0
Neutrons-I
BASIC CONSTANTS
HANS
FOR NEUTRON
BICHSEL.
Department of Radiology. University
DOSIMETRYt
Ph.D.
of Washington,
Seattle. WA 98195, U.S.A.
Radiation quality is discussed briefly. Principles for the measurement of absorbed dose in tissue are discussed. Ionization chambers are considered as a suitable instrument for this purpose. The basic quantities needed are discussed: the energy W to form an ion pair, stopping power of gases and solids, and the response function for neutrons and photons. It is concluded that systematic uncertainties in absolute dose may exceed 10% due to a lack of adequate khowledge of all these quantities. Neutron dosimetry,
RADIATION
Radiation
QUALITY
AND
quality, Absorbed
dose, Ionization chambers.
QUANTITY
In describing the properties of ionizing radiation it is necessary to distinguish two aspects: quality and quantity. Radiation quality can be expressed in biological terms of relative effectiveness (e.g. the relative amount of energy required to produce a specific biologic end point) or in terms of physical properties, e.g. spectra of energy deposition events.’ The quantity “absorbed dose” is defined as the absolute amount of energy imparted by ionizing radiation to the matter in a small volume element expressed as energy per unit mass.” The clinical effects from radiation therapy with fractionated treatment plans can only be accurately predicted from clinical experience. However, a statement of physical or biological radiation quality is useful in predicting trends and in extrapolating expectations of effects from one type of radiation from experience with another. The obvious physical description of beam quality is given in terms of the secondary charged particle fluence spectrum,38 but the accurate determination of such spectra is extremely difficult at a point in a scattering medium. If it is desired to compare the quality of beams of different particles such as neutrons and pions for extrapolating expected effects from one to another, then it may be advantageous to describe not the secondary charged particle fluence spectra but the spectra of energy deposition events that they produce.” Measurements of event spectra +This investigation was supported by United States Public Health Research Grant CA-12441 from the National
by means of proportional counters may be acceptable and probably the easiest method for this purpose. In dosimetry of fast neutron beams the radiation quality is expressed only as an inference from a statement of the total absorbed dose and the component of that dose mediated by the photon component of the mixed beam whether present in the incident beam or generated by the neutrons in interactions with the absorbing medium. In a microdosimetric spectrum this simple division can readily be determined.6.7 A division into several dose fractions of increasing event size intervals would be more meaningful.19
ABSORBED
DOSE
IN TISSUE
For the measurement of absorbed dose, it is necessary to observe a radiation effect in a dosimeter material. This radiation effect then must be converted into absorbed dose in the material and this absorbed dose must be converted into dose in tissue. If we choose an absorber which is quite similar to tissue in its composition. the latter conversion is quite simple. The ideal dosimeter would be a calorimeter with a slice of ham as the sensitive element. The requirements for tissue similarity are fundamentally different for photons and charged particles and for neutrons and stopping pions. Photons and charged particles interact mainly with atomic electrons. Therefore dosimeters should have the same electron densities as Cancer Institute.
156
tissue
Radiation
Oncology
but the atomic composition
0
Biology
0
Physics
is relatively
unim-
portant.
be extremely valuable in order to evaluate possible systematic errors. For all dosimeters. calculations must be performed to determine the energy dependence of various factors used in the conversion of the observed effect (the “response”) into absorbed dose in tissue.
For neutrons and stopping pions. the energy deposition is primarily due to nuclear reactions. and it is thus important to have dosimeters with an atomic composition close to tissue. Thus, while a wide variety of instruments can be used for photon and charged particle dosimetry, the choice is much restricted for neutrons and pions. We find that calorimeters. chemical dosimeters and ionization chambers can readily be built from materials similar to tissue but, for example, TLD. solid state devices and BFx or ‘He ion chambers cannot be used very easily in this way. A major concern of dosimetry in radiation therapy is the precision and accuracy of the method. A number of instruments are not suitable for this type dosimetry, even though they could be made tissuesimilar (photographic emulsions, track detectors, long counters, MnS04 baths, etc.) because they are not accurate. For radiation therapy, absorbed dose must be determined accurately. For example, for certain biological systems. it is possible to determine RBE with an uncertainty of 5% or less. Therefore the physical measurements of absorbed dose must be much more accurate than this uncertainty. In general. we should try to determine a quantity which is used in subsequent operations or calculations with an uncertainty five to ten times smaller than the uncertainty required in the final result. Thus the absorbed dose in the above example should have an uncertainty of no more than 1%. Similarly, in radiation therapy, changes in treatment dose of the order of 5% have produced observable clinical effects.** Again, physical dose therefore should be obtained with an uncertainty of no more than 1%. Our measuring instrument thus should be capable of a precision of close to 0.1% and the absolute accuracy should be about 1%. This condition restricts dosimeters for neutron dosimetry to ion chambers and possibly calorimeters and chemical dosimeters. The latter two instruments are discussed by Dr. Bewley in the following article (p. 163). Here, only ionization chambers will be considered. Absorbed dose can be calculated with Kerma if the particle fluence is known. For monoenergetic neutrons. this method is potentially as accurate as the best of other methods?.’ Since this method is quite different from the instrumental methods described above, a comparison between the two methods will
v indicates which chamber is under discussion: ?D and “D the photon and neutron doses respectively; and the coefficients a and b indicate the sensitivity of the chamber to photons and neutrons respectively. Here, only the ratio azlb2 for the C-CO2 chamber will
*A major problem is the accurate determination of the fluence, especially for polyenergetic neutrons. For example, in a time of flight determination of the spectrum, edge effects in the scintillation detector are difficult to determine accurateiy.q Since they are energy dependent they will tend to distort the neutron spectrum.
SIf wall and gas have the same composition and the same stopping power (expressed in MeV cm*/@, D, = 0, according to the Fano principle. BFurther correction factors related to absorption of neutrons in the wall, geometrical effects. etc. will not be discussed here.
IONIZATION CHAMBERS In the following, ionization chambers will be examined in detail. In particular, the pair of chambers used by many therapy centers is used as an example: a chamber with walls of Shonka plastic, a volume of 1 cm’, filled with air or TE gas and a chamber with graphite walls, filled with CO*. The basic response of an ion chamber is described by equation (1): Dg = JWIm,
(1)
J is the observed quantity, the number of ion pairs collected in the chamber. The mass of the gas is m,, and W, the energy used to produce an ion pair, is the conversion factor needed to convert J into dose Dg absorbed in the gas. In the next step, Dg is converted into D,. the dose in the wall materiall:: Dw = C,D,
(2)
C, is the dose conversion factor. For an infinitesimal cavity, C, = S,JS,, where S, and S, are values of the stopping power averaged over the charged particle spectrum. For a finite cavity, it is necessary to make more refined calculations.” For neutrons, many of the secondary charged particles have very short ranges. Therefore, even a very small cavity (e.g. 0.1 cm3) cannot be considered to be infintesimal. Calculations must be made considering the origin of the particles, their slowing down in the wall and their atomic interactions with the gas. Particles produced in the gas also must be taken into account.4’ In the last step, dose D in tissue is calculated§: D = (KIK,)Dw
(3)
where K is Kerma of tissue, K,, that of wall material. For the paired chamber measurements, the following expression is used: J, = a,$+
b,,D
(4)
Basic constants
for neutron dosimetry 0 H.
BICHSEL
=t
be discussed.? In the following sections, our knowledge about W, Cw and adb2 will be discussed.
60
Pamcles
(I-
THE
ENERGY
W TO PRODUCE
AN ION
PAIR Our knowledge of W is quite incomplete. In particular, the energy dependence of W is not well established for any particle. Measurements have been made only recently for several particles in tissue equivalent gas. Results for protons are shown in Fig. 1. The discrepancy in the
measurements by Leonard and Boring3’ and by Chemtob et al.ls is especially striking. The data by Rohrig and Colvett39 show fairly small fluctuations and an energy dependence of about 1.5%. Considerable fluctuations in. W as a function of energy are seen in the measurements by Chemtob et al. On the other hand, for protons with energies between 0.2 and 0.55 MeV in mixed gases,4s with 2.4 d EIMeV I 7.6 in air24 and for 0.1 I EIMeV 5 0.9 in N243 the energy
dependence
amounted
to less than
2%.
55 Ii
’\ .
331 2 g
45
\
t
251 IO
. CH,
4c
20
60
.f.
50
1
??
\
48-
I
’ \
46
-
44
-
42
-
a -
‘0
\
f
\
?? . \ ??\
\
\
\
\
\
.
IO
20
40
For alpha particles, the measurements by Chemtob in TE gas disagree with the measurements by Mac-
Donald and Sidenius32 for CH4 (see Fig. 2). All measurements of W for a-particles in nitrogen are shown in Fig. 3. The % decrease in the value between 45 and 50 keV is especially remarkable. No measurements exist in the region between 50 and 270 keV, and 650-1000 keV. The discrepancy between the data of Jesse and Sadauski8 and those by Chap. unexplained. The smooth funcpell and Sparrow’4 is tion WleV = 34.66 + (2.043 - 0.416 In E)’
ElMeV) and WleV= 30.7/( 1 - 1.68/v/E) (E < 500 keV) are shown as solid lines. The discrepancy between the data for CH, and TE gas is remarkable. 0. MacDonald (1%9)32; 0, Chemtob (1977)15; A, Jesse (1%8)“.
42
with
IO4
103
100
10’
kcV
Fig. 3. Experimental values of W in N2 for a-particles of various energies. For Jesse’s data, the function WleV = 38.30- 1.1 In EIMeV is shown. No explanation for the discrepancy between the Jesse and the Chappell and Sparrow data has come to our attention. It should not be assumed that the value measured for E = 50 keV is incorrect. It is conceivable that, e.g. W = 38 eV at E = 100 keV. Similarly, the points between 0.25 and 0.65 MeV could indicate a complex dependence on W on energy. A straight line interpolation between adjacent points should be considered for any application. The function given by equation (5) is shown as a dashed line. 0, BoriT et al. (1%5)9; +, Scholler et al. (1%3)43; 0, Jesse (l%l) ; X, Chappell and sparrow (1%7)14.
to the experimental data. Still, the average deviation of the points from this curve is only +1.8%, if the value at 50 keV is excluded. For all other gases, even less is known energy dependence for a-particles.23 W values for heavier ions are shown
method see, e.g. Bichsel et aI.’
about in Fig.
the 4.
158
Radiation
Oncology
0 Biology
0 Physics
Fig. 4. W for carbon and oxygen ions in TE gas. E = energy (keV), A = atomic weight of ion. -, W/eV=39.55/(1 -0.426/v(E/keV)). The average deviation f of the experimental points from this function is 1.3%. -----, WleV = 44.31 - 1.45 ln(E/keV), t = 1.5%. Other two-parameter functions show larger values of t. approximates these data with . . . . . ., data for 0’ in CH,.‘* The function W/eV = 38.98/( 1 - 2.041/d(E/keV)) t < 0.4% for E 2 40keV. x. 0’ Leonard (1973)“: O,e, 0’ Chemtob (1977)‘-‘: + . 0’ Rohrig ( 1976)‘9; 0, C’ Carter (1%7)“: A, 0’ Varma (1977)“.
Again,
we find significant differences
between the data
of various authors. Two of our current assumptions about W therefore must be reexamined. These are: (a) W for particles with energies above about 3 MeV/u is energy-independent. (b) W for all particles high energies.
reaches
the same
value
for
The possibility that W for a given particle will fluctuate by several percent at high energies must be considered in all applications. Similarly, W for different particles may differ by several percent at a given particle velocity. For neutron dosimetry, the study by DennisI gives useful indications about the dependence on energy of effective W values for neutrons, but it will be necessary to perform further calculations of this type to establish the sensitivity of averaged W values for neutrons to the assumed energy dependence of W for various particles. For 2 MeV neutrons the average value of W for a-particles has been calculated for an
ionization chamber with walls of Shonka plastic filled with Nz, using (a) the function given by equation (.5), w = 38.39eV; or, (b) linear interpolation between adjoining points, @ = 38.06eV. The results thus differ by about l%t. tThe alpha particle spectrum used was a constant value for 0.88 5 EJMeV 5 1.70, and the large discrepancy at E, =
STOPPING
POWER S AND GAS-WALL CONVERSION COEFFICIENT C, Stopping powers are used extensively in the calculation of the dose conversion coefficients C, used in equation (2). It is very important to realize that the stopping power of a solid and of a gas of identical composition are not the same. The difference may amount to more than 10%.‘7~u~42*49*50 In a recent experiment, an even more unexpected effect has been demonstrated: the stopping power of alpha particles in graphite and in amorphous carbon is not the same.33 For protons, no measurements of the solidgas effect are available for energies exceeding 0.35 MeV. Current information about proton stopping power
is quite inadequate to permit a trustworthy calculation of an effective stopping power ratio for neutron dosimetry with tissue equivalent materials. Even for carbon there are considerable differences between various experiments (Fig. 5). It is instructive to consider the values of C’, calculated with a given set of stopping power data using various approximations of the energy deposition processes. Results for monoenergetic neutrons of energy E. are given in Table I. Calculations have been performed for an ion chamber with walls of 50 keV thus did not enter into the calculation.
Basic constants
E.
for neutron
dosimetry
0
H. BKHSEL
159
From Table 1 it is seen that no simple function of energy will connect the three approximations. Unexat the higher energies, the third appectedly, proximation differs less from the first one than does the second one. Further improvements in the calculations could be achieved by: (a) taking into account the center electrode; (b) including further particles in the calculation (d. II, Be, etc.); (c) consideration of delta rays. In addition, the values are in error by the errors of the assumed stopping power data (possibly 5-10%).
tvw
Fig. 5. The stopping power S of protons in carbon as a function of energy E. Some of the differences at low energies could be due to different states 0: the carbon.” Arkhipov (1969) : . . ., BerGstein (1970) ; --. Bichsel (1%8). : 0. Gorodetzky (1967) ; + Johansen (1971)**: x , Moorhead (1%5?‘: 0, Ormrod (1%3)37: A, Sautter (196Sp; Van Wijngaarden (1962)“. -1
RESPONSE
Table 1. Gas-wall dose conversion coefficient C, for 1 cm3 ionization chamber (Shonka plastic wall and air) (equation 2)
neath equation (4). Estimates of this value have been made4.29 based on equation (7)
Neutron
energy (MeV)
First approximation Second approximation Third approximation
14
9
s
2
1.189 1.267 1.238
1.198 1.263 1.221
1.212 1.274 1.250
1.247 1.316 1.415
Shonka plastic, filled with air at 1 atm. The stopping power tables are based on the data given by Northcliffe and Schilling,% using the Bragg rule for Shonka plastic. The first approximation is the one used in current literature:ti the recoil protons with an energy spectrum between 0 and En are assumed to have an energy E,/2. The slowing down of the protons in the wall material is assumed to reduce the energy to the value the protons have at l/2 of their range.? The contribution by all other particles is neglected. For the second approximation: I
N,(E)S,(E)dEI
I
N,(E)S,(E)dE
NEUTRONS
AND
An ionization chamber with graphite walls, filled with CO2, is relatively insensitive to neutrons. The ratio of the sensitivities b/a has been defined under-
b/a
Preliminary results for a 6 cm’ chamber indicate an increase of 1.5% in C, at 14MeV.
C, =
FUNCTION FOR PHOTONS
=-
where p is the mass photons y (t = tissue, neutrons n (equation made as a function
,cww,df)lCL(W)
(7)
.cwwn KIKW
energy absorption coefficient for w = wall). and K the Kerma for 3). Calculations of b/a have been of neutron energy E. with the
03
02 b/b
P--___.
(6)
where N,(E) is the slowing down spectrum in the wall of the charged particles produced by the neutr0ns.S In the third approximation, the energy deposition in a spherical cavity of volume V is calculateds.‘2~‘3~4’ for protons, a-particles and C. N and 0 recoils.
Fig. 6. The ratio b/a for the response of an ionization chamber with graphite walls, filled with COz gas for neutrons and photons as a function of neutron energy E. The solid line is drawn to connect the values calculated at discrete points.*’ The single value at 8 MeV has been given by Bewley et aLJ The dashed line was measured by Kuchnir et 01.‘~
*For E. = 14 MeV. the average energy of recoil protons is 7 MeV. The range of 7 MeV protons is 65 mg/cm*. The energy of protons with range 32.5 mglcm’ is 4.6 MeV. Thus the ratio S shonLd (4.6 MeV)/Sai, (4.6 MeV) is used as the first ap-
proximation of C,,. SSince the cavity is assumed to be infinitesimal, particles are produced in the gas.
no charged
Radiation Oncology 0 Biology 0 Physics
160
following
simplifying
assumptions:
photon energy 1. ,cw = 1.00 2. p(t)Ip(w) = 1.10 I be 2 MeV of E,,. 3. W,,/ W, = 1.10, independent
assumed
to
getic neutrons were assumed. If the average value of b/a for a neutron spectrum were to be calculated. the exact shape of the spectrum clearly would influence
that value strongly.
The energy conversion factor .Cw for neutrons has been calculated for E,, = 2. 5. 9 and 14 MeV:’ values for other energies were obtained by linear interpolation. Errors of up to 10% may be caused by this approach . For Kerma, the data for carbon and muscle from ICRU No. 13” were used. Results are shown in Fig. 6, and other data are given for comparison. The remarkably large fluctuations of the calculated function are explained by the fact that strictly monoener-
CONCLUSIONS
For heavy particle radiations. it is very important to describe quality and quantity of the dose. It is suggested that microdosimetric measurements be used for the former. For the measurement of total dose, ionization chambers may be the most suitable instruments. Inadequate knowledge of W values and stopping power functions may cause errors of up to 10% for heavy particle dosimetry.
REFERENCES 1. Arkhipov, E.P., Gott, Y.V.: Slowing down of 0.530 keV protons in some materials. Soo. Phys.J.E.T.P. 29: 615-618, 1%9. 2. Barschall, H.H., Goldberg, E.: Response of tissue equivalent ionization chamber to 15 MeV neutrons. Med. Phys. 4: 141-144, 1977. 3. Bernstein, E., Cole, A.J., Wax, R.L.: Penetration of l-20 keV ions through thin carbon films. NIM 90: 325328, 1970. 4. Bewley, D.K., McCullough, E.C., Page, B.C., Sakata, S.: Determination of absorbed dose in a fast neutron beam by ionization and calorimetric methods. 1st Symp. on Neutron Dosimetry in Biology and Medicine. EUR48% dfe, 1972, pp. 159-173. Radiation 5. Bichsel, H.: Charged particle interactions. Dosimetry, 2nd Edn, ed. by Attix, Roesch., New York, Academic Press, 1%8, Chap. 4. 6. Bichsel, H.: Considerations concerning neutron dosimetry. 2nd Symp. on Neutron Dosimetry in Biology and Medicine, EUR-5273, 1974, pp. 191-225. 7. Bichsel, H., Eenmaa, J., Weaver, K.A., Wootton. P.:
Dosimetry of mixed radiation fields. Int. Symp. on 8.
9.
10.
11.
12. 13. 14.
Advances in Biomedical Dosimetry. IAEA, Vienna, IAEA SM-193178, 1975. Bichsel, H., Rubach, A., Jessen, K.: Calculation of stopping power ratios for spherical 1 cm’ ionization chambers. Basic physical data for neutron dosimetry, EUR-5629, 1976, pp. 121-126. Boring, J.W., Strohl, G.E., Woods, F.R.: Total ionization in nitrogen by heavy ions of energies 25-50 keV. Phys. Rev. 140: A1065-1069, 1965. Burlin, T.E.: Cavity-chamber theory. Radiation Dosimetry, 2nd Edn, ed. by Attix, Roesch. New York. Academic Press, 1%8, Chap. 8. Carter, B.J.: Average energy expenditure per ion pair for 0.8 MeV carbon and nitrogen recoils. Phys. Med. Biol. 12: 321-331, 1%7. Caswell, R.S.: Deposition of energy by neutrons in spherical cavities. Radiat. Res. 27: 92-107, 1%6. Caswell, R.S., Coyne. J.J.: Interaction of neutrons and secondary charged particles with tissue: secondary particle spectra. Radiat. Res. 52: 448-470, 1972. Chappell. S.E., Sparrow, J.H.: The average energy required to produce an ion pair in A. N and air for l-5 MeV a particles. Radiat. Res. 32: 383-403. 1%7.
15. Chemtob, M., Noel. J.P.. Lavigne. B., Nguyen, V.D.. Parmentier, N.C.: Some experimental results of Wvalues for heavy particles. Phys Med. Biol. 22: 208-218, 1977. 16. Dennis, J.A.: Computed ionization and Kerma values in neutron irradiated gases. Phys. Med. Biol. 18: 379-395. 1973. 17. Geary, M.J., Haque, A.K.M.M.: The stopping power and straggling for a-particles in tissue equivalent materials. Nucl. Instrum. Meth. 137: 151-155, 1976. 18. Gorodetzky, S.. Chevallier, A., Pape, A., Cl. Sens, J.. Bergdolt, A.M., Bres, M.. Armbruster, R.: Mesure des pouvoirs d’arrCt de C, Ca, Au and CaF2 pour des protons d’energie comprise entre 0.4 et 6 MeV. Nucl. Phvs. A91: 133-144, 1967. 19. Heintz, P.H., Robkin, M.A., Wootton, P., Bichsel, H.: In phantom microdosimetry with 14.6 MeV neutrons. Hfth Phys. 21: 598-602, 1971. 20. ICRU No. 11, Radiation Quantities and Units. Int. Comm. on Radiation Units and Measurements, 7910 Woodmont Ave., Wash., D.C. 20014, U.S.A. 21. ICRU No. 13, Neutron Fluence, Neutron Spectra and Kerma. Int. Comm. on Radiation Units and Measurements, 7910 Woodmont Ave., Wash., D.C. 20014, U.S.A. 22. ICRU No. 24, Determination of Absorbed Dose in a Patient Irradiated by Beams of X- or y-Rays in Radiotherapy Procedures. Int. Comm. on Radiation Units and
Measurements, 7910 Woodmont Ave., Wash., D.C. 20014, U.S.A. 33. ICRU, Report on W to be published. 24. Jentschke. W.: Messungen an harten H-Strahlen. Physikalische 2. 41: 524-528,
1940.
25. Jesse, W.P., Sadauskis, J.: Ionization by a-particles in mixtures of gases. Phys. Reo. 100: 1755-1762. 1955. 26. Jesse, W.P.: a-particle ionization in polyatomic gases and the energy dependence of W. Phys. Rev. 122: 1195-1202. l%l. 27. Jesse, W.P.: a-particle ionization in A-methane mixtures and the energy dependence of the ion pair formation energy. Phys. Rec. 174: 173-177, 1%8. 28. Johansen, A.. Steenstrup, S.. Wohlenberg, T.: Energy loss of protons in thin films of carbon, aluminum and silver. Radiat. Eflects 8: 31-32, 1971. 29. Kuchnir. F.T.. Vyborny. C.J.. Skaggs. L.S.: A precise
Basic constants for neutron dosimetry 0
30. 31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
method for measuring the neutron response of a “neutron-insensitive” dosimeter. Int. Symp. on Advances in Biomedical Dosimetry. IAEA, Vienna. IAEA SM193/51. 1975. Larson, H.V.: Energy loss per ion pair for protons in various gases. Phys. Rev. 112: 1927-1928. 1958. Leonard.3.E.. Boring, J.W.: The average energy per ion pair W for hydrogen and oxygen ions in a tissue equivalent gas. Radial. Res. 55: l-9. 1973. MacDonald, J.R.. Sidenius, G.: The total ionization in methane of ions with 1 5 z 5 22 at energies from 10 to 120keV. Phys. Lett. 28A: 543, 1%9. Matteson. S., Chau. E.K.L., Powers, D.: Stopping cross section of bulk graphite for a-particles. Phys. Rev. A14: 169-175. 1976. Meckbach, W.. Allison. S.K.: Ratio of the effective charge of He beams traversing gaseous and metallic cadmium. Phys. Rev. 132. 294-304. 1963. Moorhead, R.D.: Stopping cross section of low atomic number materials for He’. 65-180 keV. .I. Appl. Phys. 36: 391-395, 1%5. Northcliffe, L.C., Schilling, R.F.: Range and stopping power tables for heavy ions. Nucl. Data Tables A7: 233-463. 1970. Ormrod, J.H., Duckworth, H.E.: Stopping cross sections in carbon for low-energy atoms with z 5 12. Can. J. Phys. 41: 1424-1442, 1%3. Roesch, W.C.: Mathematical theory of radiation fields. In Radiation Dosimetry, 2nd Edn, ed. by Attix, Roesch. New York, Academic Press, 1968, Chap. 5. Rohrig, N., Colvett. R.D.: Experimental Determinations of @. Radiat. Res. Sot. 24th Ann. Sci. Meet., San Francisco, 1976 (Abstract). Rossi, H.H.: Microscopic energy distribution in irradiated matter. In Radiation Dosimetry, 2nd Edn, ed. by Attix, Roesch. New York, Academic Press, 1%8, Chap. 2.
H. BKHSEL
161
41. Rubach, A.H.: Calculation of neutron dose absorbed in spherical ionization chambers with finite cavity size. Master’s Thesis, University of Washington, Seattle, Washington, U.S.A., 1976. 42. Sautter. C.A., Zimmerman, E.J.: Stopping cross sections of carbon and hydrocarbon solids for low-energy protons and helium ions. Phys. Rev. 140: A49&A498, 1965. 43. Schaller, L.. Huber, P., Baumgartner, E. Messung der Arbeit pro Ionenpaar in Stickstoff fur Protonen und He-ionen im Energiegebiet unterhalb 1 MeV. Helv. Phys. Acta 36: 113-131, 1963. 44. Smith, A.R., Almond, P.R., Smathers, J.B., Otte, V.A., Attix, F.H., Theus, R.B., Wootton, P., Bichsel, H., Eenmaa. J., Williams, D., Bewley, D.K., Parnell, C.J.: intercomparisons between fast-neutron Dosimetry radiotherapy facilities. Med. Phys. 2: 195-200, 1975. 45. Tunnicliffe, P.R., Ward, A.G.: The relative ionization produced by low energy protons, deutrons and a-particles in various gases. Proc. Phys. Sot. A65: 233-240, 1952. 46. Van Wijngaarden, A., Duckworth, H.E.: Energy loss in condensed matter of ‘H and *He in the energy range 4 < E < 30 keV. Can .I. Phys. 40: 1749-1764, 1%2. 47. Varma, M.N ., Baum, J.W., Kuehner, A.V.: Radial dose, LET and W for I60 ions in nitrogen and tissue equivalent gases. BNL-21753, Radiat Res. 70: 51 l-518, 1977. 48. Watson, J.W., Graves, R.G.: Finite size effects in neutron detectors. Nucl. Instrum. Meth. 117: 541-549, 1974. 49. Williamson, J., Watt, D.E.: The influence of molecular binding on stopping power of a-particles in hydrocarbons. Phys. Med. Biol. 17: 486-492. 1972. 50. Whillock, M.J., Edwards, A.A.: The stopping powers of ethylene and polyethylene for a-particles with energies below 5 MeV. Basic physical data for neutron dosimetry, EUR-5629, 1976, pp. 115-120.
Neutrons-I
BASIC CONSTANTS
HANS
FOR NEUTRON
BICHSEL.
Department of Radiology. University
DOSIMETRYt
Ph.D.
of Washington,
Seattle. WA 98195, U.S.A.
Radiation quality is discussed briefly. Principles for the measurement of absorbed dose in tissue are discussed. Ionization chambers are considered as a suitable instrument for this purpose. The basic quantities needed are discussed: the energy W to form an ion pair, stopping power of gases and solids, and the response function for neutrons and photons. It is concluded that systematic uncertainties in absolute dose may exceed 10% due to a lack of adequate khowledge of all these quantities. Neutron dosimetry,
RADIATION
Radiation
QUALITY
AND
quality, Absorbed
dose, Ionization chambers.
QUANTITY
In describing the properties of ionizing radiation it is necessary to distinguish two aspects: quality and quantity. Radiation quality can be expressed in biological terms of relative effectiveness (e.g. the relative amount of energy required to produce a specific biologic end point) or in terms of physical properties, e.g. spectra of energy deposition events.’ The quantity “absorbed dose” is defined as the absolute amount of energy imparted by ionizing radiation to the matter in a small volume element expressed as energy per unit mass.” The clinical effects from radiation therapy with fractionated treatment plans can only be accurately predicted from clinical experience. However, a statement of physical or biological radiation quality is useful in predicting trends and in extrapolating expectations of effects from one type of radiation from experience with another. The obvious physical description of beam quality is given in terms of the secondary charged particle fluence spectrum,38 but the accurate determination of such spectra is extremely difficult at a point in a scattering medium. If it is desired to compare the quality of beams of different particles such as neutrons and pions for extrapolating expected effects from one to another, then it may be advantageous to describe not the secondary charged particle fluence spectra but the spectra of energy deposition events that they produce.” Measurements of event spectra +This investigation was supported by United States Public Health Research Grant CA-12441 from the National
by means of proportional counters may be acceptable and probably the easiest method for this purpose. In dosimetry of fast neutron beams the radiation quality is expressed only as an inference from a statement of the total absorbed dose and the component of that dose mediated by the photon component of the mixed beam whether present in the incident beam or generated by the neutrons in interactions with the absorbing medium. In a microdosimetric spectrum this simple division can readily be determined.6.7 A division into several dose fractions of increasing event size intervals would be more meaningful.19
ABSORBED
DOSE
IN TISSUE
For the measurement of absorbed dose, it is necessary to observe a radiation effect in a dosimeter material. This radiation effect then must be converted into absorbed dose in the material and this absorbed dose must be converted into dose in tissue. If we choose an absorber which is quite similar to tissue in its composition. the latter conversion is quite simple. The ideal dosimeter would be a calorimeter with a slice of ham as the sensitive element. The requirements for tissue similarity are fundamentally different for photons and charged particles and for neutrons and stopping pions. Photons and charged particles interact mainly with atomic electrons. Therefore dosimeters should have the same electron densities as Cancer Institute.
156
tissue
Radiation
Oncology
but the atomic composition
0
Biology
0
Physics
is relatively
unim-
portant.
be extremely valuable in order to evaluate possible systematic errors. For all dosimeters. calculations must be performed to determine the energy dependence of various factors used in the conversion of the observed effect (the “response”) into absorbed dose in tissue.
For neutrons and stopping pions. the energy deposition is primarily due to nuclear reactions. and it is thus important to have dosimeters with an atomic composition close to tissue. Thus, while a wide variety of instruments can be used for photon and charged particle dosimetry, the choice is much restricted for neutrons and pions. We find that calorimeters. chemical dosimeters and ionization chambers can readily be built from materials similar to tissue but, for example, TLD. solid state devices and BFx or ‘He ion chambers cannot be used very easily in this way. A major concern of dosimetry in radiation therapy is the precision and accuracy of the method. A number of instruments are not suitable for this type dosimetry, even though they could be made tissuesimilar (photographic emulsions, track detectors, long counters, MnS04 baths, etc.) because they are not accurate. For radiation therapy, absorbed dose must be determined accurately. For example, for certain biological systems. it is possible to determine RBE with an uncertainty of 5% or less. Therefore the physical measurements of absorbed dose must be much more accurate than this uncertainty. In general. we should try to determine a quantity which is used in subsequent operations or calculations with an uncertainty five to ten times smaller than the uncertainty required in the final result. Thus the absorbed dose in the above example should have an uncertainty of no more than 1%. Similarly, in radiation therapy, changes in treatment dose of the order of 5% have produced observable clinical effects.** Again, physical dose therefore should be obtained with an uncertainty of no more than 1%. Our measuring instrument thus should be capable of a precision of close to 0.1% and the absolute accuracy should be about 1%. This condition restricts dosimeters for neutron dosimetry to ion chambers and possibly calorimeters and chemical dosimeters. The latter two instruments are discussed by Dr. Bewley in the following article (p. 163). Here, only ionization chambers will be considered. Absorbed dose can be calculated with Kerma if the particle fluence is known. For monoenergetic neutrons. this method is potentially as accurate as the best of other methods?.’ Since this method is quite different from the instrumental methods described above, a comparison between the two methods will
v indicates which chamber is under discussion: ?D and “D the photon and neutron doses respectively; and the coefficients a and b indicate the sensitivity of the chamber to photons and neutrons respectively. Here, only the ratio azlb2 for the C-CO2 chamber will
*A major problem is the accurate determination of the fluence, especially for polyenergetic neutrons. For example, in a time of flight determination of the spectrum, edge effects in the scintillation detector are difficult to determine accurateiy.q Since they are energy dependent they will tend to distort the neutron spectrum.
SIf wall and gas have the same composition and the same stopping power (expressed in MeV cm*/@, D, = 0, according to the Fano principle. BFurther correction factors related to absorption of neutrons in the wall, geometrical effects. etc. will not be discussed here.
IONIZATION CHAMBERS In the following, ionization chambers will be examined in detail. In particular, the pair of chambers used by many therapy centers is used as an example: a chamber with walls of Shonka plastic, a volume of 1 cm’, filled with air or TE gas and a chamber with graphite walls, filled with CO*. The basic response of an ion chamber is described by equation (1): Dg = JWIm,
(1)
J is the observed quantity, the number of ion pairs collected in the chamber. The mass of the gas is m,, and W, the energy used to produce an ion pair, is the conversion factor needed to convert J into dose Dg absorbed in the gas. In the next step, Dg is converted into D,. the dose in the wall materiall:: Dw = C,D,
(2)
C, is the dose conversion factor. For an infinitesimal cavity, C, = S,JS,, where S, and S, are values of the stopping power averaged over the charged particle spectrum. For a finite cavity, it is necessary to make more refined calculations.” For neutrons, many of the secondary charged particles have very short ranges. Therefore, even a very small cavity (e.g. 0.1 cm3) cannot be considered to be infintesimal. Calculations must be made considering the origin of the particles, their slowing down in the wall and their atomic interactions with the gas. Particles produced in the gas also must be taken into account.4’ In the last step, dose D in tissue is calculated§: D = (KIK,)Dw
(3)
where K is Kerma of tissue, K,, that of wall material. For the paired chamber measurements, the following expression is used: J, = a,$+
b,,D
(4)
Basic constants
for neutron dosimetry 0 H.
BICHSEL
=t
be discussed.? In the following sections, our knowledge about W, Cw and adb2 will be discussed.
60
Pamcles
(I-
THE
ENERGY
W TO PRODUCE
AN ION
PAIR Our knowledge of W is quite incomplete. In particular, the energy dependence of W is not well established for any particle. Measurements have been made only recently for several particles in tissue equivalent gas. Results for protons are shown in Fig. 1. The discrepancy in the
measurements by Leonard and Boring3’ and by Chemtob et al.ls is especially striking. The data by Rohrig and Colvett39 show fairly small fluctuations and an energy dependence of about 1.5%. Considerable fluctuations in. W as a function of energy are seen in the measurements by Chemtob et al. On the other hand, for protons with energies between 0.2 and 0.55 MeV in mixed gases,4s with 2.4 d EIMeV I 7.6 in air24 and for 0.1 I EIMeV 5 0.9 in N243 the energy
dependence
amounted
to less than
2%.
55 Ii
’\ .
331 2 g
45
\
t
251 IO
. CH,
4c
20
60
.f.
50
1
??
\
48-
I
’ \
46
-
44
-
42
-
a -
‘0
\
f
\
?? . \ ??\
\
\
\
\
\
.
IO
20
40
For alpha particles, the measurements by Chemtob in TE gas disagree with the measurements by Mac-
Donald and Sidenius32 for CH4 (see Fig. 2). All measurements of W for a-particles in nitrogen are shown in Fig. 3. The % decrease in the value between 45 and 50 keV is especially remarkable. No measurements exist in the region between 50 and 270 keV, and 650-1000 keV. The discrepancy between the data of Jesse and Sadauski8 and those by Chap. unexplained. The smooth funcpell and Sparrow’4 is tion WleV = 34.66 + (2.043 - 0.416 In E)’
ElMeV) and WleV= 30.7/( 1 - 1.68/v/E) (E < 500 keV) are shown as solid lines. The discrepancy between the data for CH, and TE gas is remarkable. 0. MacDonald (1%9)32; 0, Chemtob (1977)15; A, Jesse (1%8)“.
42
with
IO4
103
100
10’
kcV
Fig. 3. Experimental values of W in N2 for a-particles of various energies. For Jesse’s data, the function WleV = 38.30- 1.1 In EIMeV is shown. No explanation for the discrepancy between the Jesse and the Chappell and Sparrow data has come to our attention. It should not be assumed that the value measured for E = 50 keV is incorrect. It is conceivable that, e.g. W = 38 eV at E = 100 keV. Similarly, the points between 0.25 and 0.65 MeV could indicate a complex dependence on W on energy. A straight line interpolation between adjacent points should be considered for any application. The function given by equation (5) is shown as a dashed line. 0, BoriT et al. (1%5)9; +, Scholler et al. (1%3)43; 0, Jesse (l%l) ; X, Chappell and sparrow (1%7)14.
to the experimental data. Still, the average deviation of the points from this curve is only +1.8%, if the value at 50 keV is excluded. For all other gases, even less is known energy dependence for a-particles.23 W values for heavier ions are shown
method see, e.g. Bichsel et aI.’
about in Fig.
the 4.
158
Radiation
Oncology
0 Biology
0 Physics
Fig. 4. W for carbon and oxygen ions in TE gas. E = energy (keV), A = atomic weight of ion. -, W/eV=39.55/(1 -0.426/v(E/keV)). The average deviation f of the experimental points from this function is 1.3%. -----, WleV = 44.31 - 1.45 ln(E/keV), t = 1.5%. Other two-parameter functions show larger values of t. approximates these data with . . . . . ., data for 0’ in CH,.‘* The function W/eV = 38.98/( 1 - 2.041/d(E/keV)) t < 0.4% for E 2 40keV. x. 0’ Leonard (1973)“: O,e, 0’ Chemtob (1977)‘-‘: + . 0’ Rohrig ( 1976)‘9; 0, C’ Carter (1%7)“: A, 0’ Varma (1977)“.
Again,
we find significant differences
between the data
of various authors. Two of our current assumptions about W therefore must be reexamined. These are: (a) W for particles with energies above about 3 MeV/u is energy-independent. (b) W for all particles high energies.
reaches
the same
value
for
The possibility that W for a given particle will fluctuate by several percent at high energies must be considered in all applications. Similarly, W for different particles may differ by several percent at a given particle velocity. For neutron dosimetry, the study by DennisI gives useful indications about the dependence on energy of effective W values for neutrons, but it will be necessary to perform further calculations of this type to establish the sensitivity of averaged W values for neutrons to the assumed energy dependence of W for various particles. For 2 MeV neutrons the average value of W for a-particles has been calculated for an
ionization chamber with walls of Shonka plastic filled with Nz, using (a) the function given by equation (.5), w = 38.39eV; or, (b) linear interpolation between adjoining points, @ = 38.06eV. The results thus differ by about l%t. tThe alpha particle spectrum used was a constant value for 0.88 5 EJMeV 5 1.70, and the large discrepancy at E, =
STOPPING
POWER S AND GAS-WALL CONVERSION COEFFICIENT C, Stopping powers are used extensively in the calculation of the dose conversion coefficients C, used in equation (2). It is very important to realize that the stopping power of a solid and of a gas of identical composition are not the same. The difference may amount to more than 10%.‘7~u~42*49*50 In a recent experiment, an even more unexpected effect has been demonstrated: the stopping power of alpha particles in graphite and in amorphous carbon is not the same.33 For protons, no measurements of the solidgas effect are available for energies exceeding 0.35 MeV. Current information about proton stopping power
is quite inadequate to permit a trustworthy calculation of an effective stopping power ratio for neutron dosimetry with tissue equivalent materials. Even for carbon there are considerable differences between various experiments (Fig. 5). It is instructive to consider the values of C’, calculated with a given set of stopping power data using various approximations of the energy deposition processes. Results for monoenergetic neutrons of energy E. are given in Table I. Calculations have been performed for an ion chamber with walls of 50 keV thus did not enter into the calculation.
Basic constants
E.
for neutron
dosimetry
0
H. BKHSEL
159
From Table 1 it is seen that no simple function of energy will connect the three approximations. Unexat the higher energies, the third appectedly, proximation differs less from the first one than does the second one. Further improvements in the calculations could be achieved by: (a) taking into account the center electrode; (b) including further particles in the calculation (d. II, Be, etc.); (c) consideration of delta rays. In addition, the values are in error by the errors of the assumed stopping power data (possibly 5-10%).
tvw
Fig. 5. The stopping power S of protons in carbon as a function of energy E. Some of the differences at low energies could be due to different states 0: the carbon.” Arkhipov (1969) : . . ., BerGstein (1970) ; --. Bichsel (1%8). : 0. Gorodetzky (1967) ; + Johansen (1971)**: x , Moorhead (1%5?‘: 0, Ormrod (1%3)37: A, Sautter (196Sp; Van Wijngaarden (1962)“. -1
RESPONSE
Table 1. Gas-wall dose conversion coefficient C, for 1 cm3 ionization chamber (Shonka plastic wall and air) (equation 2)
neath equation (4). Estimates of this value have been made4.29 based on equation (7)
Neutron
energy (MeV)
First approximation Second approximation Third approximation
14
9
s
2
1.189 1.267 1.238
1.198 1.263 1.221
1.212 1.274 1.250
1.247 1.316 1.415
Shonka plastic, filled with air at 1 atm. The stopping power tables are based on the data given by Northcliffe and Schilling,% using the Bragg rule for Shonka plastic. The first approximation is the one used in current literature:ti the recoil protons with an energy spectrum between 0 and En are assumed to have an energy E,/2. The slowing down of the protons in the wall material is assumed to reduce the energy to the value the protons have at l/2 of their range.? The contribution by all other particles is neglected. For the second approximation: I
N,(E)S,(E)dEI
I
N,(E)S,(E)dE
NEUTRONS
AND
An ionization chamber with graphite walls, filled with CO2, is relatively insensitive to neutrons. The ratio of the sensitivities b/a has been defined under-
b/a
Preliminary results for a 6 cm’ chamber indicate an increase of 1.5% in C, at 14MeV.
C, =
FUNCTION FOR PHOTONS
=-
where p is the mass photons y (t = tissue, neutrons n (equation made as a function
,cww,df)lCL(W)
(7)
.cwwn KIKW
energy absorption coefficient for w = wall). and K the Kerma for 3). Calculations of b/a have been of neutron energy E. with the
03
02 b/b
P--___.
(6)
where N,(E) is the slowing down spectrum in the wall of the charged particles produced by the neutr0ns.S In the third approximation, the energy deposition in a spherical cavity of volume V is calculateds.‘2~‘3~4’ for protons, a-particles and C. N and 0 recoils.
Fig. 6. The ratio b/a for the response of an ionization chamber with graphite walls, filled with COz gas for neutrons and photons as a function of neutron energy E. The solid line is drawn to connect the values calculated at discrete points.*’ The single value at 8 MeV has been given by Bewley et aLJ The dashed line was measured by Kuchnir et 01.‘~
*For E. = 14 MeV. the average energy of recoil protons is 7 MeV. The range of 7 MeV protons is 65 mg/cm*. The energy of protons with range 32.5 mglcm’ is 4.6 MeV. Thus the ratio S shonLd (4.6 MeV)/Sai, (4.6 MeV) is used as the first ap-
proximation of C,,. SSince the cavity is assumed to be infinitesimal, particles are produced in the gas.
no charged
Radiation Oncology 0 Biology 0 Physics
160
following
simplifying
assumptions:
photon energy 1. ,cw = 1.00 2. p(t)Ip(w) = 1.10 I be 2 MeV of E,,. 3. W,,/ W, = 1.10, independent
assumed
to
getic neutrons were assumed. If the average value of b/a for a neutron spectrum were to be calculated. the exact shape of the spectrum clearly would influence
that value strongly.
The energy conversion factor .Cw for neutrons has been calculated for E,, = 2. 5. 9 and 14 MeV:’ values for other energies were obtained by linear interpolation. Errors of up to 10% may be caused by this approach . For Kerma, the data for carbon and muscle from ICRU No. 13” were used. Results are shown in Fig. 6, and other data are given for comparison. The remarkably large fluctuations of the calculated function are explained by the fact that strictly monoener-
CONCLUSIONS
For heavy particle radiations. it is very important to describe quality and quantity of the dose. It is suggested that microdosimetric measurements be used for the former. For the measurement of total dose, ionization chambers may be the most suitable instruments. Inadequate knowledge of W values and stopping power functions may cause errors of up to 10% for heavy particle dosimetry.
REFERENCES 1. Arkhipov, E.P., Gott, Y.V.: Slowing down of 0.530 keV protons in some materials. Soo. Phys.J.E.T.P. 29: 615-618, 1%9. 2. Barschall, H.H., Goldberg, E.: Response of tissue equivalent ionization chamber to 15 MeV neutrons. Med. Phys. 4: 141-144, 1977. 3. Bernstein, E., Cole, A.J., Wax, R.L.: Penetration of l-20 keV ions through thin carbon films. NIM 90: 325328, 1970. 4. Bewley, D.K., McCullough, E.C., Page, B.C., Sakata, S.: Determination of absorbed dose in a fast neutron beam by ionization and calorimetric methods. 1st Symp. on Neutron Dosimetry in Biology and Medicine. EUR48% dfe, 1972, pp. 159-173. Radiation 5. Bichsel, H.: Charged particle interactions. Dosimetry, 2nd Edn, ed. by Attix, Roesch., New York, Academic Press, 1%8, Chap. 4. 6. Bichsel, H.: Considerations concerning neutron dosimetry. 2nd Symp. on Neutron Dosimetry in Biology and Medicine, EUR-5273, 1974, pp. 191-225. 7. Bichsel, H., Eenmaa, J., Weaver, K.A., Wootton. P.:
Dosimetry of mixed radiation fields. Int. Symp. on 8.
9.
10.
11.
12. 13. 14.
Advances in Biomedical Dosimetry. IAEA, Vienna, IAEA SM-193178, 1975. Bichsel, H., Rubach, A., Jessen, K.: Calculation of stopping power ratios for spherical 1 cm’ ionization chambers. Basic physical data for neutron dosimetry, EUR-5629, 1976, pp. 121-126. Boring, J.W., Strohl, G.E., Woods, F.R.: Total ionization in nitrogen by heavy ions of energies 25-50 keV. Phys. Rev. 140: A1065-1069, 1965. Burlin, T.E.: Cavity-chamber theory. Radiation Dosimetry, 2nd Edn, ed. by Attix, Roesch. New York. Academic Press, 1%8, Chap. 8. Carter, B.J.: Average energy expenditure per ion pair for 0.8 MeV carbon and nitrogen recoils. Phys. Med. Biol. 12: 321-331, 1%7. Caswell, R.S.: Deposition of energy by neutrons in spherical cavities. Radiat. Res. 27: 92-107, 1%6. Caswell, R.S., Coyne. J.J.: Interaction of neutrons and secondary charged particles with tissue: secondary particle spectra. Radiat. Res. 52: 448-470, 1972. Chappell. S.E., Sparrow, J.H.: The average energy required to produce an ion pair in A. N and air for l-5 MeV a particles. Radiat. Res. 32: 383-403. 1%7.
15. Chemtob, M., Noel. J.P.. Lavigne. B., Nguyen, V.D.. Parmentier, N.C.: Some experimental results of Wvalues for heavy particles. Phys Med. Biol. 22: 208-218, 1977. 16. Dennis, J.A.: Computed ionization and Kerma values in neutron irradiated gases. Phys. Med. Biol. 18: 379-395. 1973. 17. Geary, M.J., Haque, A.K.M.M.: The stopping power and straggling for a-particles in tissue equivalent materials. Nucl. Instrum. Meth. 137: 151-155, 1976. 18. Gorodetzky, S.. Chevallier, A., Pape, A., Cl. Sens, J.. Bergdolt, A.M., Bres, M.. Armbruster, R.: Mesure des pouvoirs d’arrCt de C, Ca, Au and CaF2 pour des protons d’energie comprise entre 0.4 et 6 MeV. Nucl. Phvs. A91: 133-144, 1967. 19. Heintz, P.H., Robkin, M.A., Wootton, P., Bichsel, H.: In phantom microdosimetry with 14.6 MeV neutrons. Hfth Phys. 21: 598-602, 1971. 20. ICRU No. 11, Radiation Quantities and Units. Int. Comm. on Radiation Units and Measurements, 7910 Woodmont Ave., Wash., D.C. 20014, U.S.A. 21. ICRU No. 13, Neutron Fluence, Neutron Spectra and Kerma. Int. Comm. on Radiation Units and Measurements, 7910 Woodmont Ave., Wash., D.C. 20014, U.S.A. 22. ICRU No. 24, Determination of Absorbed Dose in a Patient Irradiated by Beams of X- or y-Rays in Radiotherapy Procedures. Int. Comm. on Radiation Units and
Measurements, 7910 Woodmont Ave., Wash., D.C. 20014, U.S.A. 33. ICRU, Report on W to be published. 24. Jentschke. W.: Messungen an harten H-Strahlen. Physikalische 2. 41: 524-528,
1940.
25. Jesse, W.P., Sadauskis, J.: Ionization by a-particles in mixtures of gases. Phys. Reo. 100: 1755-1762. 1955. 26. Jesse, W.P.: a-particle ionization in polyatomic gases and the energy dependence of W. Phys. Rev. 122: 1195-1202. l%l. 27. Jesse, W.P.: a-particle ionization in A-methane mixtures and the energy dependence of the ion pair formation energy. Phys. Rec. 174: 173-177, 1%8. 28. Johansen, A.. Steenstrup, S.. Wohlenberg, T.: Energy loss of protons in thin films of carbon, aluminum and silver. Radiat. Eflects 8: 31-32, 1971. 29. Kuchnir. F.T.. Vyborny. C.J.. Skaggs. L.S.: A precise
Basic constants for neutron dosimetry 0
30. 31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
method for measuring the neutron response of a “neutron-insensitive” dosimeter. Int. Symp. on Advances in Biomedical Dosimetry. IAEA, Vienna. IAEA SM193/51. 1975. Larson, H.V.: Energy loss per ion pair for protons in various gases. Phys. Rev. 112: 1927-1928. 1958. Leonard.3.E.. Boring, J.W.: The average energy per ion pair W for hydrogen and oxygen ions in a tissue equivalent gas. Radial. Res. 55: l-9. 1973. MacDonald, J.R.. Sidenius, G.: The total ionization in methane of ions with 1 5 z 5 22 at energies from 10 to 120keV. Phys. Lett. 28A: 543, 1%9. Matteson. S., Chau. E.K.L., Powers, D.: Stopping cross section of bulk graphite for a-particles. Phys. Rev. A14: 169-175. 1976. Meckbach, W.. Allison. S.K.: Ratio of the effective charge of He beams traversing gaseous and metallic cadmium. Phys. Rev. 132. 294-304. 1963. Moorhead, R.D.: Stopping cross section of low atomic number materials for He’. 65-180 keV. .I. Appl. Phys. 36: 391-395, 1%5. Northcliffe, L.C., Schilling, R.F.: Range and stopping power tables for heavy ions. Nucl. Data Tables A7: 233-463. 1970. Ormrod, J.H., Duckworth, H.E.: Stopping cross sections in carbon for low-energy atoms with z 5 12. Can. J. Phys. 41: 1424-1442, 1%3. Roesch, W.C.: Mathematical theory of radiation fields. In Radiation Dosimetry, 2nd Edn, ed. by Attix, Roesch. New York, Academic Press, 1968, Chap. 5. Rohrig, N., Colvett. R.D.: Experimental Determinations of @. Radiat. Res. Sot. 24th Ann. Sci. Meet., San Francisco, 1976 (Abstract). Rossi, H.H.: Microscopic energy distribution in irradiated matter. In Radiation Dosimetry, 2nd Edn, ed. by Attix, Roesch. New York, Academic Press, 1%8, Chap. 2.
H. BKHSEL
161
41. Rubach, A.H.: Calculation of neutron dose absorbed in spherical ionization chambers with finite cavity size. Master’s Thesis, University of Washington, Seattle, Washington, U.S.A., 1976. 42. Sautter. C.A., Zimmerman, E.J.: Stopping cross sections of carbon and hydrocarbon solids for low-energy protons and helium ions. Phys. Rev. 140: A49&A498, 1965. 43. Schaller, L.. Huber, P., Baumgartner, E. Messung der Arbeit pro Ionenpaar in Stickstoff fur Protonen und He-ionen im Energiegebiet unterhalb 1 MeV. Helv. Phys. Acta 36: 113-131, 1963. 44. Smith, A.R., Almond, P.R., Smathers, J.B., Otte, V.A., Attix, F.H., Theus, R.B., Wootton, P., Bichsel, H., Eenmaa. J., Williams, D., Bewley, D.K., Parnell, C.J.: intercomparisons between fast-neutron Dosimetry radiotherapy facilities. Med. Phys. 2: 195-200, 1975. 45. Tunnicliffe, P.R., Ward, A.G.: The relative ionization produced by low energy protons, deutrons and a-particles in various gases. Proc. Phys. Sot. A65: 233-240, 1952. 46. Van Wijngaarden, A., Duckworth, H.E.: Energy loss in condensed matter of ‘H and *He in the energy range 4 < E < 30 keV. Can .I. Phys. 40: 1749-1764, 1%2. 47. Varma, M.N ., Baum, J.W., Kuehner, A.V.: Radial dose, LET and W for I60 ions in nitrogen and tissue equivalent gases. BNL-21753, Radiat Res. 70: 51 l-518, 1977. 48. Watson, J.W., Graves, R.G.: Finite size effects in neutron detectors. Nucl. Instrum. Meth. 117: 541-549, 1974. 49. Williamson, J., Watt, D.E.: The influence of molecular binding on stopping power of a-particles in hydrocarbons. Phys. Med. Biol. 17: 486-492. 1972. 50. Whillock, M.J., Edwards, A.A.: The stopping powers of ethylene and polyethylene for a-particles with energies below 5 MeV. Basic physical data for neutron dosimetry, EUR-5629, 1976, pp. 115-120.
