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Calculated neutron cross sections for Cu and Nb up to 32 MeV for neutron damage analysis
Journal of Nuclear Materials 61 (1976) 153-157 0 North-Holland Publishing Company
CALCULATED NEUTRON CROSS SECTIONS FOR Cu AND Nb UP TO 32 MeV FOR NEUTRON DAMAGE ANALYSIS *
C.Y. FU and F.G. PEREY Oak Ridge National Laboratory,
Oak Ridge, Tennessee 37830,
USA
Received 6 January 1976
Cross sections for neutron interaction with Cu and Nb, with emphasis on spectra of light particles from binary reactions, are calculated for neutron energies from 4 to 32 MeV for estimating recoil probability densities for the analysis of damage experiments with a Be(d, n) neutron source. Nuclear model parameters were adjusted to reproduce the available cross-set tion data around 14 MeV. Helium production cross sections were also calculated for 63Cu for neutrons below 20 MeV, as an illustration of the Hauser-Feshbach method for calculating tertiary reaction cross sections. Les sections efficaces pour I’interaction des neutrons avec Cu et Nb, en s’appuyant sur les spectres de particules lkgeres provenant de riactions binaires, ont Ctb calcul&es pour des inergies de neutrons comprises entre 4 et 32 MeV pour estimer les densites de probabilitk de recul pour l’analyse d’expiriences d’endommagement avec une source de neutron Be(d. n). Les paramitres du modile nucleaire ont 6ti ajust; afin de reproduire les do&es de section efficaces disponibles autour de 14 MeV. Les sections efficaces de production d’h&um ont &5 aussi calcult5es pour 63Cu pour des neutrons d’energie inf&ieure ?I 20 MeV, comme illustration de la methode de Hauser-Feshbach de calcul des sections efficaces pour des rhctions tertiaires. Es werden Wirkungsquerschnitte ftir die Wechselwirkung zwischen Neutronen mit einer Energie zwischen 4 und 32 MeV und Cu und Nb aus bin&en Reaktionen unter besonderer Berttcksichtigung von Spektren leichter Teilchen berechnet. Daraus werden Riickstosswahrscheinlichkeitsdichten zur Analyse der Strahlenschgdigung durch eine Be(d, n)Quelle abgeschgtzt. Die Parameter fiir das Kernmodell werden angepasst, urn die verfiigbaren Daten fiir die Wirkungsquerschnitte bei etwa 14 MeV wiedcrgeben zu kiinnen. Der Wirkungsquerschnitt ftir die He-Bildung in 63Cu mit Neutronen einer Energie unterhalb 20 MeV wird ebenfalls berechnet, als Beispiel ftir die Hauser-Feshbach-Methode zur Berechnung von Wirkungsquerschnitten von tertiiiren Reaktionen.
1. Introduction
cle emissions were assumed isotropic in the center-ofmass frame. The effects of anisotropic angular distribution and multiple-particle emission were neglected, as will be further discussed. We therefore compute the cross sections for the emission of various light particles and their energy distributions for incident neutron energies up to 32 MeV, as required for the analysis of damage experiments with a Be(d, n) neutron source
For neutron damage studies, in particular atomic displacement and sputtering, the recoil probability densities of nuclides following neutron interaction are required. To a fairly good approximation, the recoil energy is determined by the center-of-mass motion and the spectrum of the light particle from binary reactions and scattering. Except for elastically scattered neutrons, for which energy distribution and angular distribution are related uniquely, all other light-parti-
PI. Recommended neutron cross sections for Cu and Nb up to 20 MeV are available in the ENDF/B library [2]. In practice, these cross sections are only sufficient for radiation damage studies up to 15 MeV where (n, P), (n, a> and ( n, 2 n1 reactions become important, because energy distributions of the outgoing protons
* Work sponsored by the U.S. Energy Research and Develop ment Administration under contract with Union Carbide Corporation. 153
154
C. Y. Fu, F. C. Perey ! Neutron cross sections ,for Cu and Nb
and alpha-particles are not provided and, for (n, 2n) reaction, the energy distributions of the first and the second neutrons are not separated. On the other hand, experimental data are practically nonexistent above 15 MeV. Therefore, for neutron energies as high as 32 MeV, we relied on nuclear model predictions.
2. Calculational techniques Three separate codes were used to account for different reaction mechanisms. The code GENOA [3,4f is an optical model search code which we used for generating the differential shape elastic scattering from a complex optical model potential. The code TNG [5,6] is a multi-step Hauser-Feshbach code which was used to calculate the deexcitation of the compound system. The code PRECOA [7,8],uses the master-equation approach to the equilibration process and was used to generate the precompound components of various binary reactions. PRECOA also gives the ratio of total pre~ompound cross se&ions to the total compound cross sections. This ratio was then used in TNG to obtain the total compound cross sections. Another reaction mechanism is direct excitation, which we generally include in our ENDFIB evaluations IS]. For reasons to be given, we chose to omit this component. Since recent ENDF/B evaluations for Cu and Nb were available [9,10], we felt that adequate model parameters should reproduce the evaluated cross sections, in particular around 14 MeV where experimental data were generally available to the evaluators. The aim was to reproduce the evaluated integral elastic and inelastic scattering cross sections to about 5%, and the other reaction cross sections to 10%. These desired accuracies correspond to roughly half of the estimated uncertainties ]9,10] for the cross sections in the evaluations, We considered 63Cu in detail. For natural Cu, we used the same model parameters as chosen for h3Cu but used abundance-weighted Q-values for (n, p) and (n, (Y)reactions. The same set of optical model parameters was used in all three codes - in GENOA for generating the shape elastic cross sections, in TNG for computing the trausmission coefficients, and in PRECOA for obtaining the inverse reaction cross sections (we have added an optical model to PKECOA). For Cu we used the local-potential [ 111 equivalent to the neutron non-local poten-
tial of Perey and Buck ] 121, the potential of Percy 13j for protons, and those of Bobrowska et aI. ]! 3f foI alphas. For Nb we used the same neutron and proton parameters as used for Cu, but used those of Matstida et al. fl4] for alphas. For level densities of various residual nuclides, we adopted the comp~ation and formalism of Gilbert and Cameron ]I S]. br the code PBECOA, we need the residuai two-body matrix elements, IM12.Kalbach [7,8] has determined the empirical form iM12 = /cA-~~?-~ with k = 190 for nucleoninduced reactions, where E is incident neutron energy in MeV and A is mass number of the compound nucleus. We also need the single-particle level densities, which were taken as 6a/n2, where a is the Fermi gas level deusity parameter. The first state of the precompound emission was assumed to be two-particle one-hole (3 excitons). The conventions pairing correctton {I 5i was also included in the precompound calculation. By trial and error, we adjusted some of the parameters to move the calculated cross sections to approach the evaluated cross sections near 14 MeV. The real po. tent&l depth for neutron on Nb was changed from 47-0.267E (MeV) to a constant 45 MeV, which improved the fit to the experimental total cross section from 5 MeV to I5 MeV. The level densities of 6GCo were increased according to the method of Gilbert and Cameron [ 151 to obtain the foliowing new parameters: temperature T = 0.94 MeY; energy shift En = -1.02 MeV, and Fermi gas parameter a = 8.33 MeV-I. The factor k was increased to 380 for Cu and 410 for Nb by fitting the calculated neutron spectra to the measurements of Sdnikov et al. ]I 6] at I4 MeV. A larger k increases the spreading widths in the equilibration process, thus decreases the precompound emission and softens the neutron spectrum. An exciton number of 3 fits the shape of the high-energy tail of the measured spectra [16] very well.
3. Calculated cross sections and spectra We present in figs. I and 2 the calculated cross SCtions for Cu and Nb respectively. The binary reaction cross section for neutron emission is denoted as (n, n’) f (n, nx), for proton emission-as (n, p) + (n, px), and for alpha emission as (n, a) + (n, ox). In this notation, the (n, CXX) cross section includes the (n, an) cross section but excludes the (n, no) cross section. fn fig. 3‘we il-
155
C Y. Fu, I? G. Perey / Neutron cross sections for Cu and Nb
I
I
NEUTRb:NC~O~RSECTIONS; 5
2 ELASTIC SCATTERING
NONELASTIC (n, n’) + (n,nW
o/ 0
__~====~~====~====~i:::::~~~ 8
16
24
5
32
INCIDENT NEUTRON ENERGY I MeV) Fig. 1.
Calculated neutron cross sections for copper.
2
2.6 100 0 2.4
% F
1.4
9 I
12
16
20
24
Fig. 3. Calculated spectra of fust outgoing particles from neutron-copper interactions. Curves are labeled by (particle, MeV), where particle is outgoing particle and MeV is incident neutron energy.
2.0
1.8
8
OUTGOING PARTICLE ENERGY (Mb’1
2.2
x P I “E 2
4
some of the laboratory energy distributions of the first outgoing particles for Cu. These energy distributions are angle-integrated and include both precompound and compound components. With these results the study of atomic displacement [l] and sputtering can proceed if isotropic distribution of light particles (except elastic scattering) can be assumed and effects of multiple-particle emission can be neglected. We now examine the possible consequences of these two assump tions. All angular distributions we referred to are for the center-of-mass frame. Within the assumptions of each code, the precompound component of the angular distribution is isotropic, the compound component is symmetric about 90 degrees, and the direct component (which we chose to omit) is peaked forward. Thus a realistic angular distribution is somewhat forward-peaking. We now refer to fig. 2 of ref. [ 11, where the speclustrate
1.6 NONELASTIC (n,n’) + (n.n.?)
0.2 NEUTRON CROSS SECTIONS FOR NIOBIUM ,
8
0
8 16 24 32 INCIDENT NEUTRON ENERGY (MeV)
Fig. 2. Calculated neutron cross sections for niobium.
156
C. 1.. Frr. F. G. Pm-q- / Nmtrorl cross sectiow for Cu and Nb
tra for small angles contribute to small recoil energies (the part to the left of the peak in the recoil probability density); therefore, forward peaking in the anguiar distribution of the light particle tends to soften the recoil probability density. On the other hand, the inclusion of multiple-particle emission tends to harden the recoil probability density. This can be easily visualized by observing that emission of a second particle 90 degrees from the direction of the primary recoil always increases the recoil energy. It is now clear that the effects of the two assumptions on the calculated recoil energy tend to cancel each other and the combined effect is not expected to be large. This also explains why we chose to omit the otherwise-important direct component. The omission affects mainly the angular distribution. because the integral direct cross section is absorbed into the precompound component through the fitting of this component to the experimental data.
4. Helium production The helium production cross section in many r-zelides belcw 20 MeV is composed mainly of t.3, a.1 + (n, ox) and (n, no) cross sections. The calculation of (n, no‘) cross section by Hauser-Feshbach method (with TNG code) is uncommon, so we illustrate here a calculation for 53Cu, which is shown in fig. 4. The experimental cross sections shown [17] are for (n, LX) reaction which accounts for only a few percent of total helium production at 20 MeV. The 63~u(n~ elf c:m sections were calculated with 8 discrete levels of %o (with spins 7/2,3/2,5/L?, 312. 1/2,9j3,5/2, and 7,Q) up to 1.744 MeV. Above this energy, the level density of Gilbert and Cameron [l-5] was still used. The three dots at 12, 14. and 16 MeV are corresponding resdlrs obtained by setting the 8 discrete level spins to 1i2. in order to study the sensitivity of the second-particle emission rate to the residual ievel spins. The ahanges are Large indeed and we therefore conclude that :zs:. dual level spins should be explicitly included for the calculation of helium productio:l cross sections above 14 MeV for medium mass nuclides. Above 20 Me?i. (n. 3nLy) cross sections become important and can also be calculated with the TNG code if needed.
5. Concluding
”
,m.
2
.+p
____.I
__
-
__I.
-
_!
I 100
_-~~+r*_T; .-__ .-gy_._i”_
__ lxr
Lb-3 T._“_’
.-.-
.___
_A-
_
5_----I 2.
to-’
__
__i:_-_ --
I
8
.._
10
-_ --.
I
,NClDENT
14
ENERGY
I
I
I
!6
18
I
12
1
-:-I-_.; ---I._
---I - E
7’
1
6
_
___.
’ I
20
IMeV)
Fig. 4. Calculated helium production cross sections for 63Cu. “Total” is the sum of (n, a) + (II, CYX) and (n. no). Dots are test calculations for (n, n(y); see text for explanation.
remarks
Neutron damage study using high energy neutrons requires advanced knowledge in solid state, atomic, and nuclear physics. We have described our currem capability in cross-section prediction up to 32 MeV relevant to the study of atomic displacement, sputtering, and helium embrittlement in material upon neutron irradiation. Although only the more important cross-section data were calculated, we have indicated that inclusions of anisotropic angular distribution and muitiple-particle emission are within our current capability. Whether these additional cross-section data are required for neutron damage analysis is not yet clear. The calcuiated integral cross sections near ! 4 MeV are comparable in accuracy to the evaluations [9, 101, namely, about 10% for elastic and inelastic scattering, and 20% for (n, p) and (n, 2) reactions. Near reaction thresholds and above 20 MeV, the uncertainties-of rhe calculated cross sections are undoubtedly larger. Fortunately, the neutron source from Be(d, n) reaction with
C. Y. Fu, F. C. Perey /Neutron cross sections for Cu and Nb
40-MeV deuteron beam is peaked near 15 MeV, which more or less coincides with the energy where we know the cross sections best.
Note added in proof Similar calculations have been performed for Al and Au. We appreciate valuable comments from R.G. Alsmiller and R.W. Peelle, both of Oak Ridge National Laboratory.
References 111 J.B. Roberto and M.T. Robinson, J. Nucl. Mat. 61 (1976) 149.
121 ENDF/B Neutron Cross-Section Library, National Neutron Cross Section Center, Brookhaven National Laboratory. [31F.G. Perey, Phys. Rev. 131 (1963) 745. 141F.G. Perey, computer program GENOA, unpublished (1969). 151C.Y. Fu, Development of a Two-Step Hauser-Feshbach Code with Precompound Decays and Gamma-Ray Gas-
157
cades: A Theoretical Tool for Cross Section Evaluations, Proc. Nucl. Cross Sect. Tech., Washington, D.C., March 1975 NBS spec. publ. 425, Vol. 1, p. 328. [6] C.Y. Fu, Atomic Data and Nuclear Data Tables 17, no. 2 (1976). [7] C. Kalbach, Nucl. Phys. A210 (1973) 590. [ 8] C. Kalbach, PRECOA: Programme for Calculating Preequilibrium Particle Energy Spectra, DPh-N/BE/74/3, Centre D’Etudes Nucleaires De Saclay, May 1974. [ 91 M.K. Drake and M.P. Fricke, Evaluation of Neutron and Photon-Production Cross Sections for Natural Cop per, DNA 3356F, Defense Nuclear Agency, July 1974. [lo] A.B. Smith, P.T. Guenther and J.F. Whalen, Z. Physik 264 (1973) 379. [ 111 D. Wilmore and P.H. Hodgson, Nucl. Phys. 55 (1964) 673. [12] F.G. Perey and B. Buck, Nucl. Phys. 32 (1962) 353. [ 131 A. Bobrowska et al., Inst. of Nucl. Phys., Cracow, Poland, Report 777/PL (1971). [14] K. Matsuda et al., J. Phys. Sot. Japan 33 (1972) 298. [15] A. Gilbert and A.G.W. Cameron, Canadian J. of Phys. 43 (1965) 1446. [ 161 O.A. Salnikov et al., International Nuclear Data Committee INDC(CCP)-43/L (1974). [ 171 A. Schett et al., Compilation of Threshold Reaction Neutron Cross Sections, European-American Nuclear Data Committee EANDC 95 “U” (1974).
CALCULATED NEUTRON CROSS SECTIONS FOR Cu AND Nb UP TO 32 MeV FOR NEUTRON DAMAGE ANALYSIS *
C.Y. FU and F.G. PEREY Oak Ridge National Laboratory,
Oak Ridge, Tennessee 37830,
USA
Received 6 January 1976
Cross sections for neutron interaction with Cu and Nb, with emphasis on spectra of light particles from binary reactions, are calculated for neutron energies from 4 to 32 MeV for estimating recoil probability densities for the analysis of damage experiments with a Be(d, n) neutron source. Nuclear model parameters were adjusted to reproduce the available cross-set tion data around 14 MeV. Helium production cross sections were also calculated for 63Cu for neutrons below 20 MeV, as an illustration of the Hauser-Feshbach method for calculating tertiary reaction cross sections. Les sections efficaces pour I’interaction des neutrons avec Cu et Nb, en s’appuyant sur les spectres de particules lkgeres provenant de riactions binaires, ont Ctb calcul&es pour des inergies de neutrons comprises entre 4 et 32 MeV pour estimer les densites de probabilitk de recul pour l’analyse d’expiriences d’endommagement avec une source de neutron Be(d. n). Les paramitres du modile nucleaire ont 6ti ajust; afin de reproduire les do&es de section efficaces disponibles autour de 14 MeV. Les sections efficaces de production d’h&um ont &5 aussi calcult5es pour 63Cu pour des neutrons d’energie inf&ieure ?I 20 MeV, comme illustration de la methode de Hauser-Feshbach de calcul des sections efficaces pour des rhctions tertiaires. Es werden Wirkungsquerschnitte ftir die Wechselwirkung zwischen Neutronen mit einer Energie zwischen 4 und 32 MeV und Cu und Nb aus bin&en Reaktionen unter besonderer Berttcksichtigung von Spektren leichter Teilchen berechnet. Daraus werden Riickstosswahrscheinlichkeitsdichten zur Analyse der Strahlenschgdigung durch eine Be(d, n)Quelle abgeschgtzt. Die Parameter fiir das Kernmodell werden angepasst, urn die verfiigbaren Daten fiir die Wirkungsquerschnitte bei etwa 14 MeV wiedcrgeben zu kiinnen. Der Wirkungsquerschnitt ftir die He-Bildung in 63Cu mit Neutronen einer Energie unterhalb 20 MeV wird ebenfalls berechnet, als Beispiel ftir die Hauser-Feshbach-Methode zur Berechnung von Wirkungsquerschnitten von tertiiiren Reaktionen.
1. Introduction
cle emissions were assumed isotropic in the center-ofmass frame. The effects of anisotropic angular distribution and multiple-particle emission were neglected, as will be further discussed. We therefore compute the cross sections for the emission of various light particles and their energy distributions for incident neutron energies up to 32 MeV, as required for the analysis of damage experiments with a Be(d, n) neutron source
For neutron damage studies, in particular atomic displacement and sputtering, the recoil probability densities of nuclides following neutron interaction are required. To a fairly good approximation, the recoil energy is determined by the center-of-mass motion and the spectrum of the light particle from binary reactions and scattering. Except for elastically scattered neutrons, for which energy distribution and angular distribution are related uniquely, all other light-parti-
PI. Recommended neutron cross sections for Cu and Nb up to 20 MeV are available in the ENDF/B library [2]. In practice, these cross sections are only sufficient for radiation damage studies up to 15 MeV where (n, P), (n, a> and ( n, 2 n1 reactions become important, because energy distributions of the outgoing protons
* Work sponsored by the U.S. Energy Research and Develop ment Administration under contract with Union Carbide Corporation. 153
154
C. Y. Fu, F. C. Perey ! Neutron cross sections ,for Cu and Nb
and alpha-particles are not provided and, for (n, 2n) reaction, the energy distributions of the first and the second neutrons are not separated. On the other hand, experimental data are practically nonexistent above 15 MeV. Therefore, for neutron energies as high as 32 MeV, we relied on nuclear model predictions.
2. Calculational techniques Three separate codes were used to account for different reaction mechanisms. The code GENOA [3,4f is an optical model search code which we used for generating the differential shape elastic scattering from a complex optical model potential. The code TNG [5,6] is a multi-step Hauser-Feshbach code which was used to calculate the deexcitation of the compound system. The code PRECOA [7,8],uses the master-equation approach to the equilibration process and was used to generate the precompound components of various binary reactions. PRECOA also gives the ratio of total pre~ompound cross se&ions to the total compound cross sections. This ratio was then used in TNG to obtain the total compound cross sections. Another reaction mechanism is direct excitation, which we generally include in our ENDFIB evaluations IS]. For reasons to be given, we chose to omit this component. Since recent ENDF/B evaluations for Cu and Nb were available [9,10], we felt that adequate model parameters should reproduce the evaluated cross sections, in particular around 14 MeV where experimental data were generally available to the evaluators. The aim was to reproduce the evaluated integral elastic and inelastic scattering cross sections to about 5%, and the other reaction cross sections to 10%. These desired accuracies correspond to roughly half of the estimated uncertainties ]9,10] for the cross sections in the evaluations, We considered 63Cu in detail. For natural Cu, we used the same model parameters as chosen for h3Cu but used abundance-weighted Q-values for (n, p) and (n, (Y)reactions. The same set of optical model parameters was used in all three codes - in GENOA for generating the shape elastic cross sections, in TNG for computing the trausmission coefficients, and in PRECOA for obtaining the inverse reaction cross sections (we have added an optical model to PKECOA). For Cu we used the local-potential [ 111 equivalent to the neutron non-local poten-
tial of Perey and Buck ] 121, the potential of Percy 13j for protons, and those of Bobrowska et aI. ]! 3f foI alphas. For Nb we used the same neutron and proton parameters as used for Cu, but used those of Matstida et al. fl4] for alphas. For level densities of various residual nuclides, we adopted the comp~ation and formalism of Gilbert and Cameron ]I S]. br the code PBECOA, we need the residuai two-body matrix elements, IM12.Kalbach [7,8] has determined the empirical form iM12 = /cA-~~?-~ with k = 190 for nucleoninduced reactions, where E is incident neutron energy in MeV and A is mass number of the compound nucleus. We also need the single-particle level densities, which were taken as 6a/n2, where a is the Fermi gas level deusity parameter. The first state of the precompound emission was assumed to be two-particle one-hole (3 excitons). The conventions pairing correctton {I 5i was also included in the precompound calculation. By trial and error, we adjusted some of the parameters to move the calculated cross sections to approach the evaluated cross sections near 14 MeV. The real po. tent&l depth for neutron on Nb was changed from 47-0.267E (MeV) to a constant 45 MeV, which improved the fit to the experimental total cross section from 5 MeV to I5 MeV. The level densities of 6GCo were increased according to the method of Gilbert and Cameron [ 151 to obtain the foliowing new parameters: temperature T = 0.94 MeY; energy shift En = -1.02 MeV, and Fermi gas parameter a = 8.33 MeV-I. The factor k was increased to 380 for Cu and 410 for Nb by fitting the calculated neutron spectra to the measurements of Sdnikov et al. ]I 6] at I4 MeV. A larger k increases the spreading widths in the equilibration process, thus decreases the precompound emission and softens the neutron spectrum. An exciton number of 3 fits the shape of the high-energy tail of the measured spectra [16] very well.
3. Calculated cross sections and spectra We present in figs. I and 2 the calculated cross SCtions for Cu and Nb respectively. The binary reaction cross section for neutron emission is denoted as (n, n’) f (n, nx), for proton emission-as (n, p) + (n, px), and for alpha emission as (n, a) + (n, ox). In this notation, the (n, CXX) cross section includes the (n, an) cross section but excludes the (n, no) cross section. fn fig. 3‘we il-
155
C Y. Fu, I? G. Perey / Neutron cross sections for Cu and Nb
I
I
NEUTRb:NC~O~RSECTIONS; 5
2 ELASTIC SCATTERING
NONELASTIC (n, n’) + (n,nW
o/ 0
__~====~~====~====~i:::::~~~ 8
16
24
5
32
INCIDENT NEUTRON ENERGY I MeV) Fig. 1.
Calculated neutron cross sections for copper.
2
2.6 100 0 2.4
% F
1.4
9 I
12
16
20
24
Fig. 3. Calculated spectra of fust outgoing particles from neutron-copper interactions. Curves are labeled by (particle, MeV), where particle is outgoing particle and MeV is incident neutron energy.
2.0
1.8
8
OUTGOING PARTICLE ENERGY (Mb’1
2.2
x P I “E 2
4
some of the laboratory energy distributions of the first outgoing particles for Cu. These energy distributions are angle-integrated and include both precompound and compound components. With these results the study of atomic displacement [l] and sputtering can proceed if isotropic distribution of light particles (except elastic scattering) can be assumed and effects of multiple-particle emission can be neglected. We now examine the possible consequences of these two assump tions. All angular distributions we referred to are for the center-of-mass frame. Within the assumptions of each code, the precompound component of the angular distribution is isotropic, the compound component is symmetric about 90 degrees, and the direct component (which we chose to omit) is peaked forward. Thus a realistic angular distribution is somewhat forward-peaking. We now refer to fig. 2 of ref. [ 11, where the speclustrate
1.6 NONELASTIC (n,n’) + (n.n.?)
0.2 NEUTRON CROSS SECTIONS FOR NIOBIUM ,
8
0
8 16 24 32 INCIDENT NEUTRON ENERGY (MeV)
Fig. 2. Calculated neutron cross sections for niobium.
156
C. 1.. Frr. F. G. Pm-q- / Nmtrorl cross sectiow for Cu and Nb
tra for small angles contribute to small recoil energies (the part to the left of the peak in the recoil probability density); therefore, forward peaking in the anguiar distribution of the light particle tends to soften the recoil probability density. On the other hand, the inclusion of multiple-particle emission tends to harden the recoil probability density. This can be easily visualized by observing that emission of a second particle 90 degrees from the direction of the primary recoil always increases the recoil energy. It is now clear that the effects of the two assumptions on the calculated recoil energy tend to cancel each other and the combined effect is not expected to be large. This also explains why we chose to omit the otherwise-important direct component. The omission affects mainly the angular distribution. because the integral direct cross section is absorbed into the precompound component through the fitting of this component to the experimental data.
4. Helium production The helium production cross section in many r-zelides belcw 20 MeV is composed mainly of t.3, a.1 + (n, ox) and (n, no) cross sections. The calculation of (n, no‘) cross section by Hauser-Feshbach method (with TNG code) is uncommon, so we illustrate here a calculation for 53Cu, which is shown in fig. 4. The experimental cross sections shown [17] are for (n, LX) reaction which accounts for only a few percent of total helium production at 20 MeV. The 63~u(n~ elf c:m sections were calculated with 8 discrete levels of %o (with spins 7/2,3/2,5/L?, 312. 1/2,9j3,5/2, and 7,Q) up to 1.744 MeV. Above this energy, the level density of Gilbert and Cameron [l-5] was still used. The three dots at 12, 14. and 16 MeV are corresponding resdlrs obtained by setting the 8 discrete level spins to 1i2. in order to study the sensitivity of the second-particle emission rate to the residual ievel spins. The ahanges are Large indeed and we therefore conclude that :zs:. dual level spins should be explicitly included for the calculation of helium productio:l cross sections above 14 MeV for medium mass nuclides. Above 20 Me?i. (n. 3nLy) cross sections become important and can also be calculated with the TNG code if needed.
5. Concluding
”
,m.
2
.+p
____.I
__
-
__I.
-
_!
I 100
_-~~+r*_T; .-__ .-gy_._i”_
__ lxr
Lb-3 T._“_’
.-.-
.___
_A-
_
5_----I 2.
to-’
__
__i:_-_ --
I
8
.._
10
-_ --.
I
,NClDENT
14
ENERGY
I
I
I
!6
18
I
12
1
-:-I-_.; ---I._
---I - E
7’
1
6
_
___.
’ I
20
IMeV)
Fig. 4. Calculated helium production cross sections for 63Cu. “Total” is the sum of (n, a) + (II, CYX) and (n. no). Dots are test calculations for (n, n(y); see text for explanation.
remarks
Neutron damage study using high energy neutrons requires advanced knowledge in solid state, atomic, and nuclear physics. We have described our currem capability in cross-section prediction up to 32 MeV relevant to the study of atomic displacement, sputtering, and helium embrittlement in material upon neutron irradiation. Although only the more important cross-section data were calculated, we have indicated that inclusions of anisotropic angular distribution and muitiple-particle emission are within our current capability. Whether these additional cross-section data are required for neutron damage analysis is not yet clear. The calcuiated integral cross sections near ! 4 MeV are comparable in accuracy to the evaluations [9, 101, namely, about 10% for elastic and inelastic scattering, and 20% for (n, p) and (n, 2) reactions. Near reaction thresholds and above 20 MeV, the uncertainties-of rhe calculated cross sections are undoubtedly larger. Fortunately, the neutron source from Be(d, n) reaction with
C. Y. Fu, F. C. Perey /Neutron cross sections for Cu and Nb
40-MeV deuteron beam is peaked near 15 MeV, which more or less coincides with the energy where we know the cross sections best.
Note added in proof Similar calculations have been performed for Al and Au. We appreciate valuable comments from R.G. Alsmiller and R.W. Peelle, both of Oak Ridge National Laboratory.
References 111 J.B. Roberto and M.T. Robinson, J. Nucl. Mat. 61 (1976) 149.
121 ENDF/B Neutron Cross-Section Library, National Neutron Cross Section Center, Brookhaven National Laboratory. [31F.G. Perey, Phys. Rev. 131 (1963) 745. 141F.G. Perey, computer program GENOA, unpublished (1969). 151C.Y. Fu, Development of a Two-Step Hauser-Feshbach Code with Precompound Decays and Gamma-Ray Gas-
157
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