- Email: [email protected]
Neutron kerma factors for tissue and particle detector materials from 15 to 150 MeV
Nuclear Instruments
*H __
iikr
and Methods
in Physics
Research
A 388 (1997) 260-266
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NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Sectton A
ELSEVIER
Neutron kerma factors for tissue and particle detector materials from 15 to 150 MeV Dmitry Institute
V. Gorbatkov,
Vyacheslav
P. Kryuchkov*,
Oleg V. Sumaneev
fbr High Energy Physics. P.O.B. 35, 142284 Protuino, Moscow Region, Russian Federation
Abstract Charged particle emission spectra in neutron-induced reactions for elements of tissue and detector materials at energies from 15 to 150MeV have been calculated with the geometry dependent hybrid model. A comprehensive set of kerma factor values for H, C, 0, N, Si. as well as for tissue and frequently used high-energy particle detectors is given.
1. Introduction The absorbed dose is the main characteristic of effects produced in matter by ionizing radiation. Recently, nuclear data sets and codes to determine the accurate absorbed dose have become the subject of considerable interest in experimental physics, dosimetry, astronautics and various biomedical applications. Of prime importance is the exact prediction of absorbed dose distributions in the organs of cancer patients during radiotherapy treatment, as well as the determination of operating lifetime of particle detectors and electronicequipment under high radiation conditions. Provided produced charged particles are in equilibrium, at neutron energies below 100-150MeV, the absorbed dose rate (D, Gys-‘) can. with a satisfactory accuracy. be found from the following relation: D=
F(E)&(E)dE,
(1)
where F(E) is the neutron spectrum (neutron cm-‘ MeV’ s-l), K,(E) is the neutron kerma factor Cl] (Gycm2). The neutron kerma factor is defined as the average kinetic energy released in matter (per unit mass and per unit neutron fluence) and is the sum of all energy transferred to light charged particles and residual nuclei in an elastic or nonelastic nA-reaction. For composite materials the neutron kerma factor can be expressed as Kc(E) = N*C
*Corresponding
>‘igiE, = C piKr,(E),
(2)
author. E-mail: [email protected].
0168-583X/97/$17.00 Copyright PII SOl68-9002(97)00014-4
II
1997 Published
where NA is Avogadro’s number, yi is the atomic density of the ith isotope, 0; is the charged particle production cross section (ai = alo” + a;‘), Ei is the average kinetic energy of all charged particles produced by monoenergetic neutrons when interacting with a nucleus of the ith isotope, K,,(E) is the neutron kerma factor for the ith isotope, and pi is the ith isotope fraction in the mixture. The kerma factors in carbon, nitrogen and oxygen are of great importance in neutron dosimetry, since these elements are the main constituents of tissue. Motivation to improve neutron kerma factors from which radiotherapy can be optimized comes from the present success of neutrons and protons to treat specific kinds of tumours. Presently, a great amount of experimental and calculational data on neutron kerma factors for carbon and oxygen (e.g. [2-l 11) is available. Though a minimum uncertainty of k 20%. based on the analysis of more than 20 papers [12], has been assigned to the neutron kerma factors in the energy range - 50 MeV for tissue constituents. actual errors are much greater. Besides, uncertainties increase with neutron energy. Therefore. the improvement of the kerma factors, particularly at the higher neutron energies currently being used (lo-IOOMeV), is of great importance. The prediction of absorbed dose in the experimental equipment, operating under conditions of high-level radiation. is a more complicated challenge. The data set on kerma factors for detector and electronics elements is quite poor, and the data uncertainties are too large. At the same time, one of the major factors limiting the capabilities of existing experimental installations and those under design is the change of physical and chemical material properties in response to radiation exposure.
by Elsevier Science B.V. All rights reserved
D. V. Gorbatkm
et ai. / Nucl. Instr. and Merh. in Ph.vs. Res. A 388 (1997) 260-266
Consequently, the data allowing one to predict the radiation damage and service lifetime of the experimental equipment is an extremely urgent problem.
2. Calculational
method
As mentioned above, the neutron kerma factor is the sum of energy transferred to recoil nuclei in an elastic nA-interaction and to charged particles (p, d, CI,t, . ) produced in a nonelastic reaction. The elastic scattering contributes significantly to the neutron kerma factor for light elements and for neutron energies up to 70 MeV, and amounts, for example, for carbon at E, = 20 MeV to -25%. (For hydrogen, independently of the neutron energy, the kerma factor is almost completely determined by the elastic scattering.) Recoil nuclei energy calculations has been made with the well-known kinematic relationships in terms of recoil nuclei angular distributions according to the Glauber model [ 131. The neutron elastic cross sections for various nuclei have been obtained from the SADCO 2 nuclear data system [14]. But generally, the kerma factor in the energy range covered is determined by the nonelastic nA-scattering. The neutron kerma factor calculations at energies below 20 MeV are performed with basic cross section information contained in nuclear data libraries (e.g. [15]). Presently. a lot of papers on calculations of lowenergy neutron kerma factors for various elements are available [9,16]. The situation on neutron kerma factor calculations at energies above 20 MeV is much more involved, because the number of nuclear reaction channels increases with neutron energy. In this energy region, compound nuclear processes, direct processes and procompound processes are important. In addition, we do not know the evaluated basic nuclear data sets in the covered energy range. Therefore, for kerma factor calculations at high energies nuclear models are widely used. The intranuclear cascade model [17,1 S] is most commonly used for the nuclear representation in interaction the energy range 20-5000 MeV, as well as its modification - the cascadeexiton model [19]. In the framework of these models the nuclear reaction proceeds in two stages: at the first stage the hadronnucleus interaction is described in the quasi-free nucleon-nucleon scattering approximation; at the second the residual nuclear de-excitation by nucleon emission is calculated. Numerous intercomparisons by different authors (e.g. [20]) have shown, that these models may be reasonably successful in reproducing the magnitudes and spectral shapes of nucleons emitted for energies of 100-5000 MeV. However, in the low excitation energy range (E * < 15 MeV, which corresponds to an incident hadron
261
energy of 20-100 MeV) the calculation with specific models gives an obviously underestimated yield of heavy fragments, which are the most important radiation type in the absorbed dose formation. More consistently to our belief, the preequilibrium stage description has been realized by Blann in the socalled hybrid model [21], that is the combination of the exiton model [22] and the free nucleon-nucleon scattering model, modified by the Pauli exclusion principle. The ALICE/LIVERMORE 87 code [23] based on the hybrid model provides both the precompound decay and the equilibrium evaporation in the general framework of the Weisskopf-Ewing evaporation model calculation [24]. Important modifications have been made to account for nuclear density distributions and multiple precompound decay, which were excluded in earlier hybrid model formulations, and for probability of peripheral collisions (the geometry dependent hybrid model (GDH) [25]). As has been previously discussed by Barashenkov et al. [17], for small excitation energies the evaporation and exiton models accuracy strongly depend on the inverse reaction cross-section accuracy. In the ALICE code, the optical model is used to calculate inverse reaction cross sections and composite system reaction cross sections. The use of parameter sets, e.g. [Xi], obtained from the optical model search fitting procedure of experimental data allows one to fit low-energy proton and especially a particle evaporation spectra. The ALICE code is one of the most reliable algorithms and codes for nuclear reaction calculations in the energy range 1@150MeV, because no other codes have been tested in a wide range of projectiles and energies (e.g. [27730]). According to an estimate of the authors of Ref. 1311, the GDH formulation generally gives a good agreement, within the - 2&30% limit, with experimental data in absolute differential cross sections. The uncertainty of integral quantities, among these the kerma factors, can come up to 10% at most.
3. Calculational-to-experimental comparison of charged particle yields in nonelastic hA-interactions As remarked above, a good agreement of data calculated with the ALICE code with measured neutron and proton differential cross sections in the energy range 2-150 MeV has been intimated by many users. However, with accurate kerma factor calculations in mind, it is more important to perform detailed calculational-to-experimental comparisons to be certain that the GDH model adequately reproduces the yields and spectral shapes of charged particles (protons and, especially, deuterons and a particles) determining the absorbed dose completely. Comparisons of calculated (Yparticle spectra produced in a nonelastic nC-reaction at neutron energies 11, 14, 17
262
D. V. Garbatkov et at. 1 Nud
Instr. and Meth. in Phvs. Res. A 388 (19911 260-266
19 MeV with experimental data [2] are shown in Fig. 1 (aHd). As is seen from this figure the calculated and measured data are in a good agreement (within the l&20% limit) at all energies. The “C(p, p’) and 12C(p, d) experimental successfully mainly by the GDH model as well.
Comparisons of 160(n, p) and 160(n,a) results [33] at 60.7MeV neutron energy in Figs. 4 and 5 show a good agreement between the GDH and experimental particle spectra over the whole energy range, excluding low proton energies ( < 10MeV) where experimental data seem to be underestimated (Fig. 4). At the same time, data calculated with the cascade-exiton model by the Monte Carlo method [34] and presented in the same figures are by a factor of 2-3 less for the highest 10 MeV of proton energy. It must be emphasized that adequate reproduction of proton and a particle emission spectra is of basic importance in kerma factor calculations for light elements at energies up to 50 MeV, because these particles carry away most of the nuclear excitation energy.
Carbon E,=61.9 E.= 11.9
f44
MeV
MeV
1. 0 0
0
0
2
4
6
8
100
E (hi&)
I
2
3
4
5
Fig. 1. Measured (0) [2] and calculated (curves) c( particle spectra of the reaction n + “C + n + 3a at neutron energies 19 (a), 17 (b), 14 (c) and 11.9MeV (d).
E,=39
0
5
10
IS
0
10
20
30
40
E (t&V)
20
25
50
60
E
(MeV)
Fig. 3. Experimental data (0) [32] and calculated results with ALICE (curves) for (p,p’) and (p,d) spectra on “C with 61.9 MeV protons.
MeV
30
35 E
40
(MeV)
Fig. 2. Experimental (0) [32] and calculated results for (p.p’) spectra on “C with 39 MeV protons. The GDH prediction is represented by the solid curve, the Monte-Carlo calculated data from Ref. [18] are indicated by squares.
0
10
20
30
40
_50
60
E (MeV) Fig. 4. Experimental (0) [33] and calculated results for (n,p) spectra on I60 for 60.7 MeV incident neutrons. The curve is the result of GDH, the squares represent a calculation with the cascade-exiton model [34].
263
D. IT. Gorbatkov et al. /Nucl. Instr. and Meth. in Phys. Res. A 388 (1997) 260-266
100
140
120
E (MeV)
10
30
20
40
60
50
Fig. 7. Comparison between experimental (symbols) and calculated (curve) neutron kerma factors for carbon.
E (MeV) Fig. 5. As in Fig. 4 for the reaction lbO(n,cr)
0-
I
0
20
40
60
80 100 120 I40 160 E (MeV)
1o.t 0
10
20
30
40
50
60
70
80
90
Fig. 8. As in Fig. 7 for oxygen. E (MeV) Fig. 6. Experimental (symbols) [35,36] and calculated (cur ves) results for “Al(p,p’), (p. n) and 58Ni(p,p’)r (p,n) spectra for 90 MeV incident protons.
Comparisons of (p,p’) and (p, n) data [35,36] at 90 MeV proton energy in Fig. 6 show an excellent agreement between the experimental and GDH results for nuclei in the medium mass region (27Al and “Ni), and suggest that the energy range wherein the GDH model reliably reproduces particle emission spectra, can be extended at least up to lo+150 MeV. (Papers are available, e.g. [3741], in which the ALICE code gives a satisfactory agreement with experimental data at incident energies up to 900 MeV.)
4. Comparisons of results for the kerma factors The results of the comparisons given above (Figs. 1-6) show really an impressive success of the GDH model in
reproducing a large body of experimental particle spectra, and lead to the expectation that uncertainties of kerma factors calculated with this algorithm should be no more than 10%. In support of this conjecture the direct comparison of calculated and measured neutron kerma factors for carbon is shown in Fig. 7. References to sources of experimental data may be found in Ref. [12]. A good agreement of the calculated kerma factor with experimental data over the energy region considered can be seen. Figs. 8 and 9 show the calculated-to-experimental comparisons of the kerma factors for oxygen and nitrogen. The agreement again is seen to be good. The question of overestimation of the measured kerma factor value for oxygen at 60.7MeV [S] has been discussed in Ref. [12]; this experimental point seems to be too large. Comparisons of the kerma factor for carbon computed with the GDH model with other calculational results (see Ref. [12]) are shown in Fig. 10. Significant disagreements (UP to _ 40%) for the data in the energy range up to 50 MeV can be seen. There is a paucity of data for
264
D. V. Gorhatkotl et al. ! Nud. Instr. and Meth. in Ph_vs. Res. A 38X (1997) 260--766
y’
strongly depend on the neutron energy, and have various spectral shapes for carbon and oxygen. At higher energies, from 50 to 150MeV, the proton contribution to kerma factors becomes dominant. which permits to represent the carbon-to-oxygen ratio as
8 6
0
20
40
60
80
100 I20
140 I60
E (MeV) Fig. 9. As in Fig. 7 for nitrogen
ll~‘i~J’~~~‘!i~‘~~~‘~~~‘~~~‘~
0 0
20
40
60
80
100
120
140
E (MeV) Fig. 10. Calculated neutron kerma factor for carbon as a function of incident neutron energy from 15to 150 MeV. The figure shows kerma factor values of this paper (solid curve), the results
of Morstin et al. ( - . ..-- . ..~ . ..) [42], the results of Savitskaya et al. (- -) [34]. See Ref. [12] for sources of calculated data at energies below 70 MeV.
neutron energies above 70 MeV. Here good agreement of our data with the results obtained in Ref. [42] should be noted. The kerma factors calculated in Ref. [34] are underestimated in comparison with our results above 20 MeV, this disagreement at 150 MeV becomes more than 30%. The carbon-to-oxygen kerma factor ratio (R) is of great importance in verifying the calculated kerma factor adequacy. It is reasonable to expect a significant energy dependence of this carbon-to-oxygen ratio at neutron energies up to - 50 MeV, since the kerma factors for projectile energies below 50 MeV are largely determined by reactions with heavy charged particle emission (C(n,n’S@, O(n,a)). Cross sections of these reactions
cross sections for where~~~~~~ flnonO are the nonelastic carbon and oxygen. respectively, ~1,~~.ncho are the average charged particle multiplicities. &,c, EcchOare the average charged particle energies, AC, A0 are the mass numbers. In the energy region above 50 MeV nonelastic nAinteractions for light nuclei (A -c 25) are characterized by a slight A-dependence of n,,, and .&,, (nchC N nchO, EchC ZZEcho). Taking this into account and substituting the wellknown relation for the nonelastic cross section fl “0” -Q A ‘!3 into Eq. (3) one can easily derive:
Fig. 11 compares the GDH-calculated carbon-to-oxygen ratio with the experimental data [3, 5,6,43,44], as well as with the results obtained in Ref. [34]. The GDH model gives R = 1.06 for the carbon-to-oxygen ratio at 80 MeV neutron energy. As is shown in Fig. 11, our data are in a good agreement (within the 5% limit) with experimental results, which gives R = 1.1 + 0.1 for this ratio at 60 MeV. The energy dependence of the carbonto-oxygen ratio obtained from Ref. [34] is in much
.$
2
p
1.8
!z a 1.6 ::,
1.4
e
1.2
S +!
l
B
0.8
0.6 10
20
30
40
50
60
70
80
E (MeV) Fig. I I. Experimental (symbols) 13. 5, 6.43.441 and calculated carbon-to-oxygen ratios as a function of incident neutron energy. The solid curve represents data of this paper, the dashed curve is the calculated results from Ref. [34].
D. V. Gorbatkoo et al. /Nucl. Instr. and Meth. in PhJa. Rex A 388 (1997) 260-266 -
2.5
“E ZI
Table I Neutron kerma factor for H, C. 0. N, Si (fGy m*)
*‘Si
g y’
2
-
1
,-
-\ .__-.
I’ ,’ //I: ,I
-
5
IO
,-
15
20
30
25
35
40
E (MeV) Fig. 12. Neutron kerma factor for silicon calculated with the ALICE code (solid line). with the measured (symbols) [3] and calculated (dashed line) results included.
poorer
agreement
model
data
with experimental
at energies
below
‘65
data
than
the GDH
E (MeV)
H
C
0
N
Si
15 20 25 30 40 50 60 70 80 90 100 120 150
48.1 47.0 45.85 44.51 42.92 40.75 39.04 37.72 36.14 36.05 35.58 35.23 35.82
2.06 3.10 3.41 3.64 4.0 4.39 4.97 5.49 6.03 6.69 7.54 9.03 III.05
1.31 1.85 2.08 2.37 3.0 3.67 4.4 4.96 5.6 6.3 6.94 8.35 10.2
1.5 2.04 2.46 2.78 3.62 4.44 5.24 5.9 6.58 7.2 8.0 9.34 11.34
1.21
1.53 1.74 2.02 2.51 3.08 3.62 4.16 4.73 5.33 5.86 6.93 8.48
5. Results
40 MeV.
The kerma factors for “*Si are plotted in Fig. 12. As can be seen, there is a good agreement at energies below 20 MeV between the GDH-calculated and experimental data [3], as well as with data of Caswell et al. [9] calculated from the cross sections in the ENDF/B-IV evaluation [45] on the one hand, and significant disagreements for the highest 20 MeV of neutron energy on the other. To our belief, the value of the 25 MeV data point of Hartmann et al. [3] is too low. This conclusion is based upon the knowledge of systematics of cross sections for these reactions. When evaluating Caswell’s kerma factors it should be noted that these values are calculated from the ENDF/B-IV nuclear data set, wherein the database on charged particle yields at E > 20 MeV is very limited.
Table 1 gives the calculated values of the kerma factors for the main constituents of tissue(H, C, 0, N), and for Si as a function of neutron energy from 15 to 150 MeV. The neutron kerma factors for tissue and several particle detector materials (CH. NaI. CsI, BaF2, CeF,. Bi4GejOl 2(BGO), Pb02-Si02(LS)) calculated using Eq. (2) are summarized in Table 2. The data presented in Tables 1 and 2 provide the absorbed dose calculations at neutron energies from 15 to 150MeV. In the lower neutron energy region the literature data available (e.g. [9]) should be used for the absorbed dose determination. To summarize, it should be particularly emphasized, that great care must be taken in calculating the neutron absorbed dose at energies above 100 MeV with the
Table 2 Neutron
kerma
factors
for composite
materials
(fGym’)
E (MeV)
Tissue
CH
Nal
CSI
BaFl
CeF,
BGO
LS
PbWOJ
(5 20 25 30 40 50 60 70 X0 90 100 120 150
6.12 6.55 6.66 6.78 7.16 7.52 7.98 8.35 8.82 9.37 993 11.2 12.9
5.6 6.45 6.67 6.75 6.99 7.19 7.59 7.97 8.39 8.95 9.70 11.0 13.0
0.08 0.21 0.35 0.47 0.77 1.08
0.02 0.08 0.16 0.25 0.47 0.72 0.99 1.24 1.49 1.72 1.94 2.42 3.08
0.46 0.52 0.59 0.68 0.91 1.21 1.50 1.82 2.11 2.38 2.66 3.28 4.08
0.62 0.69 0.78 0.89 1.15
1.49 1.82
0.20 0.36 0.44 0.56 0.83 1.13 1.44
2.18 2.51 2.80 3.12 3.79 4.68
2.0 1 2.26 2.54 3.12 3.95
0.36 0.50 0.58 0.69 0.94 1.23 1.54 I .81 2.12 2.40 2.70 3.32 4.16
0.18 0.27 0.33 0.4 1 0.62 0.85 I.1 I 1.35 I.59 1.82 2.06 2.58 3.28
1.40 1.72 2.02 2.29 2.57 3.15 3.97
1.72
266
D. V. Gorbatkov et al. i Nucl. Instr. and Meth. in Ph_vs. Rex A 388 (I 997) 260-266
kerma factors presented here, along with any other kerma data from the literature. The reason is that the absence of high-energy charged particle equilibrium renders the kerma approximation (see Eq. (1)) impractical, especially for light (A < 30) elements. Specific neutron, proton and pion absorbed dose values, being used instead of kerma factors in Eq. (1) for the absorbed dose calculation in the energy range up to lOOOGeV, will be presented elsewhere.
6. Conclusion The kerma factors for the main constituents of tissue and detector materials have been calculated with the geometry-dependent hybrid model. Comparisons of measured and calculated data showed a really good agreement between the GDH and experimental charged particle emission spectra over a very wide energy range. According to an estimate, uncertainties of the kerma factors obtained are only of the order of 6-10%. The kerma factor values for hydrogen, carbon, oxygen, nitrogen, silicon, as well as for tissue and several detector materials at energies from 15 to 150 MeV are given.
Acknowledgements We would like to thank Dr. G.I. Britvich Kurochkin for several helpful discussions.
and LA.
References [II ICRU, Radiation Quantities and Units, Report 33 (International Commission on Radiation Units and Measurements, Bethesda, MD 1980). G. Dietze and H. Klein. Radiat. Prot. PI B. Antolkovic. Dosim. 44 (1992) 3 I. P.M. [31 C.L. Hartmann, M
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et al., Radiat. Prot. Dosim. 44 (I 992) 2 I. r51 F.P. Brady and J.L. Romero. Final Report to the National Cancer Institute (Grant No. lROl CA16261 Technical Report, University of California-Davis. Davis, CA. 1979). [61 P.M. DeLuca, Jr., H.H. Barshall. M. Burhoe et al., Nucl. Sci. Eng. 94 (1986) 192. c71 R.C. Haight, SM. Grimes. R.G. Johnson et al.. Nucl. Sci. Eng. 87 (1984) 41. @I R.G. Alsmiller Jr. and J. Barish, Health Phys. 33 (1977) 98. [91 R.L. Caswell. J.J. Coyne and M.L. Randolph, Radiat. Res. 83 (1980) 217. Cl01 P.J. Dimbilow, Phys. Med. Biol. 27 (1982) 989. Cl11 A.H. Wells. Radiat. Res. 80 (1979) I. Cl?1 R.M. White, J.J. Broerse, P.M. DeLuca Jr. et al.. Radiat. Prot. Dosim. 44 (1992) 11.
Physics, W.F. 1131 R.J. Glauber. in: Lectures in Theoretical Britten et al. (Interscience Publishers, New York, 1959). and V.P. Kryuchkov, Nucl. Instr. and Cl41 D.V. Gorbatkov Meth. A 372 (1996) 297. Summary Document. Compiled and edited Cl51 ENDF/B-VI by P.F. Rose, ENDF-201 (National Nuclear Data Center, Brookhaven National Laboratory. Upton, New York. 1991). 27, Livermore, CA (1986). [161 R.J. Howerton. UCRL-50400 and V.D. Toneyev, Interaction of HighCl71 V.S. Barashenkov Energy Particles and Nuclei with Nuclei (Atomizdat, Moscow. 1972) (in Russian). Cl81 H.W. Bertini. Phys. Rev. 131 (1963) 1801. of Nucleus Cl91 K.K. Gudima and V.D. Toneyev. Calculations Structure and Nuclear Reactions (Shtiintsa. Kishinev. 1977) (in Russian). H.W. Bertini. K. Chen et al., Nucl. cw V.S. Barashenkov. Phys. A 187 (1972) 531. Pll M. Blann, Phys. Rev. Lett. 27 (1971) 337. WI J.J. Griffin, Phys. Rev. Lett. 17 (1966) 478. UCID-19614, Livermore, ~231 M. Blann and J. Bisplinghoff, CA (1982); M. Blann. G. Reffo and F. Fabbri, LLNL Report UCRL 95371 (1986); M. Blann, ALICE/LIVERMORE 87 (1987) (unpublished). 1241 V.F. Weisskopf and D.H. Ewing, Phys. Rev. 57 (1940) 472. M. Blann, Phys. Rev. Lett. 28 (1972) 757. PI WI F.D. Becchetti and G.W. Greenlees. Phys. Rev. 182 (1969) 1190. and P. Nagel, NEA Data Bank, Newsletter r771 H. Gruppelaar 32 (1985). NEANDC-204(U). INDC (NEA) 6. P81 V.P. Lunev, D. Zeelinger. H. Kalka et al.. Yad. Fiz. 3(9) (I 990) 745. E.I. Kebin and V.G. Sukharevsky. C29] F.A. Zhivopistsev, Models of Pre-equilibrium Nuclear Reactions (Moscow State University Publishing. Moscow, 1987) fin Russian). 1301 R. Bodemann, H.-J. Lange, 1. Leya et al., Nucl. Instr. and Meth. B 82 (1993) 9. c311 M. Blann and H.K. Vonach, Phys. Rev. C 28 (1983) 1475. 1311 F.E. Bertrand and R.W. Peelle, Phys. Rev. C S(l973) 1045. 1331J.L. Romero et al., Rad. Effects 94 (1986) 13. 1341 E.N. Savitskaya and A.V. Sannikov, Radiat. Prot. Dosim. 60 (1995) 135. [3-s] A.M. Kalend et al., Phys. Rev. C 28 (1983) 105. [361 J.R. Wu. CC. Chang and H.D. Holmgren, Phys. Rev. C 19 (1979) 698. [371 R. Michel. F. Peiffer and R. Stuck. Nucl. Phys. A 441(1985) 617. C381E. Holub et al., Phys. Rev. C 33 (1986) 143. 1391 M. Blann, Phys. Rev. C 31 (1985) 1245. 900( 1990) unpublished. c401 M. Blann, ALICE/LIVERMORE c411 S. Pearlstein, J. Astrophys. 346 (1989) 1049. 1421 K. Morstin et al., in: Nuclear and Atomic Data for Radiotherapy and Related Radiobiology, IAEA, Vienna I 1987). Summary Documentation, BNLlY431D. Garber, ENDFiB 17541 (ENDF 201) (1975). 1441 P.M. DeLuca Jr., H.H. Barshall, R.C. Haight et al., in: Proc. 5th Symp. on Neutron Dosimetry, EUR-9762 (Luxembourg: CEC) (1985) p. 193. c451 P.M. DeLuca Jr.. H.H. Barshall, Y. Sunet al.. Radiat. Prot. Dosim. 23 (1988) 27.
*H __
iikr
and Methods
in Physics
Research
A 388 (1997) 260-266
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NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH Sectton A
ELSEVIER
Neutron kerma factors for tissue and particle detector materials from 15 to 150 MeV Dmitry Institute
V. Gorbatkov,
Vyacheslav
P. Kryuchkov*,
Oleg V. Sumaneev
fbr High Energy Physics. P.O.B. 35, 142284 Protuino, Moscow Region, Russian Federation
Abstract Charged particle emission spectra in neutron-induced reactions for elements of tissue and detector materials at energies from 15 to 150MeV have been calculated with the geometry dependent hybrid model. A comprehensive set of kerma factor values for H, C, 0, N, Si. as well as for tissue and frequently used high-energy particle detectors is given.
1. Introduction The absorbed dose is the main characteristic of effects produced in matter by ionizing radiation. Recently, nuclear data sets and codes to determine the accurate absorbed dose have become the subject of considerable interest in experimental physics, dosimetry, astronautics and various biomedical applications. Of prime importance is the exact prediction of absorbed dose distributions in the organs of cancer patients during radiotherapy treatment, as well as the determination of operating lifetime of particle detectors and electronicequipment under high radiation conditions. Provided produced charged particles are in equilibrium, at neutron energies below 100-150MeV, the absorbed dose rate (D, Gys-‘) can. with a satisfactory accuracy. be found from the following relation: D=
F(E)&(E)dE,
(1)
where F(E) is the neutron spectrum (neutron cm-‘ MeV’ s-l), K,(E) is the neutron kerma factor Cl] (Gycm2). The neutron kerma factor is defined as the average kinetic energy released in matter (per unit mass and per unit neutron fluence) and is the sum of all energy transferred to light charged particles and residual nuclei in an elastic or nonelastic nA-reaction. For composite materials the neutron kerma factor can be expressed as Kc(E) = N*C
*Corresponding
>‘igiE, = C piKr,(E),
(2)
author. E-mail: [email protected].
0168-583X/97/$17.00 Copyright PII SOl68-9002(97)00014-4
II
1997 Published
where NA is Avogadro’s number, yi is the atomic density of the ith isotope, 0; is the charged particle production cross section (ai = alo” + a;‘), Ei is the average kinetic energy of all charged particles produced by monoenergetic neutrons when interacting with a nucleus of the ith isotope, K,,(E) is the neutron kerma factor for the ith isotope, and pi is the ith isotope fraction in the mixture. The kerma factors in carbon, nitrogen and oxygen are of great importance in neutron dosimetry, since these elements are the main constituents of tissue. Motivation to improve neutron kerma factors from which radiotherapy can be optimized comes from the present success of neutrons and protons to treat specific kinds of tumours. Presently, a great amount of experimental and calculational data on neutron kerma factors for carbon and oxygen (e.g. [2-l 11) is available. Though a minimum uncertainty of k 20%. based on the analysis of more than 20 papers [12], has been assigned to the neutron kerma factors in the energy range - 50 MeV for tissue constituents. actual errors are much greater. Besides, uncertainties increase with neutron energy. Therefore. the improvement of the kerma factors, particularly at the higher neutron energies currently being used (lo-IOOMeV), is of great importance. The prediction of absorbed dose in the experimental equipment, operating under conditions of high-level radiation. is a more complicated challenge. The data set on kerma factors for detector and electronics elements is quite poor, and the data uncertainties are too large. At the same time, one of the major factors limiting the capabilities of existing experimental installations and those under design is the change of physical and chemical material properties in response to radiation exposure.
by Elsevier Science B.V. All rights reserved
D. V. Gorbatkm
et ai. / Nucl. Instr. and Merh. in Ph.vs. Res. A 388 (1997) 260-266
Consequently, the data allowing one to predict the radiation damage and service lifetime of the experimental equipment is an extremely urgent problem.
2. Calculational
method
As mentioned above, the neutron kerma factor is the sum of energy transferred to recoil nuclei in an elastic nA-interaction and to charged particles (p, d, CI,t, . ) produced in a nonelastic reaction. The elastic scattering contributes significantly to the neutron kerma factor for light elements and for neutron energies up to 70 MeV, and amounts, for example, for carbon at E, = 20 MeV to -25%. (For hydrogen, independently of the neutron energy, the kerma factor is almost completely determined by the elastic scattering.) Recoil nuclei energy calculations has been made with the well-known kinematic relationships in terms of recoil nuclei angular distributions according to the Glauber model [ 131. The neutron elastic cross sections for various nuclei have been obtained from the SADCO 2 nuclear data system [14]. But generally, the kerma factor in the energy range covered is determined by the nonelastic nA-scattering. The neutron kerma factor calculations at energies below 20 MeV are performed with basic cross section information contained in nuclear data libraries (e.g. [15]). Presently. a lot of papers on calculations of lowenergy neutron kerma factors for various elements are available [9,16]. The situation on neutron kerma factor calculations at energies above 20 MeV is much more involved, because the number of nuclear reaction channels increases with neutron energy. In this energy region, compound nuclear processes, direct processes and procompound processes are important. In addition, we do not know the evaluated basic nuclear data sets in the covered energy range. Therefore, for kerma factor calculations at high energies nuclear models are widely used. The intranuclear cascade model [17,1 S] is most commonly used for the nuclear representation in interaction the energy range 20-5000 MeV, as well as its modification - the cascadeexiton model [19]. In the framework of these models the nuclear reaction proceeds in two stages: at the first stage the hadronnucleus interaction is described in the quasi-free nucleon-nucleon scattering approximation; at the second the residual nuclear de-excitation by nucleon emission is calculated. Numerous intercomparisons by different authors (e.g. [20]) have shown, that these models may be reasonably successful in reproducing the magnitudes and spectral shapes of nucleons emitted for energies of 100-5000 MeV. However, in the low excitation energy range (E * < 15 MeV, which corresponds to an incident hadron
261
energy of 20-100 MeV) the calculation with specific models gives an obviously underestimated yield of heavy fragments, which are the most important radiation type in the absorbed dose formation. More consistently to our belief, the preequilibrium stage description has been realized by Blann in the socalled hybrid model [21], that is the combination of the exiton model [22] and the free nucleon-nucleon scattering model, modified by the Pauli exclusion principle. The ALICE/LIVERMORE 87 code [23] based on the hybrid model provides both the precompound decay and the equilibrium evaporation in the general framework of the Weisskopf-Ewing evaporation model calculation [24]. Important modifications have been made to account for nuclear density distributions and multiple precompound decay, which were excluded in earlier hybrid model formulations, and for probability of peripheral collisions (the geometry dependent hybrid model (GDH) [25]). As has been previously discussed by Barashenkov et al. [17], for small excitation energies the evaporation and exiton models accuracy strongly depend on the inverse reaction cross-section accuracy. In the ALICE code, the optical model is used to calculate inverse reaction cross sections and composite system reaction cross sections. The use of parameter sets, e.g. [Xi], obtained from the optical model search fitting procedure of experimental data allows one to fit low-energy proton and especially a particle evaporation spectra. The ALICE code is one of the most reliable algorithms and codes for nuclear reaction calculations in the energy range 1@150MeV, because no other codes have been tested in a wide range of projectiles and energies (e.g. [27730]). According to an estimate of the authors of Ref. 1311, the GDH formulation generally gives a good agreement, within the - 2&30% limit, with experimental data in absolute differential cross sections. The uncertainty of integral quantities, among these the kerma factors, can come up to 10% at most.
3. Calculational-to-experimental comparison of charged particle yields in nonelastic hA-interactions As remarked above, a good agreement of data calculated with the ALICE code with measured neutron and proton differential cross sections in the energy range 2-150 MeV has been intimated by many users. However, with accurate kerma factor calculations in mind, it is more important to perform detailed calculational-to-experimental comparisons to be certain that the GDH model adequately reproduces the yields and spectral shapes of charged particles (protons and, especially, deuterons and a particles) determining the absorbed dose completely. Comparisons of calculated (Yparticle spectra produced in a nonelastic nC-reaction at neutron energies 11, 14, 17
262
D. V. Garbatkov et at. 1 Nud
Instr. and Meth. in Phvs. Res. A 388 (19911 260-266
19 MeV with experimental data [2] are shown in Fig. 1 (aHd). As is seen from this figure the calculated and measured data are in a good agreement (within the l&20% limit) at all energies. The “C(p, p’) and 12C(p, d) experimental successfully mainly by the GDH model as well.
Comparisons of 160(n, p) and 160(n,a) results [33] at 60.7MeV neutron energy in Figs. 4 and 5 show a good agreement between the GDH and experimental particle spectra over the whole energy range, excluding low proton energies ( < 10MeV) where experimental data seem to be underestimated (Fig. 4). At the same time, data calculated with the cascade-exiton model by the Monte Carlo method [34] and presented in the same figures are by a factor of 2-3 less for the highest 10 MeV of proton energy. It must be emphasized that adequate reproduction of proton and a particle emission spectra is of basic importance in kerma factor calculations for light elements at energies up to 50 MeV, because these particles carry away most of the nuclear excitation energy.
Carbon E,=61.9 E.= 11.9
f44
MeV
MeV
1. 0 0
0
0
2
4
6
8
100
E (hi&)
I
2
3
4
5
Fig. 1. Measured (0) [2] and calculated (curves) c( particle spectra of the reaction n + “C + n + 3a at neutron energies 19 (a), 17 (b), 14 (c) and 11.9MeV (d).
E,=39
0
5
10
IS
0
10
20
30
40
E (t&V)
20
25
50
60
E
(MeV)
Fig. 3. Experimental data (0) [32] and calculated results with ALICE (curves) for (p,p’) and (p,d) spectra on “C with 61.9 MeV protons.
MeV
30
35 E
40
(MeV)
Fig. 2. Experimental (0) [32] and calculated results for (p.p’) spectra on “C with 39 MeV protons. The GDH prediction is represented by the solid curve, the Monte-Carlo calculated data from Ref. [18] are indicated by squares.
0
10
20
30
40
_50
60
E (MeV) Fig. 4. Experimental (0) [33] and calculated results for (n,p) spectra on I60 for 60.7 MeV incident neutrons. The curve is the result of GDH, the squares represent a calculation with the cascade-exiton model [34].
263
D. IT. Gorbatkov et al. /Nucl. Instr. and Meth. in Phys. Res. A 388 (1997) 260-266
100
140
120
E (MeV)
10
30
20
40
60
50
Fig. 7. Comparison between experimental (symbols) and calculated (curve) neutron kerma factors for carbon.
E (MeV) Fig. 5. As in Fig. 4 for the reaction lbO(n,cr)
0-
I
0
20
40
60
80 100 120 I40 160 E (MeV)
1o.t 0
10
20
30
40
50
60
70
80
90
Fig. 8. As in Fig. 7 for oxygen. E (MeV) Fig. 6. Experimental (symbols) [35,36] and calculated (cur ves) results for “Al(p,p’), (p. n) and 58Ni(p,p’)r (p,n) spectra for 90 MeV incident protons.
Comparisons of (p,p’) and (p, n) data [35,36] at 90 MeV proton energy in Fig. 6 show an excellent agreement between the experimental and GDH results for nuclei in the medium mass region (27Al and “Ni), and suggest that the energy range wherein the GDH model reliably reproduces particle emission spectra, can be extended at least up to lo+150 MeV. (Papers are available, e.g. [3741], in which the ALICE code gives a satisfactory agreement with experimental data at incident energies up to 900 MeV.)
4. Comparisons of results for the kerma factors The results of the comparisons given above (Figs. 1-6) show really an impressive success of the GDH model in
reproducing a large body of experimental particle spectra, and lead to the expectation that uncertainties of kerma factors calculated with this algorithm should be no more than 10%. In support of this conjecture the direct comparison of calculated and measured neutron kerma factors for carbon is shown in Fig. 7. References to sources of experimental data may be found in Ref. [12]. A good agreement of the calculated kerma factor with experimental data over the energy region considered can be seen. Figs. 8 and 9 show the calculated-to-experimental comparisons of the kerma factors for oxygen and nitrogen. The agreement again is seen to be good. The question of overestimation of the measured kerma factor value for oxygen at 60.7MeV [S] has been discussed in Ref. [12]; this experimental point seems to be too large. Comparisons of the kerma factor for carbon computed with the GDH model with other calculational results (see Ref. [12]) are shown in Fig. 10. Significant disagreements (UP to _ 40%) for the data in the energy range up to 50 MeV can be seen. There is a paucity of data for
264
D. V. Gorhatkotl et al. ! Nud. Instr. and Meth. in Ph_vs. Res. A 38X (1997) 260--766
y’
strongly depend on the neutron energy, and have various spectral shapes for carbon and oxygen. At higher energies, from 50 to 150MeV, the proton contribution to kerma factors becomes dominant. which permits to represent the carbon-to-oxygen ratio as
8 6
0
20
40
60
80
100 I20
140 I60
E (MeV) Fig. 9. As in Fig. 7 for nitrogen
ll~‘i~J’~~~‘!i~‘~~~‘~~~‘~~~‘~
0 0
20
40
60
80
100
120
140
E (MeV) Fig. 10. Calculated neutron kerma factor for carbon as a function of incident neutron energy from 15to 150 MeV. The figure shows kerma factor values of this paper (solid curve), the results
of Morstin et al. ( - . ..-- . ..~ . ..) [42], the results of Savitskaya et al. (- -) [34]. See Ref. [12] for sources of calculated data at energies below 70 MeV.
neutron energies above 70 MeV. Here good agreement of our data with the results obtained in Ref. [42] should be noted. The kerma factors calculated in Ref. [34] are underestimated in comparison with our results above 20 MeV, this disagreement at 150 MeV becomes more than 30%. The carbon-to-oxygen kerma factor ratio (R) is of great importance in verifying the calculated kerma factor adequacy. It is reasonable to expect a significant energy dependence of this carbon-to-oxygen ratio at neutron energies up to - 50 MeV, since the kerma factors for projectile energies below 50 MeV are largely determined by reactions with heavy charged particle emission (C(n,n’S@, O(n,a)). Cross sections of these reactions
cross sections for where~~~~~~ flnonO are the nonelastic carbon and oxygen. respectively, ~1,~~.ncho are the average charged particle multiplicities. &,c, EcchOare the average charged particle energies, AC, A0 are the mass numbers. In the energy region above 50 MeV nonelastic nAinteractions for light nuclei (A -c 25) are characterized by a slight A-dependence of n,,, and .&,, (nchC N nchO, EchC ZZEcho). Taking this into account and substituting the wellknown relation for the nonelastic cross section fl “0” -Q A ‘!3 into Eq. (3) one can easily derive:
Fig. 11 compares the GDH-calculated carbon-to-oxygen ratio with the experimental data [3, 5,6,43,44], as well as with the results obtained in Ref. [34]. The GDH model gives R = 1.06 for the carbon-to-oxygen ratio at 80 MeV neutron energy. As is shown in Fig. 11, our data are in a good agreement (within the 5% limit) with experimental results, which gives R = 1.1 + 0.1 for this ratio at 60 MeV. The energy dependence of the carbonto-oxygen ratio obtained from Ref. [34] is in much
.$
2
p
1.8
!z a 1.6 ::,
1.4
e
1.2
S +!
l
B
0.8
0.6 10
20
30
40
50
60
70
80
E (MeV) Fig. I I. Experimental (symbols) 13. 5, 6.43.441 and calculated carbon-to-oxygen ratios as a function of incident neutron energy. The solid curve represents data of this paper, the dashed curve is the calculated results from Ref. [34].
D. V. Gorbatkoo et al. /Nucl. Instr. and Meth. in PhJa. Rex A 388 (1997) 260-266 -
2.5
“E ZI
Table I Neutron kerma factor for H, C. 0. N, Si (fGy m*)
*‘Si
g y’
2
-
1
,-
-\ .__-.
I’ ,’ //I: ,I
-
5
IO
,-
15
20
30
25
35
40
E (MeV) Fig. 12. Neutron kerma factor for silicon calculated with the ALICE code (solid line). with the measured (symbols) [3] and calculated (dashed line) results included.
poorer
agreement
model
data
with experimental
at energies
below
‘65
data
than
the GDH
E (MeV)
H
C
0
N
Si
15 20 25 30 40 50 60 70 80 90 100 120 150
48.1 47.0 45.85 44.51 42.92 40.75 39.04 37.72 36.14 36.05 35.58 35.23 35.82
2.06 3.10 3.41 3.64 4.0 4.39 4.97 5.49 6.03 6.69 7.54 9.03 III.05
1.31 1.85 2.08 2.37 3.0 3.67 4.4 4.96 5.6 6.3 6.94 8.35 10.2
1.5 2.04 2.46 2.78 3.62 4.44 5.24 5.9 6.58 7.2 8.0 9.34 11.34
1.21
1.53 1.74 2.02 2.51 3.08 3.62 4.16 4.73 5.33 5.86 6.93 8.48
5. Results
40 MeV.
The kerma factors for “*Si are plotted in Fig. 12. As can be seen, there is a good agreement at energies below 20 MeV between the GDH-calculated and experimental data [3], as well as with data of Caswell et al. [9] calculated from the cross sections in the ENDF/B-IV evaluation [45] on the one hand, and significant disagreements for the highest 20 MeV of neutron energy on the other. To our belief, the value of the 25 MeV data point of Hartmann et al. [3] is too low. This conclusion is based upon the knowledge of systematics of cross sections for these reactions. When evaluating Caswell’s kerma factors it should be noted that these values are calculated from the ENDF/B-IV nuclear data set, wherein the database on charged particle yields at E > 20 MeV is very limited.
Table 1 gives the calculated values of the kerma factors for the main constituents of tissue(H, C, 0, N), and for Si as a function of neutron energy from 15 to 150 MeV. The neutron kerma factors for tissue and several particle detector materials (CH. NaI. CsI, BaF2, CeF,. Bi4GejOl 2(BGO), Pb02-Si02(LS)) calculated using Eq. (2) are summarized in Table 2. The data presented in Tables 1 and 2 provide the absorbed dose calculations at neutron energies from 15 to 150MeV. In the lower neutron energy region the literature data available (e.g. [9]) should be used for the absorbed dose determination. To summarize, it should be particularly emphasized, that great care must be taken in calculating the neutron absorbed dose at energies above 100 MeV with the
Table 2 Neutron
kerma
factors
for composite
materials
(fGym’)
E (MeV)
Tissue
CH
Nal
CSI
BaFl
CeF,
BGO
LS
PbWOJ
(5 20 25 30 40 50 60 70 X0 90 100 120 150
6.12 6.55 6.66 6.78 7.16 7.52 7.98 8.35 8.82 9.37 993 11.2 12.9
5.6 6.45 6.67 6.75 6.99 7.19 7.59 7.97 8.39 8.95 9.70 11.0 13.0
0.08 0.21 0.35 0.47 0.77 1.08
0.02 0.08 0.16 0.25 0.47 0.72 0.99 1.24 1.49 1.72 1.94 2.42 3.08
0.46 0.52 0.59 0.68 0.91 1.21 1.50 1.82 2.11 2.38 2.66 3.28 4.08
0.62 0.69 0.78 0.89 1.15
1.49 1.82
0.20 0.36 0.44 0.56 0.83 1.13 1.44
2.18 2.51 2.80 3.12 3.79 4.68
2.0 1 2.26 2.54 3.12 3.95
0.36 0.50 0.58 0.69 0.94 1.23 1.54 I .81 2.12 2.40 2.70 3.32 4.16
0.18 0.27 0.33 0.4 1 0.62 0.85 I.1 I 1.35 I.59 1.82 2.06 2.58 3.28
1.40 1.72 2.02 2.29 2.57 3.15 3.97
1.72
266
D. V. Gorbatkov et al. i Nucl. Instr. and Meth. in Ph_vs. Rex A 388 (I 997) 260-266
kerma factors presented here, along with any other kerma data from the literature. The reason is that the absence of high-energy charged particle equilibrium renders the kerma approximation (see Eq. (1)) impractical, especially for light (A < 30) elements. Specific neutron, proton and pion absorbed dose values, being used instead of kerma factors in Eq. (1) for the absorbed dose calculation in the energy range up to lOOOGeV, will be presented elsewhere.
6. Conclusion The kerma factors for the main constituents of tissue and detector materials have been calculated with the geometry-dependent hybrid model. Comparisons of measured and calculated data showed a really good agreement between the GDH and experimental charged particle emission spectra over a very wide energy range. According to an estimate, uncertainties of the kerma factors obtained are only of the order of 6-10%. The kerma factor values for hydrogen, carbon, oxygen, nitrogen, silicon, as well as for tissue and several detector materials at energies from 15 to 150 MeV are given.
Acknowledgements We would like to thank Dr. G.I. Britvich Kurochkin for several helpful discussions.
and LA.
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