Author's Accepted Manuscript

Analysis of neutron scattering components inside a room with concrete walls Rahim Khabaz

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S0969-8043(14)00332-7 http://dx.doi.org/10.1016/j.apradiso.2014.09.009 ARI6773

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Applied Radiation and Isotopes

Received date: 28 May 2014 Revised date: 3 September 2014 Accepted date: 12 September 2014 Cite this article as: Rahim Khabaz, Analysis of neutron scattering components inside a room with concrete walls, Applied Radiation and Isotopes, http://dx.doi.org/ 10.1016/j.apradiso.2014.09.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Analysis of neutron scattering components inside a room with concrete walls Rahim Khabaz Physics Department, Faculty of Sciences, Golestan University Gorgan, Iran, Postal code: 49138-15739 E-mail: [email protected]; [email protected] Abstract This paper describes the scattering corrections needed when neutron detectors are calibrated with a neutron point source at the center of a calibration room. The independence of scattering value from the geometric shape of the room was studied, which for more confidence in this case, two sets of rooms with same inner surface area were evaluated. The parameters that relate the air scattering part (A) and room-return part (R) with the additional contribution from scattered neutrons have been calculated for neutrons whose energy goes from 10-8 to 20 MeV. These parameters were calculated using Monte Carlo method for 150, 200, 300, 407, 500, 800 and 1000 cm-radius spherical cavity containing air. In the calculations, monoenergetic neutron sources were placed at the center of cavity, and then neutron fluences were determined at several distances of source to detector along the spherical cavity radius. The parameter R has been fitted as a function of surface area (or radius) of spherical room, and the related coefficient has been calculated for 16 monoenergetic neutron sources. It may produce a reasonable estimate (with difference < 10 %) for the contribution of walls scattering in any geometry of a calibration room.

Keywords: Scattering factor; Room-return; Air scattering; Monte Carlo

Introduction In practical neutron measurements, the detector responds to both direct neutrons that came directly from a neutron source and scattered neutrons that came from surrounding materials. The contribution of scattered neutrons to the response of detector can be significant, so that in some situations, the detector’s response can be completely dominated by the scattered neutrons [Eisenhauer, 1992; Vega-Carrillo et al., 2007; Sílvia et al., 2012; Nakamura, 2003]. To avoid this situation, the neutron calibration facility ideally should be in a vacuum and free of any neutron scattering surfaces; however, this is impossible in practice. Neutron detector calibrations are typically performed with both the source and detector at a certain height above the ground of

calibration room. In such a configuration, neutrons scattered from the walls and, to a lesser extent, from air nuclei, contribute to the detector response. These scattered neutrons have different spectrum and a different variation with distance from the source [Khabaz and Miri, 2011a, 2011b]. Then, they must not be considered a proper part of the calibration field but should rather be considered a type of background. Therefore, in calibration of detector, a correction for scattering should be made [ISO 8529, 2000]. For an isotropic point source and a point detector in a large evacuated space, the product M×d2 is a constant, where M is the dead-time corrected count rate of the detector, induced by the source at a separation distance d. A general functional relationship for the detector reading in open geometry, M(d), at a separation distance between the neutron source and detector, d, is given by [Kluge et al., 1990] M (d )

R)

B

ª F1 (d ) ˜ exp(6d )  F2' (d )  1º ¼ 4S d ¬ 2

(1)

where R is the detector efficiency or fluence response of the instrument; B is the source strength at the time of the measurement; F1(d) is the geometry correction factor (represents the additional number of neutrons entering a device compared with an irradiation by a plane-parallel beam) [Khabaz, 2013; Khabaz, 2014]; the exponential term takes into account the attenuation of the direct incident neutrons by the air between the source and the detector;  is the linear attenuation coefficient of air obtained by averaging the total neutron cross sections of all nuclei of air over the neutron energy distribution of the source; F2' (d ) is the additional contribution from inscattered neutrons. There are many techniques that have been used to evaluate scattering corrections necessary for proper calibration of neutron instruments. These can generally be grouped into two categories. The first involves measurement of the total response to all neutrons followed by measurement of the scattered contribution by a shadow cone placed between the source and detector. This detector response can then be subtracted from the response measured with no shadow cone, to obtain the response from neutrons coming directly from the source [ISO 10647, 1996; Khabaz and Miri, 2011c; Mirzajani et al., 2013]. In other techniques, one measures only the total response to all neutrons. A combination of calculations and subsidiary measurements is then used to correct the observed response to a response from source neutrons alone [Liu et al., 1990].

For isotropically emitting neutron sources at, or near the center of a calibration room, the contribution to the instrument reading due to scattered by the walls should be approximately constant in the vicinity of the source [Dietze et al., 1972], and that the air-inscattered component should be inversely proportional to the separation distance [Eisenhauer et al., 1982; Eisenhauer et al., 1987]. Hunt [Hunt, 1984] combined these two relationships, then proposed that the inscattering correction, F2' (d ) , can be written as F2' ( d ) 1  AI d  R d 2

(2)

where Rd2 is the fractional component due to neutrons reflected by the surfaces of the calibration room. The term AId is the fractional component due to neutrons inscattered by the air throughout the calibration room. In Eq. (1), for a point-like detector F1(d)=1, and by expanding exp(-d) for small values of d to first order only, then this equation can be rewritten as M (d )

R)

B 4S d 2

F2 (d )

(3)

with F2 ( d ) 1  A d  R d 2

(4)

where A

AI  6

(5)

Then, term Ad represents the net air-scattering effect. A series of measurements of total count rate as a function of the separation distance, d, corrected for any geometry effects [Khabaz, 2013; Khabaz, 2014], can be mathematically fitted to a second-order polynomial function of d using the least square technique. From this analysis, both the air-scattered component, A, and the room-scattered component, R, may be obtained. During calibration of neutron measuring instruments, the instrument readout must be corrected for neutrons scattered by different items such as source holder, calibration room walls, and air scattering. From all these factors, the room-return neutron is the factor with larger influence; therefore it is important to establish a reliable procedure to estimate its influence [Hertel et al., 2004; Vega-Carrillo et al., 2007b]. The purpose of this study was to investigate the accuracy of Eq. (4) by Monte Carlo calculation to determine the features of A and R values. Thus, several calculations have been performed to

transport neutrons inside seven different sizes of spherical rooms using 16 monoenergetic neutrons whose energy goes from 108 to 20 MeV, in the aim to determine the behavior of A and R values in terms of neutron energy, source to detector distance (d), and room size. To take into account the presence of air, the calculations were carried out including air in the rooms. McCall et al. [McCall et al., 1999] have devised a method for estimating the epicadmium neutron fluence due to room scattering, which is independent of room shape, detection position, and source neutron energy. In the present work, the treatment of A and R values on the room shape also was evaluated. The results of calculations in this study can be applied to assessment the scattering value from a neutron source in a concrete room with certain dimensions.

Materials and methods In order to perform numerical calculations, a 100 cm thick concrete spherical room was modeled using Monte Carlo radiation transport code MCNP4C [Briesmeister, 2000]. The concrete density was 2.35 g/cm3 whose elemental composition was 0.6 % H, 50.0 % O, 1.7 % Na, 4.8 % Al, 31.5 % Si, 1.9% K, 8.3 % Ca and 1.2 % Fe [Harmon et al., 1994]. In the simulation, a point-like neutron source was placed at the center of the spherical room, and detectors were located at different distances from the source until a point located near the room inner surface. The calculations were performed up to reasonable histories ( 107), which provide an acceptable statistical error (< 1%). Seven different sizes of spherical room containing air were simulated whose inner radii (rsp) are 150, 200, 300, 407, 500, 800 and 1000 cm. Air features were, dry, near sea level, with density of 1.205 kg/m3, which its element concentration was considered as 79.1 % N and 20.9 % O. The isotropic neutron source was assumed to be at the geometrical center of room, and detector at variable distances along the spherical cavity radius. These distances are listed in Table 1 for each room. For each situation, the total fluence due to direct and scattered neutrons was calculated using tally F5. The calculations were also made for cubical and rectangular parallelepiped cavities whose total inner surface area was equal to two spherical rooms, i.e., with radii of 406.84 and 800 cm. For spherical room with radius of 406.84 cm, the dimensions of cubical and rectangular parallelepiped rooms were 588.78 cm × 588.78 cm × 588.78 cm and 800 cm × 600 cm × 400 cm, respectively. The corresponding dimensions were also as 1157.76 cm × 1157.76 cm × 1157.76

cm and 1530.63 cm × 1200 cm × 800 cm, for spherical cavity with radius of 800 cm. These simulations were carried out to evaluate whether the contribution of scattering is independent of room geometric shape, and is only dependent to the surface area of calibration room. To study the contribution of air scattering, other calculations were performed for 407 cm radius spherical cavity with and without air. By calculating the ratio of the total neutron fluence to the direct fluence for each d, the scattering correction factor F2(d) is obtained. Then, by fitting these values as a function of d based on Eq. (4), one can determine the A and R parameters for each neutron energy and room size.

Results and discussion For investigating dependency or independency of the contribution of neutron scattering from the geometric shape of calibration room, the Monte Carlo calculations were made for two sets of rooms having equal inner surface area using 4 monoenergetic neutrons whose energy goes from 108 to 20 MeV. Figure 1 shows the comparison of the total, scattered and direct neutron fluences at different source to detector distances (d) in spherical (rsp=4.07 m), cubical (5.89 m × 5.89 m × 5.89 m) and rectangular parallelepiped (8 m × 6 m × 4 m) rooms, which inner surface area (S) of rooms is 208 m2. Figure 2 also shows the corresponding results for different sizes of spherical (rsp=8 m), cubical (11.58 m × 11.58 m × 11.58 m) and rectangular parallelepiped (15.31 m × 12 m × 8 m) rooms with inner surface area of 804.25 m2. As it can be seen, the direct neutron components decrease according to 1/d2 and the scattered neutron components is approximately constant in all positions of room for each neutron energy. The contribution of scattering is dependent to the inner surface area of room, and is also approximately independent to the geometric shape of it. The largest difference is for places where the detector is close to the wall with relative differences less than 15%, while for other points are less than 8%. For evaluating the contribution of air scattering relative to the contribution of walls scattering, in another simulation, the total neutron fluence was calculated at different distances from the neutron source inside a 407 cm-radius sphere containing air. Figure 3 shows the difference of the contribution of room scattering and air scattering for four neutron energies inside this room. The highest contribution of air scattering was for neutrons with energy of 10-8 MeV and in short d.

To compare the variations in the contribution of scattering, results of different neutron energies as representative samples are plotted for the smallest and largest room radii. Figs. 4 and 5 show the total, scattered, and direct neutron fluences inside 150 and 1000 cm-radius concrete rooms for 16 monoenergetic neutrons, respectively. It can be noticed that the total or scattered neutron fluence depends on the neutron energy. The maximum and minimum contributions of scattering are for 10-2 MeV and 10-8 MeV, respectively. Inside seven sizes of concrete cavity, the ratio of scattered neutron fluence to the direct neutron fluence was calculated at different distances for 16 monoenergetic neutron sources. The results for each room size were fitted based on Eq. (4), and parameters A and R of the F2(d) were obtained for different values of neutron energy in the range of 10-8 to 20 MeV. An example fitting to get parameters A and R shows in the Fig. 6 for neutrons with energy of 10-2 MeV inside 500 cm-radius concrete room. The quantified values of parameters A and R are listed in Tables 2 and 3, respectively. Additionally, the energy dependency of these parameters is shown in Figs. 7 and 8. As it can be observed in Table 2 and Fig. 7, most of the values for parameter A are negative. According to the Eq. (5), this means that the fractional component due to neutron inscattering by the air throughout the calibration room is less than the contribution of neutron outscatering due solely to the air between the source and detector; however, for energies of 10-8 and 1.0 MeV in some rooms, this parameter is positive, and inscattered part by the air is larger than outscattered part. According to the Table 3 and Fig. 8, for any energy the value of parameter R decreases with the increase of room radius. This is because of decreasing the room-return fraction by increasing the room size. During this work, it was observed that the parameter R could be well fitted as a function of spherical room area or radius by the following equation R

P

B S

K

B rsp2

(6)

where, P and K are coefficient; B is the neutron source strength; and S is the total inner surface area in the room. It should be noted that the MCNP calculations are normalized to one neutron of source, then this fitting is performed for B=1.

For example, the correlation of the parameter R with the radius of spherical concrete room is plotted in Fig. 9 for neutrons with energy of 1.0 MeV. The results of coefficient K are given in Table 4 and Fig. 10 for each monoenergetic neutron source. It can be seen that this coefficient has a maximum in 10-2 MeV, which it is due to have a higher scattering contribution in this energy. As an example of the quality of the fitting, the total neutron fluences were calculated using Eq. (6) and interpolated coefficient listed in Table 4, for an arbitrarily chosen spherical room radius (rsp=600 cm), which was not previously calculated by MCNP code with several monoenergetic neutron sources. Figure 11 compares the resulting total neutron fluence from Eq. (6) and Monte Carlo calculation for a few energies inside a 600 cm-radius room without air. It can be seen that the Eq. (6) fits the calculated data well, while differences are less than 10 % over the whole energy range. Then, use of the Eqs. (4) and (6) may produce a reasonable initial estimate for the contribution of walls scattering in any size of a spherical room. Furthermore, based on independence of room-return scattering from the room geometric shape (Figs. 1 and 2), these equations can be applied for any calibration room having an inner surface area equal to the area of a specific spherical cavity. In other words, the radius of this spherical cavity, which has the same surface area with an actual room, is calculated using

rsp

1 2

1

S

¦ ai

(7)

i

where ai is the surface area of the ith surface inside the room. The common number of surfaces of a room is six, four walls, one ceiling, and one floor. Conclusions

A number of Monte Carlo calculations have been carried out to evaluate the total neutron fluence rate produced by those neutrons emitted by the neutron source located at the center of several concrete wall spherical cavities. The neutrons emitted by the source collide with the concrete walls, and after suffering collisions are returned to the detector. The room-return neutrons are practically independent of the source to detector distance; however, this behavior tends to change when the observation point is near the wall surface. It is concluded from the comparison of the results of calculation by MCNP4C for the two sets of rooms having same inner surface area and different geometric shapes, which for each neutron

energy, the contribution of scattering is independent of the source to detector distance and also approximately independent of the room shape. The contribution of air scattering for most cases of room size and neutron energy is as an outscattering effect, and causes to reduce the neutron fluence at the measurement point. The parameter R, related to the scattering due to neutron reflected by the surfaces of the calibration room, decreases with increasing the room size. This parameter has an inverse relation with the inner surface area of room. Therefore, the parameter R has been fitted as a function of surface area (or radius) of spherical room, and the related coefficient has been calculated for 16 monoenergetic neutron sources. Because of reasonable difference (less than 10 %) between the total neutron fluences obtained from Monte Carlo calculations and the fitted formula, the suggested equations (Eqs. (4) and (6)) can be as a good initial estimate to determine the contribution of scattering in any geometry of calibration room, and to have an appropriate design of calibration setup. It must be noticed that, it was assumed a point-like source and detector in these calculations, and then the contribution of scattering was evaluated; however, the neutron source holder and detection setup can have size and impact on the scattering contribution. The dimensions of detection system can be also considered in the final simulation of calibration process.

References

Briesmeister, J.F., 2000. MCNP-A general Monte Carlo N-particle transport code, Version 4C. Los Alamos National Laboratory Report LA-13709-M. Dietze, G., Jahr, R., Scholermann, H., 1972. Effect of neutron background on the standardization of Neutron fields. Publications of the PTB-section 6.5, ib. Vol. II, 915-929. Eisenhauer, C.M., Schwartz, R.B., Johnson, T., 1982. Measurement of neutrons reflected from the surfaces of a calibration room. Health Phys. 42, 489–495. Eisenhauer, C.M., Schwartz, R.B., McCall, R.C., 1987. Effect of air scatter on calibration of instruments for detecting neutrons. Radiat. Prot. Dosim. 19, 77-84. Eisenhauer, C.M., 1992. Two-component analytical model to calculate roomreturn correction for calibration of neutron instruments. Radiat. Prot. Dosim. 42, 267–277. Harmon, Ch.D., Busch, R.D., Briestmeister, J.F. and Forster, R.A. 1994. Criticality calculations with MCNPTM: a primer. Los Alamos National Laboratory Report LA-12827-M.

Hertel, N.E., Shannon, M.P., Wang, Z.L., Valezano, M.P., Mengesha, W., Crowe, R.J., 2004. Neutron measurements in the vicinity of a self-shielded PET cyclotron. Radiat. Prot. Dosim. 108, 255–261. Hunt, J.B., 1984. The calibration of neutron sensitive spherical devices. Radiat. Prot. Dosim. 8, 239 251. ISO, 1996. Procedure for calibrating and determining the response of neutron-measuring devices used for radiation protection purposes. International Standard ISO 10647. International Organization for Standardization, Geneva. ISO, 2000. Reference neutron radiations-part 2: calibration fundamentals of radiation protection devices related to the basic quantities characterizing the radiation field. International Standard ISO 8529-2, International Organization for Standardization, Geneva. Khabaz, R., Miri, H., 2011a. Development of a Bonner sphere spectrometer with emphasis on decreasing the contribution of scattering by using a new designed shadow cone. J Radioanal. Nucl. Chem. 289, 789–794. Khabaz, R., Miri, H., 2011b. Measurement of neutron spectrum with multi-sphere using BF3 and evaluation of scattering effect on spectrum. Nucl. Technol. Radiat. Prot. 26,140–146. Khabaz, R., Miri, H., 2011c. Determination of 241Am–Be spectra using Bonner sphere spectrometer by applying shadow cone technique in calibration. J. Appl. Sci. 11, 2849–2854. Khabaz, R., 2013. Examining the departure in response of non-point detectors due to non uniform illumination and displacement of effective center. Nucl. Instrum. Methods. A 728, 145149. Khabaz, R., 2014. Investigation of the effects of beam divergence on the response of neutron voluminous detectors. J. Radioanal. Nucl. Chem. 300, 911-917. Kluge, H., Weise, K., Hunt, J.B., 1990. Calibration of neutron sensitive spherical devices with bare and D2O-moderated 252Cf sources in rooms of different sizes. Radiat. Prot. Dosim. 32, 233–244. Liu, J.C., Hajnal, F., Sims, C.S., Kuiper, J., 1990. Neutron spectral measurements at ORNL. Radiat. Prot. Dosim. 30, 169-178. McCall, R.C., McGinley, P.H., Huffman, K.E., 1999. Room scattered neutrons. Med. Phys. 26, 206–207. Mirzajani, N., Ciolini, R., Curzio, G. 2013. Analysis of the application of the shadow cone technique for the determination of neutron spectrum with Bonner sphere spectrometer. Nucl. Instrum. Methods A 722, 24-28.

Nakamura, T., 2003. Recent development of advanced neutron detection technology. J. Nucl. Radiochem. Sci. 4, 15–24. Sílvia, B.S., Gallego, E., Lorente, A., Gonçalves, I.F., Vaz, P., Vega-Carrillo, H.R., 2012. Dosimetric assessment and characterisation of the neutron field around a Howitzer container using a Bonner sphere spectrometer, Monte Carlo simulations and the NSDann and NSDUAZ unfolding codes. Radiat. Prot. Dosim. 154, 346-355. Vega-Carrillo, H.R., Manzanares-Acuña, E., Iñiguez, M.P., Gallego, E., Lorente, A., 2007a. Study of room-return neutrons. Radiat. Meas. 42, 413–419. Vega-Carrillo, H.R., Manzanares-Acuña, E., Iñiguez, M.P., Gallego, E., Lorente, A., 2007b. Spectrum of isotopic neutron sources inside concrete wall spherical cavities. Radiat. Meas. 42, 1373-1379. Figure and table captions by page:

Page 4: Table 1 Spherical room size and distances of source to detector for each. Page 5: Fig. 1. Comparison of the total, scattered and direct neutron fluences at different distances in three geometric shapes of room (S=208 m2) for four neutron energies (to prevent clutter, the results of En=1.0 MeV and En=20 MeV have been multiplied by factors of 3 and 20, respectively). Page 5: Fig. 2. Comparison of the total, scattered and direct neutron fluences at different distances in three geometric shapes of room (S=804.25 m2) for four neutron energies (to prevent clutter, the results of En=1.0 MeV and En=20 MeV have been multiplied by factors of 3 and 20, respectively). Page 6: Fig. 3. Comparison of the scattering fluence inside a 407 cm-radius spherical room with and without air for four neutron energies. Page 6: Fig. 4. Total (T), scattered (S) and direct neutron fluences at different source to detector distances for several neutron energies (MeV), inside 150 cm-radius concrete room. Page 6: Fig. 5. Total (T), scattered (S) and direct neutron fluences at different source to detector distances for several neutron energies (MeV), inside 1000 cm-radius concrete room.

Page 7: Fig. 6. A typical fitting plot representing the F2(d) as a function of d (Eq. (4)) for neutrons with energy of 10-2 MeV inside 500 cm-radius concrete room. Page 7: Table 2 Parameter A of the Eq. (4) for the best fit of the calculated fractional component of scattering versus the source to detector distance (d), for the different monoenergetic neutron sources inside seven spherical rooms. Page 7: Table 3 Parameter R of the Eq. (4) for the best fit of the calculated fractional component of scattering versus the source to detector distance (d), for the different monoenergetic neutron sources inside seven spherical rooms.

Page 7: Fig. 7. Parameter A of the F2(d) versus the neutron source energy for different spherical cavities.

Page 7: Fig. 8. Parameter R of the F2(d) versus the neutron source energy for different spherical cavities.

Page 8: Fig. 9. Correlation between the parameter R with the radius of spherical concrete room for neutrons with energy of 1.0 MeV.

Page 8: Table 4 Interpolated coefficient K of Eq. (6) for the calculated room-return parameter R versus room radius or room surface area. Page 8: Fig. 10. Coefficient values of K as a function of neutron energy. Page 8: Fig. 11. Comparison of the total neutron fluences obtained from MCNP calculation and Eq. (6) for four neutron energies inside 600 cm-radius concrete room (to prevent clutter, the results of En=10-6 MeV and En=2.0 MeV have been multiplied by factors of 4 and 5, respectively). 



Spherical room radius (cm) 150 200 300 407 500 800 1000

Source to detector distance (cm) 10, 20, 40, 50, 80, 100, 125, 140 10, 20, 40, 50, 80, 100, 125, 150, 175, 190 10, 20, 40, 50, 80, 100, 125, 150, 200, 250, 290 10, 20, 40, 50, 80, 100, 125, 150, 200, 250, 280, 300, 350, 380 10, 20, 40, 50, 80, 100, 125, 150, 200, 250, 300, 350, 400, 450, 490 10, 20, 40, 50, 80, 100, 125, 150, 200, 250, 300, 350, 400, 450, 500, 550, 650, 790 10, 50, 100, 150, 200, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 850, 950, 990

 Energ y (MeV)

rsp=1 50 cm

Erro r

1.00E08

9.40 E-04

2.90 E04

1.00E07

1.43 E-03

5.00 E04

1.00E06

1.96 E-03

6.30 E04

1.00E05

2.35 E-03

7.20 E04

1.00E04

2.67 E-03

8.40 E04

1.00E03

2.83 E-03

9.00 E04

1.00E02

2.72 E-03

8.30 E04

5.00E01

2.09 E-03

6.70 E04

1.00E +00

5.10 E-04

1.40 E04

1.50E +00

1.70 E-03

4.60 E04

rsp =20 0 cm 7.30 E04 1.15 E03 1.57 E03 1.83 E03 2.11 E03 2.33 E03 2.23 E03 1.28 E03 4.10 E04 1.41 E03

Erro r

1.80 E04 3.50 E04 4.40 E04 5.00 E04 5.70 E04 6.30 E04 6.10 E04 3.20 E04 1.20 E04 3.50 E04

rsp =30 0 cm 3.60 E04 6.50 E04 9.30 E04 1.16 E03 1.33 E03 1.45 E03 1.33 E03 6.80 E04 1.60 E04 8.60 E04

Erro r

rsp =407 cm

Erro r

rsp =500 cm

Erro r

rsp =800 cm

1.10 E04

1.00 E-04

2.00 E05

6.00 E-05

1.50 E05

+8.00 E-05

2.00 E05

+9.00 E-05

2.00 E05

2.20 E04

3.50 E-04

1.10 E04

3.40 E-04

1.10 E04

1.70 E-04

5.00 E05

9.00 E-05

2.00 E05

2.70 E04

5.80 E-04

1.70 E04

6.00 E-04

1.70 E04

3.00 E-04

8.00 E05

2.30 E-04

7.00 E05

3.40 E04

6.90 E-04

1.90 E04

7.50 E-04

2.30 E04

3.60 E-04

1.00 E04

3.20 E-04

9.00 E05

3.80 E04

8.30 E-04

2.20 E04

8.40 E-04

2.40 E04

4.00 E-04

1.10 E04

4.30 E-04

1.10 E04

4.30 E04

8.90 E-04

2.30 E04

8.10 E-04

2.20 E04

3.90 E-04

1.00 E04

3.80 E-04

9.00 E05

3.70 E04

7.70 E-04

2.10 E04

7.40 E-04

2.10 E04

4.00 E-04

1.00 E04

2.80 E-04

7.00 E05

1.70 E04

4.60 E-04

1.10 E04

5.30 E-04

1.40 E04

1.80 E-04

4.00 E05

2.00 E-04

5.00 E05

4.00 E05

+1.00 E-04

2.00 E05

+9.00 E-05

2.50 E06

+1.60 E-04

4.00 E05

+1.60 E-04

4.00 E05

2.20 E04

5.80 E-04

1.40 E04

6.00 E-04

1.80 E04

3.60 E-04

9.00 E05

2.70 E-04

5.00 E05

Erro r

rsp =100 0 cm

Erro r

2.00E +00

1.16 E-03

4.10 E04

3.00E +00

1.35 E-03

3.40 E04

5.00E +00

4.10 E-04

1.10 E04

1.00E +01

4.00 E-04

1.10 E04

1.48E +01

8.00 E-04

2.40 E04

2.00E +01

5.20 E-04

1.70 E04

9.30 E04 1.05 E03 3.30 E04 4.40 E04 5.80 E04 3.20 E04

2.90 E04 2.20 E04 8.00 E05 1.00 E04 1.70 E04 1.10 E04

6.10 E04 6.90 E04 2.00 E04 3.30 E04 3.90 E04 2.60 E04

2.00 E04

3.50 E-04

1.00 E04

3.60 E-04

9.00 E05

2.60 E-04

7.00 E05

1.50 E-04

4.00 E05

1.60 E04

4.50 E-04

1.00 E04

3.50 E-04

7.00 E05

2.60 E-04

5.00 E05

2.40 E-04

5.00 E05

5.00 E05

9.00 E-05

2.00 E05

1.00 E-04

3.00 E05

6.00 E-05

1.50 E05

3.00 E-05

7.00 E06

1.00 E04

1.40 E-04

4.00 E05

1.90 E-04

4.00 E05

1.30 E-04

3.00 E05

1.30 E-04

3.00 E05

1.20 E04

2.40 E-04

7.00 E05

2.30 E-04

6.00 E05

1.60 E-04

4.00 E05

1.40 E-04

3.00 E05

7.00 E05

1.90 E-04

5.00 E05

1.40 E-04

4.00 E05

1.30 E-04

3.00 E05

7.00 E-05

2.00 E05

rsp =10 00 cm 2.18 E-06 3.27 E-06 5.15 E-06 7.38 E-06 9.72 E-06 1.00 E-05 1.00 E-05 1.00 E-05 1.00 E-05 9.09 E-06 8.00 E-06 6.41 E-06 2.78 E-06 3.63 E-06 3.29 E-06

 Energy (MeV)

rsp=1 50 cm

Erro r

rsp =20 0 cm

Erro r

rsp =30 0 cm

Erro r

rsp =40 7 cm

Erro r

rsp =50 0 cm

Erro r

rsp =80 0 cm

Erro r

1.00E08 1.00E07 1.00E06 1.00E05 1.00E04 1.00E03 1.00E02 5.00E01 1.00E+ 00 1.50E+ 00 2.00E+ 00 3.00E+ 00 5.00E+ 00 1.00E+ 01 1.48E+ 01

1.00 E-04 1.50 E-04 2.30 E-04 3.30 E-04 4.30 E-04 5.10 E-04 5.70 E-04 5.20 E-04 4.30 E-04 3.70 E-04 3.20 E-04 2.50 E-04 1.10 E-04 1.40 E-04 1.30 E-04

3.32 E-06 4.28 E-06 5.32 E-06 6.16 E-06 7.18 E-06 7.61 E-06 7.04 E-06 5.69 E-06 2.42 E-06 3.93 E-06 3.48 E-06 2.86 E-06 9.58 E-07 2.77 E-06 2.03 E-06

6.00 E-05 8.00 E-05 1.30 E-04 1.90 E-04 2.40 E-04 2.90 E-04 3.30 E-04 2.60 E-04 2.50 E-04 2.10 E-04 1.90 E-04 1.50 E-04 6.00 E-05 8.00 E-05 7.00 E-05

1.80 E-06 2.22 E-06 2.78 E-06 3.16 E-06 3.58 E-06 4.01 E-06 3.89 E-06 2.01 E-06 1.57 E-06 1.95 E-07 1.86 E-06 1.41 E-06 5.37 E-07 1.56 E-06 1.07 E-06

3.00 E-05 4.00 E-05 6.00 E-05 8.00 E-05 1.10 E-04 1.30 E-04 1.50 E-04 1.20 E-04 1.10 E-04 1.00 E-04 9.00 E-05 7.00 E-05 3.00 E-05 4.00 E-05 3.00 E-05

7.56 E-07 9.48 E-07 1.17 E-06 1.46 E-06 1.61 E-06 1.82 E-06 1.60 E-06 7.37 E-07 7.21 E-07 9.36 E-07 8.50 E-07 6.70 E-07 2.22 E-07 8.22 E-07 5.18 E-07

1.00 E-05 2.00 E-05 3.00 E-05 4.00 E-05 6.00 E-05 7.00 E-05 8.00 E-05 6.00 E-05 6.00 E-05 5.00 E-05 5.00 E-05 4.00 E-05 2.00 E-05 2.00 E-05 2.00 E-05

3.09 E-07 4.24 E-07 5.62 E-07 6.19 E-07 7.24 E-07 7.50 E-07 6.91 E-07 3.69 E-07 2.98 E-07 4.50 E-07 3.37 E-07 3.33 E-07 8.62 E-08 2.76 E-07 2.12 E-07

8.85 E-06 1.00 E-05 2.00 E-05 3.00 E-05 4.00 E-05 5.00 E-05 5.00 E-05 4.00 E-05 4.00 E-05 4.00 E-05 3.00 E-05 2.00 E-05 1.00 E-05 1.00 E-05 1.00 E-05

2.26 E-07 3.26 E-07 4.25 E-07 5.69 E-07 6.14 E-07 5.55 E-07 5.24 E-07 3.57 E-07 2.31 E-07 4.50 E-07 2.37 E-07 1.66 E-07 6.82 E-08 2.40 E-07 1.56 E-07

3.37 E-06 5.19 E-06 8.10 E-06 1.00 E-05 1.00 E-05 2.00 E-05 2.00 E-05 2.00 E-05 2.00 E-05 1.00 E-05 1.00 E-05 9.86 E-06 4.35 E-06 5.60 E-06 5.08 E-06

7.85 E-08 1.26 E-07 1.54 E-07 1.66 E-07 1.78 E-07 1.65 E-07 1.73 E-07 7.47 E-08 9.90 E-08 1.46 E-07 1.21 E-07 8.37 E-08 3.03 E-08 9.07 E-08 6.55 E-08

Erro r

5.53 E-08 5.92 E-08 8.53 E-08 1.10 E-07 1.42 E-07 1.13 E-07 8.87 E-08 6.87 E-08 6.97 E-08 7.05 E-08 4.75 E-08 6.05 E-08 2.78 E-06 9.01 E-09 6.04 E-08

2.00E+ 01

1.30 E-04

1.41 E-06

8.00 E-05

9.03 E-07

4.00 E-05

2.99 E-07

2.00 E-05

1.65 E-07

1.00 E-05

8.87 E-08

5.42 E-06

6.20 E-08

3.44 E-06

 

Energy (MeV) 1.00E-08 1.00E-07 1.00E-06 1.00E-05 1.00E-04 1.00E-03 1.00E-02 5.00E-01 1.00E+00 1.50E+00 2.00E+00 3.00E+00 5.00E+00 1.00E+01 1.48E+01 2.00E+01

K - parameter 2.296 3.340 5.187 7.443 9.670 11.521 12.942 11.335 9.766 8.379 7.345 5.750 2.480 3.180 2.890 3.020

Error 0.053 0.045 0.022 0.055 0.049 0.045 0.086 0.119 0.068 0.080 0.106 0.093 0.046 0.044 0.036 0.073



Highlights



x

Scattering correction was investigated for calibration of neutron instruments.

x

Additional contribution from scattered monoenergetic neutrons was obtained.

x

The parameter related to the room-return scattering was fitted based on room size

3.65 E-08

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11