E03 9.915E03 1.057E02 1.129E02 1.204E02 1.284E02 1.367E02 1.454E02 1.544E02 1.731E02 1.929E02 2.136E02 2.351E02 2.918E02 3.521E02 4.154E02 4.812E02 6.192E02 7.643E02 9.154E02 1.071E01 1.230E01 1.393E01 1.558E01 1.726E01 2.069E01 2.420E01 2.777E01 3.140E01 4.067E01 5.016E01 5.982E01 6.962E01

1.433Eþ01 1.252Eþ01 1.116Eþ01 1.011Eþ01 8.564Eþ00 7.487Eþ00 6.690Eþ00 6.075Eþ00 5.584Eþ00 5.183Eþ00 4.850Eþ00 4.568Eþ00 4.116Eþ00 3.769Eþ00 3.496Eþ00 3.274Eþ00 2.867Eþ00 2.592Eþ00 2.394Eþ00 2.245Eþ00 2.038Eþ00 1.902Eþ00 1.808Eþ00 1.741Eþ00 1.690Eþ00 1.652Eþ00 1.623Eþ00 1.600Eþ00 1.568Eþ00 1.549Eþ00 1.537Eþ00 1.531Eþ00 1.529Eþ00 1.538Eþ00 1.551Eþ00 1.567Eþ00 1.600Eþ00 1.634Eþ00 1.667Eþ00 1.698Eþ00 1.728Eþ00 1.757Eþ00 1.785Eþ00 1.812Eþ00 1.864Eþ00 1.914Eþ00 1.963Eþ00 2.011Eþ00 2.127Eþ00 2.241Eþ00 2.354Eþ00 2.465Eþ00

5.074E04 6.946E04 9.065E04 1.142E03 1.682E03 2.308E03 3.016E03 3.802E03 4.661E03 5.592E03 6.590E03 7.653E03 9.964E03 1.251E02 1.526E02 1.822E02 2.642E02 3.561E02 4.566E02 5.646E02 7.991E02 1.054E01 1.323E01 1.606E01 1.897E01 2.197E01 2.502E01 2.812E01 3.444E01 4.086E01 4.735E01 5.387E01 7.022E01 8.653E01 1.027Eþ00 1.188Eþ00 1.503Eþ00 1.813Eþ00 2.116Eþ00 2.413Eþ00 2.705Eþ00 2.992Eþ00 3.274Eþ00 3.552Eþ00 4.096Eþ00 4.625Eþ00 5.141Eþ00 5.645Eþ00 6.853Eþ00 7.998Eþ00 9.086Eþ00 1.012Eþ01

2.793E04 3.269E04 3.727E04 4.169E04 5.011E04 5.810E04 6.573E04 7.305E04 8.011E04 8.694E04 9.355E04 9.998E04 1.124E03 1.242E03 1.356E03 1.466E03 1.726E03 1.970E03 2.201E03 2.422E03 2.839E03 3.235E03 3.616E03 3.986E03 4.350E03 4.708E03 5.064E03 5.417E03 6.121E03 6.824E03 7.529E03 8.239E03 1.003E02 1.186E02 1.371E02 1.559E02 1.941E02 2.330E02 2.723E02 3.121E02 3.520E02 3.920E02 4.321E02 4.722E02 5.521E02 6.315E02 7.102E02 7.881E02 9.782E02 1.161E01 1.337E01 1.505E01

1.880Eþ01 1.631Eþ01 1.447Eþ01 1.305Eþ01 1.099Eþ01 9.562Eþ00 8.512Eþ00 7.704Eþ00 7.063Eþ00 6.541Eþ00 6.108Eþ00 5.742Eþ00 5.158Eþ00 4.713Eþ00 4.361Eþ00 4.077Eþ00 3.558Eþ00 3.207Eþ00 2.955Eþ00 2.767Eþ00 2.504Eþ00 2.333Eþ00 2.214Eþ00 2.128Eþ00 2.064Eþ00 2.015Eþ00 1.976Eþ00 1.944Eþ00 1.898Eþ00 1.867Eþ00 1.846Eþ00 1.831Eþ00 1.810Eþ00 1.803Eþ00 1.803Eþ00 1.806Eþ00 1.816Eþ00 1.828Eþ00 1.841Eþ00 1.853Eþ00 1.864Eþ00 1.875Eþ00 1.884Eþ00 1.894Eþ00 1.911Eþ00 1.925Eþ00 1.939Eþ00 1.951Eþ00 1.976Eþ00 1.996Eþ00 2.013Eþ00 2.028Eþ00

3.810E03 3.821E03 3.828E03 3.833E03 3.845E03 3.857E03 3.868E03 3.879E03 3.890E03 3.903E03 3.919E03 3.936E03 3.972E03 4.012E03 4.055E03 4.100E03 4.222E03 4.354E03 4.496E03 4.648E03 4.979E03 5.342E03 5.734E03 6.150E03 6.589E03 7.048E03 7.525E03 8.018E03 9.051E03 1.014E02 1.127E02 1.245E02 1.556E02 1.888E02 2.238E02 2.604E02 3.374E02 4.187E02 5.037E02 5.916E02 6.818E02 7.741E02 8.682E02 9.640E02 1.160E01 1.361E01 1.566E01 1.775E01 2.310E01 2.859E01 3.420E01 3.989E01

1.880Eþ01 1.632Eþ01 1.448Eþ01 1.305Eþ01 1.099Eþ01 9.566Eþ00 8.515Eþ00 7.708Eþ00 7.067Eþ00 6.545Eþ00 6.112Eþ00 5.746Eþ00 5.162Eþ00 4.717Eþ00 4.365Eþ00 4.081Eþ00 3.562Eþ00 3.211Eþ00 2.960Eþ00 2.771Eþ00 2.509Eþ00 2.338Eþ00 2.219Eþ00 2.134Eþ00 2.070Eþ00 2.022Eþ00 1.983Eþ00 1.952Eþ00 1.907Eþ00 1.877Eþ00 1.857Eþ00 1.843Eþ00 1.826Eþ00 1.822Eþ00 1.825Eþ00 1.832Eþ00 1.850Eþ00 1.870Eþ00 1.891Eþ00 1.912Eþ00 1.932Eþ00 1.952Eþ00 1.971Eþ00 1.990Eþ00 2.027Eþ00 2.061Eþ00 2.095Eþ00 2.128Eþ00 2.207Eþ00 2.282Eþ00 2.355Eþ00 2.427Eþ00

3.763E04 5.195E04 6.825E04 8.647E04 1.284E03 1.773E03 2.328E03 2.946E03 3.625E03 4.361E03 5.152E03 5.996E03 7.836E03 9.866E03 1.207E02 1.444E02 2.103E02 2.844E02 3.656E02 4.530E02 6.433E02 8.502E02 1.070E01 1.300E01 1.538E01 1.783E01 2.032E01 2.286E01 2.805E01 3.334E01 3.870E01 4.410E01 5.774E01 7.145E01 8.517E01 9.884E01 1.260Eþ00 1.529Eþ00 1.795Eþ00 2.058Eþ00 2.318Eþ00 2.575Eþ00 2.830Eþ00 3.083Eþ00 3.581Eþ00 4.070Eþ00 4.551Eþ00 5.025Eþ00 6.178Eþ00 7.292Eþ00 8.370Eþ00 9.416Eþ00

1.112E04 1.291E04 1.463E04 1.629E04 1.947E04 2.250E04 2.541E04 2.822E04 3.094E04 3.358E04 3.616E04 3.867E04 4.354E04 4.823E04 5.276E04 5.715E04 6.764E04 7.756E04 8.702E04 9.612E04 1.135E03 1.302E03 1.464E03 1.622E03 1.779E03 1.935E03 2.090E03 2.245E03 2.556E03 2.871E03 3.189E03 3.511E03 4.335E03 5.186E03 6.060E03 6.957E03 8.809E03 1.072E02 1.269E02 1.471E02 1.675E02 1.882E02 2.092E02 2.303E02 2.729E02 3.158E02 3.589E02 4.021E02 5.099E02 6.167E02 7.219E02 8.252E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

113

1.000E03 1.000E03 1.250E03 1.500E03 1.750E03 2.000E03 2.500E03 3.000E03 3.500E03 4.000E03 4.500E03 5.000E03 5.500E03 6.000E03 7.000E03 8.000E03 9.000E03 1.000E02 1.250E02 1.500E02 1.750E02 2.000E02 2.500E02 3.000E02 3.500E02 4.000E02 4.500E02 5.000E02 5.500E02 6.000E02 7.000E02 8.000E02 9.000E02 1.000E01 1.250E01 1.500E01 1.750E01 2.000E01 2.500E01 3.000E01 3.500E01

Energy (MeV)

7.478Eþ01 1.198Eþ02 1.037Eþ02 9.177Eþ01 8.257Eþ01 7.521Eþ01 6.416Eþ01 5.621Eþ01 5.018Eþ01 4.543Eþ01 4.159Eþ01 3.841Eþ01 3.573Eþ01 3.344Eþ01 2.971Eþ01 2.681Eþ01 2.448Eþ01 2.256Eþ01 1.897Eþ01 1.647Eþ01 1.461Eþ01 1.317Eþ01 1.109Eþ01 9.653Eþ00 8.592Eþ00 7.777Eþ00 7.130Eþ00 6.603Eþ00 6.166Eþ00 5.797Eþ00 5.207Eþ00 4.757Eþ00 4.402Eþ00 4.115Eþ00 3.591Eþ00 3.238Eþ00 2.984Eþ00 2.793Eþ00 2.528Eþ00 2.355Eþ00 2.235Eþ00

Collision (MeV cm2 g1)

Table A.4. Continued

4.138E03 2.830E03 2.995E03 3.122E03 3.224E03 3.307E03 3.436E03 3.530E03 3.602E03 3.657E03 3.701E03 3.737E03 3.766E03 3.791E03 3.828E03 3.855E03 3.875E03 3.890E03 3.915E03 3.928E03 3.935E03 3.939E03 3.952E03 3.965E03 3.976E03 3.987E03 3.998E03 4.011E03 4.027E03 4.044E03 4.081E03 4.122E03 4.165E03 4.211E03 4.336E03 4.471E03 4.616E03 4.771E03 5.110E03 5.482E03 5.883E03

Radiative (MeV cm2 g1)

Stopping power

7.478Eþ01 1.198Eþ02 1.037Eþ02 9.177Eþ01 8.257Eþ01 7.522Eþ01 6.417Eþ01 5.621Eþ01 5.018Eþ01 4.543Eþ01 4.159Eþ01 3.841Eþ01 3.573Eþ01 3.344Eþ01 2.972Eþ01 2.682Eþ01 2.448Eþ01 2.257Eþ01 1.898Eþ01 1.647Eþ01 1.461Eþ01 1.318Eþ01 1.110Eþ01 9.657Eþ00 8.596Eþ00 7.781Eþ00 7.134Eþ00 6.607Eþ00 6.170Eþ00 5.801Eþ00 5.211Eþ00 4.762Eþ00 4.407Eþ00 4.120Eþ00 3.596Eþ00 3.242Eþ00 2.988Eþ00 2.798Eþ00 2.533Eþ00 2.360Eþ00 2.241Eþ00

Total (MeV cm2 g1)

Water, liquid

6.686E06 4.174E06 6.424E06 8.993E06 1.187E05 1.505E05 2.227E05 3.062E05 4.005E05 5.054E05 6.205E05 7.457E05 8.808E05 1.025E04 1.343E04 1.698E04 2.089E04 2.515E04 3.728E04 5.147E04 6.761E04 8.566E04 1.272E03 1.756E03 2.306E03 2.919E03 3.591E03 4.320E03 5.103E03 5.940E03 7.762E03 9.773E03 1.196E02 1.431E02 2.083E02 2.817E02 3.622E02 4.487E02 6.372E02 8.421E02 1.060E01

CSDA range (g cm2)

2.767E05 1.181E05 1.471E05 1.750E05 2.022E05 2.288E05 2.806E05 3.308E05 3.797E05 4.275E05 4.741E05 5.199E05 5.647E05 6.088E05 6.949E05 7.785E05 8.598E05 9.392E05 1.130E04 1.313E04 1.488E04 1.657E04 1.981E04 2.290E04 2.587E04 2.873E04 3.150E04 3.419E04 3.681E04 3.937E04 4.432E04 4.909E04 5.370E04 5.817E04 6.883E04 7.892E04 8.854E04 9.779E04 1.155E03 1.324E03 1.488E03

Brems yield

1.187Eþ02 1.192Eþ02 1.030Eþ02 9.107Eþ01 8.185Eþ01 7.451Eþ01 6.349Eþ01 5.557Eþ01 4.958Eþ01 4.486Eþ01 4.105Eþ01 3.790Eþ01 3.524Eþ01 3.297Eþ01 2.929Eþ01 2.642Eþ01 2.411Eþ01 2.222Eþ01 1.867Eþ01 1.620Eþ01 1.437Eþ01 1.295Eþ01 1.090Eþ01 9.484Eþ00 8.439Eþ00 7.637Eþ00 7.000Eþ00 6.482Eþ00 6.052Eþ00 5.689Eþ00 5.110Eþ00 4.667Eþ00 4.318Eþ00 4.036Eþ00 3.522Eþ00 3.174Eþ00 2.924Eþ00 2.737Eþ00 2.477Eþ00 2.307Eþ00 2.189Eþ00

Collision (MeV cm2 g1) 2.784E03 2.554E03 2.686E03 2.785E03 2.864E03 2.928E03 3.025E03 3.095E03 3.147E03 3.188E03 3.221E03 3.247E03 3.268E03 3.286E03 3.314E03 3.335E03 3.351E03 3.363E03 3.382E03 3.395E03 3.406E03 3.415E03 3.431E03 3.444E03 3.456E03 3.469E03 3.482E03 3.497E03 3.513E03 3.530E03 3.565E03 3.603E03 3.643E03 3.686E03 3.799E03 3.921E03 4.052E03 4.190E03 4.493E03 4.825E03 5.182E03

Radiative (MeV cm2 g1)

Stopping power

1.187Eþ02 1.192Eþ02 1.030Eþ02 9.107Eþ01 8.186Eþ01 7.451Eþ01 6.349Eþ01 5.557Eþ01 4.958Eþ01 4.487Eþ01 4.106Eþ01 3.790Eþ01 3.525Eþ01 3.298Eþ01 2.929Eþ01 2.642Eþ01 2.411Eþ01 2.222Eþ01 1.868Eþ01 1.620Eþ01 1.437Eþ01 1.296Eþ01 1.091Eþ01 9.487Eþ00 8.443Eþ00 7.640Eþ00 7.004Eþ00 6.486Eþ00 6.056Eþ00 5.693Eþ00 5.113Eþ00 4.671Eþ00 4.322Eþ00 4.040Eþ00 3.525Eþ00 3.178Eþ00 2.929Eþ00 2.741Eþ00 2.482Eþ00 2.312Eþ00 2.194Eþ00

Total (MeV cm2 g1)

WT1, ‘‘solid water’’

4.213E06 4.194E06 6.457E06 9.044E06 1.194E05 1.515E05 2.245E05 3.089E05 4.043E05 5.105E05 6.271E05 7.540E05 8.909E05 1.038E04 1.360E04 1.720E04 2.117E04 2.549E04 3.782E04 5.223E04 6.865E04 8.700E04 1.293E03 1.786E03 2.345E03 2.969E03 3.653E03 4.396E03 5.195E03 6.047E03 7.904E03 9.954E03 1.218E02 1.458E02 2.123E02 2.872E02 3.693E02 4.576E02 6.500E02 8.592E02 1.081E01

CSDA range (g cm2)

1.173E05 1.071E05 1.332E05 1.582E05 1.825E05 2.061E05 2.519E05 2.960E05 3.389E05 3.807E05 4.214E05 4.614E05 5.005E05 5.390E05 6.140E05 6.869E05 7.580E05 8.274E05 9.946E05 1.155E04 1.309E04 1.458E04 1.745E04 2.019E04 2.283E04 2.537E04 2.784E04 3.024E04 3.258E04 3.486E04 3.930E04 4.357E04 4.770E04 5.171E04 6.128E04 7.034E04 7.899E04 8.732E04 1.033E03 1.185E03 1.334E03

Brems yield

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

114

4.000E01 4.500E01 5.000E01 5.500E01 6.000E01 7.000E01 8.000E01 9.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 1.750Eþ00 2.000Eþ00 2.500Eþ00 3.000Eþ00 3.500Eþ00 4.000Eþ00 4.500Eþ00 5.000Eþ00 5.500Eþ00 6.000Eþ00 7.000Eþ00 8.000Eþ00 9.000Eþ00 1.000Eþ01 1.250Eþ01 1.500Eþ01 1.750Eþ01 2.000Eþ01

2.148Eþ00 2.083Eþ00 2.034Eþ00 1.995Eþ00 1.963Eþ00 1.917Eþ00 1.886Eþ00 1.864Eþ00 1.849Eþ00 1.829Eþ00 1.822Eþ00 1.821Eþ00 1.824Eþ00 1.834Eþ00 1.846Eþ00 1.858Eþ00 1.870Eþ00 1.882Eþ00 1.892Eþ00 1.902Eþ00 1.911Eþ00 1.928Eþ00 1.943Eþ00 1.956Eþ00 1.968Eþ00 1.993Eþ00 2.014Eþ00 2.031Eþ00 2.046Eþ00

6.309E03 6.758E03 7.228E03 7.716E03 8.221E03 9.278E03 1.039E02 1.155E02 1.276E02 1.594E02 1.934E02 2.292E02 2.666E02 3.454E02 4.286E02 5.156E02 6.056E02 6.978E02 7.922E02 8.885E02 9.865E02 1.187E01 1.392E01 1.602E01 1.816E01 2.363E01 2.924E01 3.497E01 4.079E01

2.154Eþ00 2.090Eþ00 2.041Eþ00 2.003Eþ00 1.972Eþ00 1.926Eþ00 1.896Eþ00 1.876Eþ00 1.862Eþ00 1.845Eþ00 1.841Eþ00 1.844Eþ00 1.850Eþ00 1.868Eþ00 1.889Eþ00 1.910Eþ00 1.931Eþ00 1.951Eþ00 1.971Eþ00 1.991Eþ00 2.010Eþ00 2.047Eþ00 2.082Eþ00 2.116Eþ00 2.150Eþ00 2.230Eþ00 2.306Eþ00 2.381Eþ00 2.454Eþ00

1.288E01 1.523E01 1.766E01 2.013E01 2.265E01 2.778E01 3.302E01 3.832E01 4.367E01 5.718E01 7.075E01 8.432E01 9.786E01 1.248Eþ00 1.514Eþ00 1.777Eþ00 2.037Eþ00 2.295Eþ00 2.550Eþ00 2.802Eþ00 3.052Eþ00 3.545Eþ00 4.030Eþ00 4.506Eþ00 4.975Eþ00 6.116Eþ00 7.219Eþ00 8.286Eþ00 9.320Eþ00

1.649E03 1.808E03 1.966E03 2.124E03 2.281E03 2.597E03 2.915E03 3.238E03 3.565E03 4.400E03 5.261E03 6.147E03 7.056E03 8.932E03 1.087E02 1.287E02 1.491E02 1.698E02 1.908E02 2.120E02 2.334E02 2.765E02 3.200E02 3.637E02 4.074E02 5.165E02 6.245E02 7.308E02 8.352E02

2.104Eþ00 2.038Eþ00 1.987Eþ00 1.947Eþ00 1.915Eþ00 1.868Eþ00 1.836Eþ00 1.814Eþ00 1.799Eþ00 1.778Eþ00 1.770Eþ00 1.770Eþ00 1.773Eþ00 1.783Eþ00 1.796Eþ00 1.809Eþ00 1.821Eþ00 1.833Eþ00 1.844Eþ00 1.854Eþ00 1.863Eþ00 1.880Eþ00 1.895Eþ00 1.909Eþ00 1.921Eþ00 1.945Eþ00 1.965Eþ00 1.982Eþ00 1.995Eþ00

5.561E03 5.960E03 6.378E03 6.812E03 7.260E03 8.200E03 9.189E03 1.022E02 1.129E02 1.413E02 1.715E02 2.034E02 2.367E02 3.069E02 3.810E02 4.584E02 5.384E02 6.208E02 7.050E02 7.910E02 8.784E02 1.057E01 1.241E01 1.428E01 1.619E01 2.108E01 2.610E01 3.123E01 3.644E01

2.109Eþ00 2.044Eþ00 1.994Eþ00 1.954Eþ00 1.922Eþ00 1.876Eþ00 1.845Eþ00 1.824Eþ00 1.810Eþ00 1.792Eþ00 1.788Eþ00 1.790Eþ00 1.796Eþ00 1.814Eþ00 1.834Eþ00 1.854Eþ00 1.875Eþ00 1.895Eþ00 1.914Eþ00 1.933Eþ00 1.951Eþ00 1.986Eþ00 2.020Eþ00 2.052Eþ00 2.083Eþ00 2.156Eþ00 2.226Eþ00 2.294Eþ00 2.360Eþ00

1.314E01 1.555E01 1.803E01 2.056E01 2.314E01 2.841E01 3.379E01 3.924E01 4.475E01 5.864E01 7.262E01 8.659E01 1.005Eþ00 1.282Eþ00 1.557Eþ00 1.828Eþ00 2.096Eþ00 2.361Eþ00 2.624Eþ00 2.884Eþ00 3.141Eþ00 3.649Eþ00 4.148Eþ00 4.640Eþ00 5.123Eþ00 6.303Eþ00 7.444Eþ00 8.550Eþ00 9.624Eþ00

1.479E03 1.623E03 1.767E03 1.910E03 2.053E03 2.342E03 2.633E03 2.929E03 3.228E03 3.994E03 4.784E03 5.597E03 6.431E03 8.152E03 9.933E03 1.176E02 1.363E02 1.553E02 1.746E02 1.941E02 2.137E02 2.533E02 2.934E02 3.336E02 3.739E02 4.747E02 5.748E02 6.738E02 7.712E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

115

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

A.2

LOW-ENERGY PHOTON SOURCES Table A.5. Physical data for selected low-energy photon-emitting radionuclides. Based on data of Tables A.6 and A.7. Radio-nuclide

Half-life (d)

Average number of photons per disintegration

Average photon energy (keV)

Air-kerma rate constant, ˜ 10 keV (m2mGy h  1 MBq  1) A

125

59.40 16.99 32.03 340

1.476 0.771 3.33 1.51

28.4 20.7 92.8 41.5

0.0355 0.0361 0.0430 0.0188

I Pd 169 Yb 145 Sm 103

Table A.6. Decay data for selected low-energy photon-emitting radionuclides. Data compiled from National Nuclear Data Center (2001) and Lund/LBNL Nuclear Data Search (1999). Energy (keV)

Photons per disintegration

125

I decays by electron capture, T1/2 ¼ 59.40 – 0.01 d, limiting specific activity ¼ 6.51 · 1014 Bq g1 (1.76 · 104 Ci g1) Te Ka2 x ray Te Ka1 x ray Te Kb1,3,5 x ray Te Kb2,4 x ray g

27.202 27.472 30.98 31.71 35.492

0.406 0.757 0.202 0.0439 0.0668

103 Pd decays by electron capture, T1/2 ¼ 16.991 – 0.019 d, limiting specific activity ¼ 2.76 · 1015 Bq g1 (7.47 · 104 Ci g1)

Rh Ka2 x ray Rh Ka1 x ray Rh Kb1,3,5 x ray Rh Kb2,4 x ray g g

20.074 20.216 22.72 23.18 39.75 357.5

0.224 0.423 0.104 0.0194 0.00068 0.00022

145

Sm decays by electron capture, T1/2 ¼ 340 – 3 d, limiting specific activity ¼ 9.81 · 1013 Bq g1 (2650 Ci g1) Pm Ka2 x ray Pm Ka1 x ray Pm Kb1,3,5 x ray Pm Kb2,4 x ray g g

38.171 38.725 43.79 44.98 61.22 492.4

0.399 0.724 0.208 0.0616 0.122 0.000033

169

Yb decays by electron capture, T1/2 ¼ 32.026 – 0.005 d, limiting specific activity ¼ 8.93 · 1014 Bq g1 (2.41 · 104 Ci g1) g Tm Ka2 x ray Tm Ka1 x ray Tm Kb1,3,5 x ray Tm Kb2,4 x ray g g g g g g g g g g

20.752 49.773 50.742 57.44 59.07 63.121 93.615 109.78 118.19 130.52 177.21 197.96 240.33 261.08 307.74

0.00190 0.532 0.940 0.295 0.0819 0.442 0.0261 0.175 0.0187 0.113 0.222 0.358 0.00114 0.0171 0.101

116

2.256Eþ03 7.267Eþ02 3.172Eþ02 9.576Eþ01 4.021Eþ01 3.907Eþ01 5.326Eþ01 2.901Eþ01 1.708Eþ01 7.337Eþ00 3.771Eþ00 1.106Eþ00 4.605E01 1.378E01 6.411E02 4.018E02 3.095E02 2.561E02 2.520E02 2.737E02 2.937E02 3.159E02 3.245E02 3.265E02 3.249E02 3.172E02 3.070E02 2.934E02 2.805E02 2.578E02 2.247E02 2.025E02 1.867E02 1.751E02 1.592E02 1.489E02 1.346E02

2.628Eþ03 2.392Eþ03 2.176Eþ03 2.182Eþ03 8.622Eþ02 3.800Eþ02 2.053Eþ02 2.072Eþ02 1.707Eþ02 1.405Eþ02 1.420Eþ02 1.188Eþ02 5.054Eþ01 2.587Eþ01 1.494Eþ01 6.300Eþ00 3.268Eþ00 1.083Eþ00 5.677E01 3.063E01 2.396E01 2.123E01 1.974E01 1.800E01 1.688E01 1.500E01 1.368E01 1.187E01 1.062E01 9.696E02 8.965E02 7.873E02 7.078E02 6.330E02 5.760E02 4.940E02 3.955E02

2.259Eþ03 7.282Eþ02 3.183Eþ02 9.652Eþ01 4.081Eþ01 3.966Eþ01 5.629Eþ01 3.069Eþ01 1.813Eþ01 7.914Eþ00 4.186Eþ00 1.394Eþ00 7.068E01 3.481E01 2.562E01 2.198E01 2.008E01 1.803E01 1.680E01 1.485E01 1.353E01 1.173E01 1.049E01 9.579E02 8.857E02 7.777E02 6.992E02 6.253E02 5.691E02 4.880E02 3.907E02 3.335E02 2.958E02 2.690E02 2.338E02 2.117E02 1.819E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 4.038E03 4.038E03a 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01

1.000E03 1.035E03 1.072E03 1.072E03b 1.500E03 2.000E03 2.472E03 2.472E03c 2.641E03 2.822E03 2.822E03d 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Adipose tissue (ICRU-44)

A-150 Tissue-equivalent plastic

2.623Eþ03 2.387Eþ03 2.171Eþ03 2.177Eþ03 8.601Eþ02 3.787Eþ02 2.043Eþ02 2.060Eþ02 1.696Eþ02 1.396Eþ02 1.409Eþ02 1.178Eþ02 4.983Eþ01 2.531Eþ01 1.446Eþ01 5.917Eþ00 2.935Eþ00 8.103E01 3.251E01 9.495E02 4.575E02 3.085E02 2.567E02 2.358E02 2.433E02 2.737E02 2.959E02 3.194E02 3.283E02 3.304E02 3.289E02 3.211E02 3.108E02 2.970E02 2.839E02 2.610E02 2.275E02

men/r (cm2 g1) 1.000E03 1.500E03 2.000E03 3.000E03 3.203E03 3.203E03e 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01

Energy (MeV)

3.606Eþ03 1.191Eþ03 5.279Eþ02 1.625Eþ02 1.340Eþ02 1.485Eþ02 7.788Eþ01 4.027Eþ01 2.341Eþ01 9.921Eþ00 5.120Eþ00 1.614Eþ00 7.779E01 3.538E01 2.485E01 2.080E01 1.875E01 1.662E01 1.541E01 1.356E01 1.233E01 1.067E01 9.549E02 8.712E02 8.055E02 7.074E02 6.358E02 5.687E02 5.175E02 4.447E02 3.581E02 3.079E02 2.751E02 2.522E02 2.225E02 2.045E02 1.810E02

m/r (cm2 g1)

Air, dry (near sea level)

3.599Eþ03 1.188Eþ03 5.262Eþ02 1.614Eþ02 1.330Eþ02 1.460Eþ02 7.636Eþ01 3.931Eþ01 2.270Eþ01 9.446Eþ00 4.742Eþ00 1.334Eþ00 5.389E01 1.537E01 6.833E02 4.098E02 3.041E02 2.407E02 2.325E02 2.496E02 2.672E02 2.872E02 2.949E02 2.966E02 2.953E02 2.882E02 2.789E02 2.666E02 2.547E02 2.345E02 2.057E02 1.870E02 1.740E02 1.647E02 1.525E02 1.450E02 1.353E02

men/r (cm2 g1)

Table A.7. Photon mass total-attenuation coefficients, m/r, and mass energy-absorption coefficients, men/r. Values obtained from Hubbell and Seltzer (1995) and methods described in Seltzer (1993b). Note that values of m/r include the contribution of coherent scattering.

APPENDIX A: COMPILATION OF PHYSICAL DATA

117

m/r (cm2 g1)

3.064Eþ03 1.010Eþ03 4.470Eþ02 1.374Eþ02 5.847Eþ01 2.991Eþ01 1.725Eþ01 7.248Eþ00 3.738Eþ00 1.210Eþ00 6.158E01 3.158E01 2.402E01 2.099E01 1.938E01 1.756E01 1.643E01 1.456E01 1.328E01 1.151E01 1.030E01 9.400E02 8.691E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01

Alanine

Energy (MeV)

(b)

K edge of Ca: 4.0381E03 MeV. K edge of Na: 1.0721E03 MeV. (c) K edge of S : 2.4720E03 MeV. (d) K edge of Cl : 2.8224E03 MeV. (e) K edge of A: 3.2029E03 MeV.

(a)

118 3.057Eþ03 1.007Eþ03 4.456Eþ02 1.365Eþ02 5.777Eþ01 2.934Eþ01 1.676Eþ01 6.854Eþ00 3.398Eþ00 9.363E01 3.743E01 1.076E01 5.034E02 3.275E02 2.643E02 2.345E02 2.387E02 2.660E02 2.871E02 3.096E02 3.182E02 3.202E02 3.187E02

men/r (cm2 g1)

1.275E02

1.000E03 1.500E03 1.560E03 1.560E03a 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01

Energy (MeV) 1.185Eþ03 4.022Eþ02 3.621Eþ02 3.957Eþ03 2.263Eþ03 7.880Eþ02 3.605Eþ02 1.934Eþ02 1.153Eþ02 5.033Eþ01 2.623Eþ01 7.955Eþ00 3.441Eþ00 1.128Eþ00 5.685E01 3.681E01 2.778E01 2.018E01 1.704E01 1.378E01 1.223E01 1.042E01 9.276E02

m/r (cm2 g1)

Aluminum

3.377E02 2.995E02 2.725E02 2.368E02 2.145E02 1.843E02 1.698E02

1.675E02

2.000Eþ01

4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Adipose tissue (ICRU-44)

A-150 Tissue-equivalent plastic

Table A.7. Continued

1.183Eþ03 4.001Eþ02 3.600Eþ02 3.829Eþ03 2.204Eþ03 7.732Eþ02 3.545Eþ02 1.902Eþ02 1.133Eþ02 4.918Eþ01 2.543Eþ01 7.487Eþ00 3.094Eþ00 8.779E01 3.601E01 1.840E01 1.099E01 5.511E02 3.795E02 2.827E02 2.745E02 2.816E02 2.862E02

men/r (cm2 g1)

2.050E02 1.891E02 1.773E02 1.612E02 1.509E02 1.365E02 1.293E02

men/r (cm2 g1)

1.000E03 1.500E03 1.560E03 1.560E03a 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01

Energy (MeV)

2.000Eþ01

Energy (MeV)

2.788Eþ03 9.421Eþ02 8.469Eþ02 2.750Eþ03 1.525Eþ03 5.193Eþ02 2.346Eþ02 1.249Eþ02 7.406Eþ01 3.211Eþ01 1.668Eþ01 5.074Eþ00 2.229Eþ00 7.750E01 4.226E01 2.952E01 2.368E01 1.858E01 1.632E01 1.370E01 1.230E01 1.055E01 9.413E02

m/r (cm2 g1)

Aluminum oxide

1.705E02

m/r (cm2 g1)

Air, dry (near sea level)

2.780Eþ03 9.389Eþ02 8.439Eþ02 2.680Eþ03 1.493Eþ03 5.108Eþ02 2.310Eþ02 1.229Eþ02 7.269Eþ01 3.128Eþ01 1.608Eþ01 4.691Eþ00 1.929Eþ00 5.462E01 2.261E01 1.182E01 7.327E02 4.079E02 3.117E02 2.676E02 2.714E02 2.845E02 2.905E02

men/r (cm2 g1)

1.311E02

men/r (cm2 g1)

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 4.038E03 4.038E03a 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01

5.248Eþ03 1.843Eþ03 8.509Eþ02 2.779Eþ02 1.237Eþ02 1.204Eþ02 5.848Eþ02 3.410Eþ02 2.100Eþ02 9.642Eþ01 5.194Eþ01 1.651Eþ01 7.255Eþ00 2.313Eþ00 1.077Eþ00 6.311E01 4.311E01 2.674E01 2.048E01 1.491E01 1.278E01 1.067E01 9.437E02 8.570E02 7.905E02 6.924E02

3.154Eþ03 1.056Eþ03 4.714Eþ02 1.465Eþ02 6.272Eþ01 3.221Eþ01 1.863Eþ01 7.845Eþ00 4.040Eþ00 1.285Eþ00 6.345E01 3.063E01 2.244E01 1.924E01 1.758E01 1.578E01 1.471E01 1.299E01 1.184E01 1.025E01 9.172E02 8.372E02 7.740E02 6.798E02 6.112E02 5.465E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00

3.144Eþ03 1.053Eþ03 4.698Eþ02 1.456Eþ02 6.201Eþ01 3.164Eþ01 1.814Eþ01 7.459Eþ00 3.713Eþ00 1.030Eþ00 4.125E01 1.175E01 5.335E02 3.328E02 2.580E02 2.176E02 2.168E02 2.380E02 2.561E02 2.758E02 2.833E02 2.851E02 2.838E02 2.771E02 2.682E02 2.562E02

m/r (cm2 g1)

8.445E02 7.802E02 6.841E02 6.146E02 5.496E02 5.006E02 4.324E02 3.541E02 3.106E02 2.836E02 2.655E02 2.437E02 2.318E02 2.195E02 2.168E02

m/r (cm2 g1) Energy (MeV)

5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

Energy (MeV)

men/r (cm2 g1)

3.112E02 3.012E02 2.878E02 2.751E02 2.530E02 2.210E02 1.996E02 1.846E02 1.736E02 1.587E02 1.493E02 1.362E02 1.299E02

Calcium fluoride

K edge of Al: 1.5596E03 MeV.

7.632E02 6.862E02 6.137E02 5.584E02 4.792E02 3.843E02 3.289E02 2.924E02 2.666E02 2.328E02 2.119E02 1.838E02 1.706E02

Beryllium oxide

(a)

8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

5.228Eþ03 1.836Eþ03 8.472Eþ02 2.757Eþ02 1.220Eþ02 1.187Eþ02 5.151Eþ02 3.070Eþ02 1.919Eþ02 8.965Eþ01 4.867Eþ01 1.546Eþ01 6.692Eþ00 2.002Eþ00 8.406E01 4.298E01 2.512E01 1.137E01 6.741E02 3.682E02 3.112E02 2.944E02 2.933E02 2.920E02 2.892E02 2.811E02

men/r (cm2 g1)

2.868E02 2.851E02 2.778E02 2.686E02 2.565E02 2.451E02 2.266E02 2.024E02 1.882E02 1.795E02 1.739E02 1.678E02 1.650E02 1.631E02 1.633E02

1.000E03 1.500E03 2.000E03 2.472E03 2.472E03b 3.000E03 4.000E03 4.038E03 4.038E03a 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01

Energy (MeV)

5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

4.163Eþ03 1.429Eþ03 6.529Eþ02 3.627Eþ02 7.993Eþ02 4.961Eþ02 2.289Eþ02 2.231Eþ02 4.895Eþ02 2.820Eþ02 1.727Eþ02 7.858Eþ01 4.210Eþ01 1.329Eþ01 5.831Eþ00 1.876Eþ00 8.928E01 5.381E01 3.788E01 2.474E01 1.962E01 1.487E01 1.293E01 1.088E01 9.653E02 8.777E02

m/r (cm2 g1)

Calcium sulfate

8.579E02 7.928E02 6.957E02 6.252E02 5.591E02 5.091E02 4.388E02 3.567E02 3.103E02 2.808E02 2.607E02 2.355E02 2.210E02 2.040E02 1.981E02

4.153Eþ03 1.425Eþ03 6.503Eþ02 3.606Eþ02 7.659Eþ02 4.774Eþ02 2.215Eþ02 2.159Eþ02 4.431Eþ02 2.595Eþ02 1.606Eþ02 7.394Eþ01 3.977Eþ01 1.247Eþ01 5.352Eþ00 1.587Eþ00 6.646E01 3.403E01 2.001E01 9.291E02 5.732E02 3.443E02 3.057E02 2.981E02 2.994E02 2.989E02

men/r (cm2 g1)

2.917E02 2.901E02 2.829E02 2.736E02 2.614E02 2.498E02 2.305E02 2.043E02 1.881E02 1.776E02 1.704E02 1.616E02 1.568E02 1.515E02 1.498E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

119

120 1.000E03 1.035E03 1.072E03 1.072E03a 1.500E03 2.000E03 2.146E03 2.146E03b 2.303E03 2.472E03 2.472E03c 2.641E03 2.822E03 2.822E03d 3.000E03 4.000E03 5.000E03 6.000E03

3.599Eþ03 3.282Eþ03 2.992Eþ03 2.998Eþ03 1.206Eþ03 5.386Eþ02 4.410Eþ02 4.432Eþ02 3.619Eþ02 2.952Eþ02 3.007Eþ02 2.489Eþ02 2.053Eþ02 2.067Eþ02 1.733Eþ02 7.446Eþ01 3.834Eþ01 2.221Eþ01

2.211Eþ03 7.002Eþ02 3.026Eþ02 9.033Eþ01 3.778Eþ01 1.912Eþ01 1.095Eþ01 4.576Eþ00 2.373Eþ00 8.071E01 4.420E01 2.562E01 2.076E01 1.871E01 1.753E01 1.610E01 1.514E01 1.347E01

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01

2.209Eþ03 6.990Eþ02 3.016Eþ02 8.963Eþ01 3.723Eþ01 1.866Eþ01 1.054Eþ01 4.243Eþ00 2.078Eþ00 5.627E01 2.238E01 6.614E02 3.343E02 2.397E02 2.098E02 2.037E02 2.147E02 2.449E02

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Eye lens (ICRU-44)

6.217E02 5.558E02 5.065E02 4.380E02 3.606E02 3.184E02 2.923E02 2.753E02 2.553E02 2.450E02 2.356E02 2.351E02

Carbon, graphite

(b)

K edge of Ca: 4.0381E03 MeV. K edge of S : 2.4720E03 MeV.

(a)

1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

4.974E02 4.271E02 3.431E02 2.943E02 2.622E02 2.397E02 2.103E02 1.922E02 1.684E02 1.574E02

1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

2.449E02 2.254E02 1.971E02 1.786E02 1.656E02 1.561E02 1.435E02 1.355E02 1.248E02 1.197E02

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Calcium fluoride

Beryllium oxide

Table A.7. Continued

3.588Eþ03 3.273Eþ03 2.984Eþ03 2.989Eþ03 1.203Eþ03 5.368Eþ02 4.393Eþ02 4.414Eþ02 3.603Eþ02 2.938Eþ02 2.989Eþ02 2.469Eþ02 2.038Eþ02 2.051Eþ02 1.719Eþ02 7.353Eþ01 3.764Eþ01 2.163Eþ01

men/r (cm2 g1)

2.715E02 2.591E02 2.476E02 2.290E02 2.058E02 1.927E02 1.850E02 1.804E02 1.758E02 1.743E02 1.745E02 1.759E02

men/r (cm2 g1)

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01

Energy (MeV)

6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

Energy (MeV)

2.594Eþ03 8.437Eþ02 3.705Eþ02 1.129Eþ02 4.776Eþ01 2.436Eþ01 1.402Eþ01 5.892Eþ00 3.052Eþ00 1.014Eþ00 5.366E01 2.943E01 2.322E01 2.066E01 1.925E01 1.759E01 1.651E01 1.467E01

m/r (cm2 g1)

GAFchromic sensor

8.100E02 7.100E02 6.377E02 5.701E02 5.193E02 4.488E02 3.679E02 3.232E02 2.954E02 2.770E02 2.547E02 2.428E02 2.305E02 2.282E02

m/r (cm2 g1)

Calcium sulfate

2.589Eþ03 8.419Eþ02 3.693Eþ02 1.120Eþ02 4.713Eþ01 2.384Eþ01 1.357Eþ01 5.523Eþ00 2.728Eþ00 7.481E01 2.990E01 8.734E02 4.248E02 2.905E02 2.448E02 2.282E02 2.368E02 2.674E02

men/r (cm2 g1)

2.964E02 2.884E02 2.787E02 2.660E02 2.542E02 2.350E02 2.102E02 1.958E02 1.869E02 1.814E02 1.753E02 1.727E02 1.711E02 1.716E02

men/r (cm2 g1)

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

121

1.229E01 1.066E01 9.546E02 8.715E02 8.058E02 7.076E02 6.361E02 5.690E02 5.179E02 4.442E02 3.562E02 3.047E02 2.708E02 2.469E02 2.154E02 1.959E02 1.698E02 1.575E02

K edge of Na: 1.0721E03 MeV. K edge of P: 2.1455E03 MeV. (c) K edge of S: 2.4720E03 MeV. (d) K edge of Cl: 2.8224E03 MeV.

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02

4.200Eþ03 1.467Eþ03 6.698Eþ02 2.135Eþ02 9.282Eþ01 4.815Eþ01 2.802Eþ01 1.187Eþ01 6.101Eþ00

2.731Eþ03 8.874Eþ02 3.895Eþ02 1.185Eþ02 5.013Eþ01 2.555Eþ01 1.470Eþ01 6.161Eþ00 3.180Eþ00

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02

2.726Eþ03 8.855Eþ02 3.882Eþ02 1.177Eþ02 4.949Eþ01 2.502Eþ01 1.424Eþ01 5.794Eþ00 2.861Eþ00

m/r (cm2 g1)

m/r (cm2 g1)

9.372Eþ00 4.829Eþ00 1.531Eþ00 7.510E01 3.570E01 2.590E01 2.209E01 2.013E01 1.803E01 1.679E01 1.482E01 1.350E01 1.169E01 1.046E01 9.547E02 8.827E02 7.752E02 6.969E02 6.232E02 5.671E02 4.869E02 3.908E02 3.349E02 2.981E02 2.722E02 2.383E02 2.174E02 1.896E02 1.767E02

Energy (MeV)

Energy (MeV)

8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

Lithium fluoride men/r (cm2 g1)

2.655E02 2.870E02 2.950E02 2.969E02 2.956E02 2.885E02 2.792E02 2.669E02 2.551E02 2.345E02 2.048E02 1.849E02 1.709E02 1.607E02 1.468E02 1.379E02 1.257E02 1.197E02

‘‘Kapton’’ polyimide film

(b)

(a)

2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

4.175Eþ03 1.460Eþ03 6.667Eþ02 2.121Eþ02 9.188Eþ01 4.742Eþ01 2.742Eþ01 1.142Eþ01 5.733Eþ00

men/r (cm2 g1)

8.931Eþ00 4.458Eþ00 1.242Eþ00 4.988E01 1.421E01 6.418E02 3.961E02 3.035E02 2.518E02 2.490E02 2.719E02 2.922E02 3.146E02 3.231E02 3.252E02 3.237E02 3.160E02 3.058E02 2.922E02 2.793E02 2.570E02 2.247E02 2.033E02 1.883E02 1.774E02 1.626E02 1.534E02 1.407E02 1.346E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02

Energy (MeV)

2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

3.373Eþ03 1.128Eþ03 5.033Eþ02 1.563Eþ02 6.687Eþ01 3.433Eþ01 1.984Eþ01 8.343Eþ00 4.290Eþ00

m/r (cm2 g1)

Lithium tetraborate

1.339E01 1.161E01 1.039E01 9.487E02 8.772E02 7.704E02 6.926E02 6.194E02 5.637E02 4.835E02 3.872E02 3.308E02 2.935E02 2.672E02 2.324E02 2.108E02 1.815E02 1.675E02

3.363Eþ03 1.124Eþ03 5.015Eþ02 1.553Eþ02 6.612Eþ01 3.373Eþ01 1.933Eþ01 7.946Eþ00 3.954Eþ00

men/r (cm2 g1)

2.894E02 3.125E02 3.212E02 3.233E02 3.218E02 3.142E02 3.040E02 2.906E02 2.778E02 2.553E02 2.227E02 2.008E02 1.853E02 1.739E02 1.583E02 1.483E02 1.344E02 1.275E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

122 3.275Eþ03 2.298Eþ03 1.604Eþ03 2.262Eþ03 1.584Eþ03 7.274Eþ02 2.337Eþ02 1.018Eþ02 5.279Eþ01

1.000E03 1.035E03 1.072E03 1.072E03b 1.500E03 2.000E03 2.146E03 2.146E03c 2.303E03

3.719Eþ03 3.393Eþ03 3.094Eþ03 3.100Eþ03 1.251Eþ03 5.594Eþ02 4.581Eþ02 4.626Eþ02 3.782Eþ02

3.284Eþ03 2.304Eþ03 1.609Eþ03 2.284Eþ03 1.599Eþ03 7.334Eþ02 2.358Eþ02 1.030Eþ02 5.363Eþ01

3.709Eþ03 3.383Eþ03 3.085Eþ03 3.091Eþ03 1.247Eþ03 5.574Eþ02 4.564Eþ02 4.606Eþ02 3.762Eþ02

men/r (cm2 g1)

1.000E03 1.142E03 1.305E03 1.305E03a 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03

Energy (MeV)

m/r (cm2 g1)

men/r (cm2 g1)

m/r (cm2 g1)

Energy (MeV)

1.612Eþ00 6.494E01 1.826E01 7.891E02 4.541E02 3.223E02 2.385E02 2.229E02 2.332E02 2.484E02 2.663E02 2.734E02 2.749E02 2.736E02 2.671E02 2.585E02 2.470E02 2.361E02 2.173E02 1.907E02 1.733E02 1.614E02 1.528E02 1.414E02 1.345E02 1.253E02 1.211E02

Muscle, skeletal (ICRU-44)

1.884Eþ00 8.792E01 3.727E01 2.486E01 2.020E01 1.791E01 1.563E01 1.441E01 1.260E01 1.145E01 9.899E02 8.853E02 8.076E02 7.467E02 6.557E02 5.894E02 5.271E02 4.798E02 4.122E02 3.321E02 2.857E02 2.554E02 2.343E02 2.069E02 1.903E02 1.687E02 1.592E02

men/r (cm2 g1)

Magnesium tetraborate

1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

1.042Eþ00 5.415E01 2.880E01 2.235E01 1.973E01 1.830E01 1.665E01 1.560E01 1.385E01 1.263E01 1.095E01 9.799E02 8.944E02 8.270E02 7.262E02 6.529E02 5.839E02 5.314E02 4.561E02 3.659E02 3.133E02 2.787E02 2.543E02 2.223E02 2.025E02 1.762E02 1.638E02

1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

7.837E01 3.127E01 9.045E02 4.318E02 2.888E02 2.389E02 2.182E02 2.247E02 2.525E02 2.729E02 2.946E02 3.027E02 3.047E02 3.033E02 2.961E02 2.865E02 2.739E02 2.618E02 2.407E02 2.104E02 1.902E02 1.760E02 1.656E02 1.516E02 1.427E02 1.306E02 1.247E02

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Lithium fluoride

‘‘Kapton’’ polyimide film

Table A.7. Continued

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02

Energy (MeV)

1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

Energy (MeV)

2.468Eþ03 7.992Eþ02 3.501Eþ02 1.063Eþ02 4.491Eþ01 2.288Eþ01 1.317Eþ01 5.533Eþ00 2.871Eþ00

m/r (cm2 g1)

Nylon, type 6 and type 6/6

1.357Eþ00 6.652E01 3.165E01 2.298E01 1.960E01 1.786E01 1.599E01 1.489E01 1.314E01 1.197E01 1.036E01 9.271E02 8.461E02 7.823E02 6.870E02 6.177E02 5.523E02 5.026E02 4.318E02 3.471E02 2.979E02 2.657E02 2.432E02 2.137E02 1.958E02 1.721E02 1.613E02

m/r (cm2 g1)

Lithium tetraborate

2.463Eþ03 7.975Eþ02 3.489Eþ02 1.055Eþ02 4.430Eþ01 2.237Eþ01 1.272Eþ01 5.169Eþ00 2.550Eþ00

men/r (cm2 g1)

1.096Eþ00 4.384E01 1.244E01 5.612E02 3.469E02 2.665E02 2.221E02 2.201E02 2.408E02 2.589E02 2.787E02 2.863E02 2.881E02 2.868E02 2.800E02 2.710E02 2.589E02 2.474E02 2.278E02 1.994E02 1.808E02 1.678E02 1.585E02 1.459E02 1.381E02 1.276E02 1.227E02

men/r (cm2 g1)

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

123

3.131Eþ01 1.332Eþ01 6.865Eþ00 2.122Eþ00 9.862E01 4.114E01 2.705E01 2.177E01 1.919E01 1.666E01 1.531E01 1.337E01 1.214E01 1.049E01 9.380E02 8.558E02 7.912E02 6.946E02 6.245E02 5.584E02 5.083E02 4.370E02 3.524E02 3.035E02 2.718E02 2.496E02 2.211E02 2.039E02 1.817E02 1.722E02

(b)

K edge of Mg: 1.3050E03 MeV. K edge of Na: 1.0721E03 MeV. (c) K edge of P : 2.1455E03 MeV. (d) K edge of S : 2.4720E03 MeV. (e) K edge of Cl : 2.8224E03 MeV. (f) K edge of K : 3.6074E03 MeV.

(a)

6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

3.064Eþ01 1.283Eþ01 6.470Eþ00 1.831Eþ00 7.409E01 2.092E01 9.011E02 5.137E02 3.600E02 2.602E02 2.398E02 2.480E02 2.635E02 2.822E02 2.896E02 2.913E02 2.899E02 2.830E02 2.738E02 2.616E02 2.500E02 2.303E02 2.023E02 1.842E02 1.717E02 1.629E02 1.512E02 1.441E02 1.350E02 1.309E02

2.472E03 2.472E03d 2.641E03 2.822E03 2.822E03e 3.000E03 3.607E03 3.607E03f 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

3.085Eþ02 3.140Eþ02 2.597Eþ02 2.145Eþ02 2.160Eþ02 1.812Eþ02 1.057Eþ02 1.100Eþ02 8.127Eþ01 4.206Eþ01 2.446Eþ01 1.037Eþ01 5.356Eþ00 1.693Eþ00 8.205E01 3.783E01 2.685E01 2.262E01 2.048E01 1.823E01 1.693E01 1.492E01 1.358E01 1.176E01 1.052E01 9.598E02 8.874E02 7.793E02 7.007E02 6.265E02 5.701E02 4.896E02 3.931E02 3.369E02 3.000E02 2.741E02 2.401E02 2.192E02 1.915E02 1.786E02

3.069Eþ02 3.121Eþ02 2.579Eþ02 2.130Eþ02 2.143Eþ02 1.796Eþ02 1.046Eþ02 1.083Eþ02 7.992Eþ01 4.116Eþ01 2.377Eþ01 9.888Eþ00 4.964Eþ00 1.396Eþ00 5.638E01 1.610E01 7.192E02 4.349E02 3.258E02 2.615E02 2.544E02 2.745E02 2.942E02 3.164E02 3.249E02 3.269E02 3.254E02 3.177E02 3.074E02 2.938E02 2.808E02 2.584E02 2.259E02 2.045E02 1.895E02 1.786E02 1.639E02 1.547E02 1.421E02 1.361E02

1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

9.635E01 5.165E01 2.895E01 2.310E01 2.067E01 1.931E01 1.768E01 1.661E01 1.477E01 1.348E01 1.170E01 1.047E01 9.557E02 8.838E02 7.761E02 6.977E02 6.240E02 5.678E02 4.870E02 3.898E02 3.328E02 2.952E02 2.685E02 2.332E02 2.113E02 1.815E02 1.671E02

6.982E01 2.791E01 8.201E02 4.046E02 2.815E02 2.404E02 2.275E02 2.375E02 2.691E02 2.915E02 3.148E02 3.236E02 3.257E02 3.242E02 3.165E02 3.063E02 2.928E02 2.799E02 2.572E02 2.242E02 2.020E02 1.863E02 1.747E02 1.588E02 1.486E02 1.343E02 1.272E02

APPENDIX A: COMPILATION OF PHYSICAL DATA

2.022Eþ03 6.397Eþ02 2.761Eþ02 8.203Eþ01 3.407Eþ01 1.707Eþ01 9.650Eþ00 3.883Eþ00 1.903Eþ00 5.158E01 2.059E01 6.211E02 3.256E02 2.424E02 2.180E02 2.172E02 2.310E02 2.650E02 2.876E02 3.110E02 3.197E02 3.218E02 3.204E02 3.128E02 3.027E02 2.894E02 2.766E02 2.542E02 2.214E02 1.992E02 1.835E02 1.718E02 1.558E02 1.455E02 1.309E02 1.236E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

2.538Eþ03 8.217Eþ02 3.599Eþ02 1.093Eþ02 4.616Eþ01 2.351Eþ01 1.352Eþ01 5.675Eþ00 2.938Eþ00 9.774E01 5.178E01 2.847E01 2.249E01 2.003E01 1.866E01 1.705E01 1.600E01 1.422E01 1.297E01 1.125E01 1.007E01 9.193E02 8.501E02 7.465E02 6.711E02 6.002E02 5.463E02 4.686E02 3.755E02 3.210E02 2.851E02 2.597E02 2.263E02 2.056E02 1.777E02 1.644E02

2.024Eþ03 6.409Eþ02 2.770Eþ02 8.270Eþ01 3.461Eþ01 1.753Eþ01 1.005Eþ01 4.220Eþ00 2.204Eþ00 7.705E01 4.358E01 2.647E01 2.194E01 1.997E01 1.881E01 1.736E01 1.635E01 1.458E01 1.331E01 1.155E01 1.034E01 9.443E02 8.732E02 7.668E02 6.894E02 6.166E02 5.611E02 4.810E02 3.848E02 3.282E02 2.907E02 2.641E02 2.290E02 2.069E02 1.770E02 1.624E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

2.533Eþ03 8.199Eþ02 3.587Eþ02 1.085Eþ02 4.555Eþ01 2.300Eþ01 1.308Eþ01 5.314Eþ00 2.622Eþ00 7.176E01 2.865E01 8.367E02 4.077E02 2.795E02 2.361E02 2.206E02 2.293E02 2.591E02 2.804E02 3.028E02 3.112E02 3.132E02 3.118E02 3.044E02 2.946E02 2.816E02 2.691E02 2.474E02 2.159E02 1.949E02 1.800E02 1.691E02 1.542E02 1.447E02 1.316E02 1.252E02

men/r (cm2 g1)

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Polycarbonate, ‘‘makrolon’’, ‘‘lexan’’

Plastic scintillator (vinyltoluene)

Table A.7. Continued

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

Energy (MeV) 2.911Eþ03 9.536Eþ02 4.206Eþ02 1.288Eþ02 5.466Eþ01 2.792Eþ01 1.608Eþ01 6.750Eþ00 3.481Eþ00 1.132Eþ00 5.798E01 3.009E01 2.304E01 2.020E01 1.868E01 1.695E01 1.586E01 1.406E01 1.282E01 1.111E01 9.947E02 9.079E02 8.395E02 7.372E02 6.628E02 5.927E02 5.395E02 4.630E02 3.715E02 3.181E02 2.829E02 2.582E02 2.257E02 2.057E02 1.789E02 1.664E02

m/r (cm2 g1)

2.905Eþ03 9.513Eþ02 4.192Eþ02 1.279Eþ02 5.398Eþ01 2.737Eþ01 1.561Eþ01 6.370Eþ00 3.153Eþ00 8.668E01 3.462E01 9.972E02 4.695E02 3.082E02 2.508E02 2.247E02 2.297E02 2.567E02 2.772E02 2.990E02 3.073E02 3.093E02 3.079E02 3.005E02 2.909E02 2.780E02 2.657E02 2.444E02 2.135E02 1.931E02 1.787E02 1.682E02 1.540E02 1.450E02 1.327E02 1.267E02

men/r (cm2 g1)

Polyethylene terephthalate, ‘‘mylar’’

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

124

125

K edge of Na: 1.0721E03 MeV.

(a)

3.915Eþ03 3.573Eþ03 3.259Eþ03 3.292Eþ03 1.335Eþ03 5.984Eþ02 1.863Eþ02 7.961Eþ01 4.070Eþ01 2.337Eþ01 9.633Eþ00 4.802Eþ00 1.334Eþ00 5.346E01 1.514E01 6.777E02 4.137E02 3.138E02 2.570E02 2.526E02 2.748E02 2.951E02 3.175E02 3.262E02 3.282E02 3.267E02 3.189E02 3.087E02 2.950E02 2.819E02 2.594E02 2.269E02 2.054E02 1.904E02 1.795E02 1.648E02 1.556E02 1.431E02 1.371E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

2.794Eþ03 9.153Eþ02 4.037Eþ02 1.236Eþ02 5.247Eþ01 2.681Eþ01 1.545Eþ01 6.494Eþ00 3.357Eþ00 1.101Eþ00 5.714E01 3.032E01 2.350E01 2.074E01 1.924E01 1.751E01 1.641E01 1.456E01 1.328E01 1.152E01 1.031E01 9.410E02 8.701E02 7.641E02 6.870E02 6.143E02 5.591E02 4.796E02 3.844E02 3.286E02 2.919E02 2.659E02 2.317E02 2.105E02 1.820E02 1.684E02

3.927Eþ03 3.584Eþ03 3.269Eþ03 3.303Eþ03 1.339Eþ03 6.005Eþ02 1.875Eþ02 8.047Eþ01 4.139Eþ01 2.395Eþ01 1.008Eþ01 5.182Eþ00 1.630Eþ00 7.917E01 3.697E01 2.653E01 2.249E01 2.043E01 1.825E01 1.697E01 1.497E01 1.363E01 1.180E01 1.056E01 9.637E02 8.909E02 7.825E02 7.035E02 6.291E02 5.724E02 4.916E02 3.947E02 3.384E02 3.014E02 2.754E02 2.414E02 2.205E02 1.928E02 1.800E02

1.000E03 1.035E03 1.072E03 1.072E03a 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

2.788Eþ03 9.131Eþ02 4.024Eþ02 1.228Eþ02 5.181Eþ01 2.627Eþ01 1.498Eþ01 6.114Eþ00 3.026Eþ00 8.324E01 3.328E01 9.646E02 4.599E02 3.067E02 2.530E02 2.302E02 2.368E02 2.657E02 2.872E02 3.099E02 3.185E02 3.206E02 3.191E02 3.116E02 3.015E02 2.882E02 2.755E02 2.533E02 2.210E02 1.995E02 1.843E02 1.731E02 1.579E02 1.482E02 1.348E02 1.282E02

men/r (cm2 g1)

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Polymethylmethacrylate, ‘‘lucite’’, ‘‘perspex’’

Polymer gel, ‘‘bang-2’’

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

Energy (MeV) 2.040Eþ03 6.462Eþ02 2.792Eþ02 8.338Eþ01 3.489Eþ01 1.767Eþ01 1.013Eþ01 4.252Eþ00 2.219Eþ00 7.738E01 4.363E01 2.640E01 2.183E01 1.986E01 1.870E01 1.725E01 1.624E01 1.448E01 1.322E01 1.147E01 1.027E01 9.379E02 8.672E02 7.615E02 6.847E02 6.123E02 5.573E02 4.777E02 3.822E02 3.261E02 2.889E02 2.626E02 2.278E02 2.060E02 1.763E02 1.620E02

m/r (cm2 g1)

Polystyrene

2.038Eþ03 6.450Eþ02 2.783Eþ02 8.271Eþ01 3.435Eþ01 1.721Eþ01 9.730Eþ00 3.915Eþ00 1.918Eþ00 5.200E01 2.075E01 6.247E02 3.264E02 2.421E02 2.172E02 2.160E02 2.296E02 2.632E02 2.857E02 3.088E02 3.175E02 3.196E02 3.182E02 3.106E02 3.006E02 2.874E02 2.747E02 2.524E02 2.199E02 1.979E02 1.824E02 1.708E02 1.550E02 1.448E02 1.305E02 1.232E02

men/r (cm2 g1)

APPENDIX A: COMPILATION OF PHYSICAL DATA

4.797Eþ03 1.664Eþ03 7.567Eþ02 2.396Eþ02 1.035Eþ02 5.329Eþ01 3.077Eþ01 1.278Eþ01 6.408Eþ00 1.796Eþ00 7.222E01 2.022E01 8.674E02 4.943E02 3.470E02 2.523E02 2.335E02 2.424E02 2.579E02 2.763E02 2.836E02 2.852E02 2.838E02 2.771E02 2.681E02 2.562E02 2.448E02 2.255E02 1.984E02 1.809E02 1.690E02 1.606E02 1.496E02 1.430E02 1.346E02 1.310E02

3.572Eþ03 3.258Eþ03 2.970Eþ03 2.982Eþ03 1.201Eþ03 5.362Eþ02 4.390Eþ02 4.412Eþ02 3.603Eþ02 2.939Eþ02 2.976Eþ02 2.459Eþ02 2.030Eþ02 2.074Eþ02 1.741Eþ02 1.016Eþ02 1.026Eþ02 7.571Eþ01 3.907Eþ01 2.267Eþ01 9.588Eþ00 4.947Eþ00 1.570Eþ00 7.681E01 3.626E01 2.618E01 2.226E01 2.025E01 1.811E01 1.686E01 1.488E01 1.355E01 1.173E01 1.050E01 9.580E02 8.857E02 7.778E02 6.993E02 6.254E02

4.823Eþ03 1.672Eþ03 7.601Eþ02 2.411Eþ02 1.045Eþ02 5.409Eþ01 3.142Eþ01 1.327Eþ01 6.805Eþ00 2.088Eþ00 9.667E01 4.025E01 2.647E01 2.132E01 1.880E01 1.632E01 1.500E01 1.310E01 1.189E01 1.027E01 9.187E02 8.380E02 7.747E02 6.803E02 6.115E02 5.469E02 4.979E02 4.280E02 3.456E02 2.981E02 2.674E02 2.460E02 2.185E02 2.020E02 1.811E02 1.722E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

1.000E03 1.035E03 1.072E03 1.072E03a 1.500E03 2.000E03 2.146E03 2.146E03b 2.303E03 2.472E03 2.472E03c 2.641E03 2.822E03 2.822E03d 3.000E03 3.607E03 3.607E03e 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Skin (ICRU-44)

Polytetrafluoroethylene, ‘‘teflon’’

Table A.7. Continued

3.562Eþ03 3.249Eþ03 2.962Eþ03 2.973Eþ03 1.197Eþ03 5.344Eþ02 4.374Eþ02 4.395Eþ02 3.587Eþ02 2.925Eþ02 2.959Eþ02 2.444Eþ02 2.017Eþ02 2.057Eþ02 1.725Eþ02 1.004Eþ02 1.014Eþ02 7.463Eþ01 3.830Eþ01 2.206Eþ01 9.134Eþ00 4.570Eþ00 1.278Eþ00 5.147E01 1.470E01 6.622E02 4.067E02 3.098E02 2.549E02 2.509E02 2.731E02 2.934E02 3.157E02 3.243E02 3.263E02 3.248E02 3.171E02 3.069E02 2.933E02

men/r (cm2 g1) 1.000E03 1.500E03 1.839E03 1.839E03f 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

Energy (MeV) 1.570Eþ03 5.355Eþ02 3.092Eþ02 3.192Eþ03 2.777Eþ03 9.784Eþ02 4.529Eþ02 2.450Eþ02 1.470Eþ02 6.468Eþ01 3.389Eþ01 1.034Eþ01 4.464Eþ00 1.436Eþ00 7.012E01 4.385E01 3.207E01 2.228E01 1.835E01 1.448E01 1.275E01 1.082E01 9.614E02 8.748E02 8.077E02 7.082E02 6.361E02 5.688E02 5.183E02 4.480E02 3.678E02 3.240E02 2.967E02 2.788E02 2.574E02 2.462E02 2.352E02 2.338E02

m/r (cm2 g1)

Silicon

1.567Eþ03 5.331Eþ02 3.070Eþ02 3.059Eþ03 2.669Eþ03 9.516Eþ02 4.427Eþ02 2.400Eþ02 1.439Eþ02 6.313Eþ01 3.289Eþ01 9.794Eþ00 4.076Eþ00 1.165Eþ00 4.782E01 2.430E01 1.434E01 6.896E02 4.513E02 3.086E02 2.905E02 2.932E02 2.968E02 2.971E02 2.951E02 2.875E02 2.778E02 2.652E02 2.535E02 2.345E02 2.101E02 1.963E02 1.878E02 1.827E02 1.773E02 1.753E02 1.746E02 1.757E02

men/r (cm2 g1)

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

126

3.818Eþ03 1.283Eþ03 5.736Eþ02 1.781Eþ02 7.598Eþ01 3.880Eþ01 2.226Eþ01 9.163Eþ00 4.564Eþ00 1.266Eþ00 5.070E01 1.438E01 6.474E02 3.987E02 3.051E02 2.530E02 2.501E02 2.732E02 2.936E02 3.161E02 3.247E02 3.267E02 3.252E02 3.175E02 3.073E02 2.937E02

4.078Eþ03 1.376Eþ03 6.173Eþ02 1.929Eþ02 8.278Eþ01 4.258Eþ01 2.464Eþ01 1.037Eþ01 5.329Eþ00 1.673Eþ00 8.096E01 3.756E01 2.683E01 2.269E01 2.059E01 1.837E01 1.707E01 1.505E01 1.370E01 1.186E01 1.061E01 9.687E02 8.956E02 7.865E02 7.072E02 6.323E02

3.829Eþ03 1.286Eþ03 5.755Eþ02 1.792Eþ02 7.681Eþ01 3.947Eþ01 2.283Eþ01 9.604Eþ00 4.937Eþ00 1.558Eþ00 7.616E01 3.604E01 2.609E01 2.223E01 2.025E01 1.813E01 1.688E01 1.490E01 1.356E01 1.175E01 1.051E01 9.593E02 8.870E02 7.789E02 7.003E02 6.262E02

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00

1.000E03 1.500E03 2.000E03 3.000E03 4.000E03 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Water, liquid

5.691E02 4.886E02 3.921E02 3.360E02 2.990E02 2.730E02 2.390E02 2.180E02 1.900E02 1.770E02

Tissue, soft (ICRU four-component)

(b)

K edge of Na: 1.0721E03 MeV. K edge of P : 2.1455E03 MeV (c) K edge of S : 2.4720E03 MeV. (d) K edge of Cl : 2.8224E03 MeV. (e) K edge of K : 3.6074E03 MeV. (f) K edge of Si: 1.8389E03 MeV.

(a)

1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

4.065Eþ03 1.372Eþ03 6.152Eþ02 1.917Eþ02 8.191Eþ01 4.188Eþ01 2.405Eþ01 9.915Eþ00 4.944Eþ00 1.374Eþ00 5.503E01 1.557E01 6.947E02 4.223E02 3.190E02 2.597E02 2.546E02 2.764E02 2.967E02 3.192E02 3.279E02 3.299E02 3.284E02 3.206E02 3.103E02 2.965E02

men/r (cm2 g1)

2.803E02 2.579E02 2.254E02 2.039E02 1.889E02 1.779E02 1.631E02 1.537E02 1.410E02 1.349E02

1.000E03 1.500E03 2.000E03 2.822E03 2.822E03a 3.000E03 4.000E03 4.038E03 4.038E03b 5.000E03 6.000E03 8.000E03 1.000E02 1.500E02 2.000E02 3.000E02 4.000E02 5.000E02 6.000E02 8.000E02 1.000E01 1.500E01 2.000E01 3.000E01 4.000E01 5.000E01

Energy (MeV)

2.594Eþ03 8.454Eþ02 3.720Eþ02 1.362Eþ02 1.376Eþ02 1.151Eþ02 4.895Eþ01 4.758Eþ01 6.839Eþ01 3.742Eþ01 2.216Eþ01 9.681Eþ00 5.109Eþ00 1.671Eþ00 8.220E01 3.799E01 2.677E01 2.242E01 2.021E01 1.792E01 1.662E01 1.463E01 1.332E01 1.153E01 1.032E01 9.415E02

m/r (cm2 g1)

WT1, ‘‘solid water’’

2.589Eþ03 8.435Eþ02 3.708Eþ02 1.353Eþ02 1.366Eþ02 1.141Eþ02 4.826Eþ01 4.690Eþ01 6.465Eþ01 3.539Eþ01 2.092Eþ01 9.029Eþ00 4.657Eþ00 1.372Eþ00 5.718E01 1.695E01 7.686E02 4.634E02 3.425E02 2.670E02 2.551E02 2.710E02 2.894E02 3.106E02 3.189E02 3.208E02

men/r (cm2 g1)

APPENDIX A: COMPILATION OF PHYSICAL DATA

127

(b)

K edge of Cl : 2.8224E03 MeV. K edge of Ca: 4.0381E03 MeV.

(a)

2.806E02 2.582E02 2.258E02 2.044E02 1.894E02 1.785E02 1.638E02 1.546E02 1.420E02 1.360E02

5.754E02 4.942E02 3.969E02 3.403E02 3.031E02 2.770E02 2.429E02 2.219E02 1.941E02 1.813E02

5.699E02 4.893E02 3.929E02 3.367E02 2.998E02 2.739E02 2.400E02 2.191E02 1.913E02 1.785E02

1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

m/r (cm2 g1)

Energy (MeV)

m/r (cm2 g1)

Energy (MeV)

men/r (cm2 g1)

Water, liquid

Tissue, soft (ICRU four-component)

Table A.7. Continued

2.833E02 2.608E02 2.281E02 2.066E02 1.915E02 1.806E02 1.658E02 1.566E02 1.441E02 1.382E02

men/r (cm2 g1) 6.000E01 8.000E01 1.000Eþ00 1.250Eþ00 1.500Eþ00 2.000Eþ00 3.000Eþ00 4.000Eþ00 5.000Eþ00 6.000Eþ00 8.000Eþ00 1.000Eþ01 1.500Eþ01 2.000Eþ01

Energy (MeV) 8.705E02 7.643E02 6.872E02 6.145E02 5.593E02 4.798E02 3.847E02 3.290E02 2.923E02 2.664E02 2.324E02 2.112E02 1.829E02 1.695E02

m/r (cm2 g1)

WT1, ‘‘solid water’’

3.193E02 3.117E02 3.016E02 2.883E02 2.755E02 2.533E02 2.212E02 1.997E02 1.846E02 1.735E02 1.584E02 1.488E02 1.356E02 1.291E02

men/r (cm2 g1)

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

128

APPENDIX A: COMPILATION OF PHYSICAL DATA A.3 DIFFERENCE OF MASS STOPPING POWERS AND MASS ENERGY-ABSORPTION COEFFICIENTS OF A GIVEN MATERIAL FROM THAT OF WATER

129

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

130

APPENDIX A: COMPILATION OF PHYSICAL DATA

131

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

132

APPENDIX A: COMPILATION OF PHYSICAL DATA

133

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

134

APPENDIX A: COMPILATION OF PHYSICAL DATA

135

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

136

APPENDIX A: COMPILATION OF PHYSICAL DATA

137

DOSIMETRY OF BETA RAYS AND LOW-ENERGY PHOTONS FOR THERAPEUTIC APPLICATIONS

138