Double differential neutron emission cross sections for n + 230,231,232,233,234Th reactions

Nuclear Physics A 753 (2005) 53–82

Double differential neutron emission cross sections for n + 230,231,232,233,234Th reactions Yinlu Han a,∗ , Zhengjun Zhang b a China Institute of Atomic Energy, P.O. Box 275(41), Beijing 102413, People’s Republic of China b Northwest University, Department of Physics, Xi’an 710069, People’s Republic of China

Received 29 November 2004; received in revised form 27 December 2004; accepted 24 January 2005

Abstract Consistent calculation and analysis of neutron-induced reaction cross sections of 232 Th with optical model, the unified Hauser–Feshbach and exciton model, the linear angular momentum dependent exciton density model, the coupled channel theory and the distorted wave Born approximation is carried out in the En
20 MeV energy range based on the experimental data of total, nonelastic, fission, and other reaction cross section and elastic scattering angular distributions. Especially, the analysis includes the elastic and inelastic scattering angular distribution, the inelastic scattering cross sections of discrete levels, the prompt fission neutron spectra, the double differential cross section and the angle-integrated spectra for neutron emission. Theoretical calculations are compared with recent experimental data, other theoretical calculations and evaluated data from ENDF/B6 and JENDL-3. Theoretical models predict the results for n + 230,231,233,234 Th reactions.  2005 Elsevier B.V. All rights reserved. Keywords: Optical model; Unified Hauser–Feshbach and exciton model; Linear angular momentum dependent exciton density model; Coupled channel theory; Fission cross sections; Double differential cross sections; Fission neutron spectra PACS: 25.85.Ec; 24.75.+i; 24.10.Ht; 24.60.Dr; 24.10.Eg; 24.40.Dn; 24.40.Fq

* Corresponding author.

E-mail address: [email protected] (Y. Han). 0375-9474/$ – see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysa.2005.01.018

54

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

1. Introduction The neutron interactions cross sections and prompt fission neutron spectrum in the energy range below 20 MeV are of fundamental importance for fission and accelerator-driven reactors because they dominate the neutron transport and neutron regeneration, respectively. Therefore, the high precise nuclear reaction data are required for the nuclear and shielding design of fission reactors and accelerator-based system such as accelerator-driven transmutation system. On the other hand, since the neutron emission double differential cross section and spectra provide a complementary information on prompt fission neutrons, and inelastic scattering for discrete and continuum levels of target nucleus, theoretical model calculation can obtain more information about nucleus structure and nuclear reaction. Recently, several new experimental data of n + 232 Th reaction have been reported for the total, capture, fission and neutron emission double differential cross sections and fission spectra. Abfalterer et al. [1] have given measurement of neutron total cross sections up to 560 MeV. The neutron capture cross section has been measured in the energy region between 0.5 keV and 2 MeV in different laboratories [2–6]. Shcherbakov et al. [7] measured neutron-induced fission cross sections in the energy range 1 to 200 MeV. Baba et al. [8] have given the neutron-induced fission spectra at incident energy 4.1 MeV. Several experimental data have been given for the inelastic scattering cross section for low lying discrete levels, but only few experimental data are available for the neutron emission spectra despite of their importance in the analysis of neutron moderation. In particular, the double differential neutron emission cross sections of n + 232 Th reaction were only given for 1.2, 2.03, 2.6, 3.6, 4.25, 6.1, 14.05, 14.1 and 18.0 MeV incident neutrons energy [9–11]. Younes and Britt [12] have presented a reliable set of estimated 231,233 Th(n, f) cross sections that are “unmeasurable” by direct techniques due to lifetime limitations of appropriate target material. Neutron-induced fission cross sections have been extracted from 100 keV to 2.5 MeV using surrogate (t, pf) fission-probability data and a detailed statistical model to compensate for the difference between neutron-induced and (t, p) reactions. Ignatyuk et al. [13] have given neutron and proton cross section evaluations for 232 Th up to 150 MeV based on the coupled-channel model and the statistical model of preequilibrium and equilibrium particle emission, with theoretical model parameters adjusted to the available experimental data. For incident neutron energies below 20 MeV the combination of BROND-2 and ENDF/B-VI evaluations was used. The Kalbach parameterization of angular distributions was used to describe the double differential cross sections of emitted neutrons and charged particles. Maslov et al. [14] have performed consistent evaluation of the 232 Th capture cross section in the energy range from 4 keV to 5 MeV. The Hauser– Feshbach–Moldauer theory and coupled channel optical model were employed. Total, differential scattering, fission, and inelastic scattering data were consistently reproduced as a major constraint for the capture cross-section estimate. Soukhovitskii et al. [15] have given the global coupled-channel optical potential for nucleon–actinide interaction from 1 keV to 200 MeV. Maslov [16] calculated consistently the 232 Th neutron-induced fission cross section with the 232 Th(n, 2n) reaction cross section up to 20 MeV within the Hauser– Feshbach theory, the coupled channel optical model and the double-humped fission barrier model.

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

55

The optical model, the unified Hauser–Feshbach and exciton model, the linear angular momentum dependent exciton density model, the coupled channel theory and the distorted wave Born approximation are employed to consistently calculate all nuclear reaction cross sections, number of neutron per fission, the prompt fission neutron spectra, the angle-integrated spectra for neutron emission, and neutron-induced double differential cross sections for n + 232 Th reaction in the neutron energy region En
20 MeV based on recent experimental data in this work. The calculated results are analyzed and compared with experimental data and other theoretical calculations and evaluated data from ENDF/B6 and JENDL-3. The results for n + 230,231,233,234 Th reactions are predicted. Section 2 provides the theoretical models used in this work. Section 3 gives analysis and comparisons of calculated results with experimental data. Section 4 gives simple conclusions.

2. Theoretical models The optical model is used to describe measured total, nonelastic, elastic scattering cross sections and elastic scattering angular distributions, and to calculate the transmission coefficient of the compound nucleus and the preequilibrium emission process as well as the inverse cross section of the reaction channels. The optical potentials considered here are Woods–Saxon form for the real part, Woods–Saxon and derivative Woods–Saxon form for the imaginary parts corresponding to the volume and surface absorptions respectively, and the Thomas form for the spin-orbit part. In order to obtain a set of neutron optical potential parameters for 232 Th, the optical model code APMN [17] was used in this work. In this code the best neutron optical potential parameters are searched automatically to fit with the relevant experimental data of total cross sections, nonelastic-scattering cross sections, elastic-scattering cross sections, and elastic-scattering angular distributions. The adjustment of optical potential parameters is performed to minimize a quantity called χ 2 which represents the deviation of the theoretical calculated results from the experimental values. The optical potential are expressed by
 V (r) = Vr (r) + i Ws (r) + Wv (r) + Vso (r) + Vc (r) (1) where Vr (r) is the real part potential, Ws (r) and Wv (r) are the imaginary part potential of surface absorption and volume absorption, Vso (r) is the spin–orbit potential, Vc (r) is the Coulomb potential. The energy dependencies of potential depths and optimum neutron optical potential parameters of 232 Th obtained are expressed as follows: V (E) = 51.0445 − 0.3125E + 0.008986E 2 − 24.0(N − Z)/A,

(2)

Ws (E) = 7.2421 + 0.1119E − 12.0(N − Z)/A,

(3)

Uso = 6.2,

(4)

rr = 1.2386,

rs = 1.2499,

rso = 1.2386,

(5)

ar = 0.5932,

as = 0.7548,

aso = 0.5932,

(6)

56

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

where Z, N and A are charge, neutron and mass numbers of target nucleus, respectively, E is incident neutron energy in the center of mass system. The units of the potential V , Ws , Wv , Uso are in MeV, the lengths rr , rs , rso , ar , as , aso are in fermi units and energies E is in MeV. Since the optical model potential depths is dependence of mass number A, charged number Z and neutron number N of target, and the asymmetry term is included, this set of optical model potential parameter is used in n + 230,231,233,234 Th reactions. The direct inelastic scattering cross sections to low-lying states are important in nuclear data theoretical calculations. The code ECIS [18] with a coupled channel theory is used. The direct inelastic scattering cross sections and angular distributions of the 230,231,232,233,234 Th ground state rotational band are calculated by ECIS. The coupled channel optical model parameters and deformation parameters (β2 = 0.1950, β4 = 0.0820) used in ECIS for 232 Th are taken from Ref. [19]. This set of coupled channel optical model parameters is also used, and the deformation parameters are obtained from systematics of nuclear structure properties for 230,231,233,234 Th. The discrete levels are taken into account from ground (0.0 0+ ) up to the thirty-fourth (1.4009 2+ ) excited state of 230 Th, ground (0.0 5/2+ ) up to the twenty-third (0.4522 9/2− ) excited state of 231 Th, ground (0.0 0+ ) up to the twenty-second (1.0787 0+ ) excited state of 232 Th, and ground (0.0 1/2+ ) up to the fourteen (0.2970 13/2+ ) excited state of 233 Th, ground (0.0 0+ ) up to the ninth (1.9120 2+ ) excited state of 234 Th. Levels above 1.4009, 0.4522, 1.0787, 0.2970 and 1.9120 MeV are assumed to be overlapping and level density formalism to be used. Additionally, the code DWUCK [20] with a distorted wave Born approximation theory were used to calculate inelastic scattering cross sections and angular distributions for other excited levels, and the optical potential parameters obtained here is used. The unified Hauser–Feshbach and exciton model [21] is used to describe the nuclear reaction equilibrium and preequilibrium decay processes. The Hauser–Feshbach model with width fluctuation correction describe the emissions from compound nucleus to the discrete levels and continuum states of the residual nuclei in equilibrium processes, while the preequilibrium processes is described by the angular momentum dependent exciton model. The emissions to the discrete level and continuum states in the multi-particle emissions for all opened channels are included. At incident neutron energies below 20 MeV, the secondary particle emissions are described by multi-step Hauser–Feshbach model. To consider the angular momentum and parity conservation the angular momentum (J ) and parity (π ) should be addressed in the master equation of exciton model, the master equation of J π channel is as follows [22]: dq J π (n, t) = λJ+π (n − 2, t)q J π (n − 2, t) + λJ−π (n + 2, t)q J π (n + 2, t) dt
 − λJ+π (n) + λJ−π (n) + WtJ π (n) q J π (n, t)

(7)

where λJ±π is the internal transition rate and WtJ π is the total emission rate of the exciton state in J π channel. The J π dependent internal transition rate can be written in the form λJv π (n) = λv (n)χ J (n),

v = +, 0, −,

(8)

where λv (n) is the internal transition used in the usual J π independent exciton model, while χ J (n) stands for the angular momentum factor. In Feshbach–Kerman–Koonin

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

57

(FKK) model [23] the angular momentum conservation was considered properly. Following the approach of FKK model the angular momentum factor can be constructed. But in FKK model only spin-zero nucleon was used. In this work the spin-1/2 nucleon is used to provide the angular momentum factor. The δ type residual two-body interaction is used for the particle–hole excitation. In the unified Hauser–Feshbach and exciton model the formula of the energy spectrum can be obtained as follows: W J π (n, E ∗ , ε) dσ  J π  J π σa P (n) b J π = dε WT (n, E ∗ ) n

(9)

Jπ

where σaJ π stands for the absorption cross section, P J π (n) refers to the occupation probability of the n exciton state in the J π channel and WbJ π (n, E ∗ , ε) is the emission rate of particle b at the exciton state n with outgoing energy ε, which can be obtained from Eq. (7). In the present case of incident neutron energy below 20 MeV, only n = 3 exciton states is taken into account for the preequilibrium mechanism. Therefore, the formula of the energy spectrum in practical calculation is given   W J π (3, E ∗ , ε) W J π (E ∗ , ε) dσ  J π = + QJ π (3) b J π (10) σa P J π (3) b J π dε WT (3, E ∗ ) WT (E ∗ ) Jπ where QJ π (3) = 1 − P J π (3) is the occupation probability of equilibrium state in the J π channel and WbJ π (E ∗ , ε) is the emission rate in the Hauser–Feshbach model, in which the width fluctuation correction is included. The double differential cross sections of neutron and proton are calculated by the linear angular momentum dependent exciton density model [24]. Since the improved pick-up mechanism has been employed based on the Iwamoto–Harada model [25], the double differential cross sections of alpha, 3 He, deuteron and triton are calculated by using a new method based on the Fermi gas model [26]. The recoil effects in multi-particle emissions from continuum state to discrete level as well as from continuum to continuum state are taken into account strictly, so the energy balance is held accurately in every reaction channels. The normalized double differential cross section in the standard form is  2l + 1 d 2σ = fl (ε)Pl (cos θ ) (11) dε dΩ 4π l

where fl (ε) is the Legendre expansion coefficient, Pl (cos θ ) refers to the Legendre polynomial. The particle emissions have three cases, (1) from continuum states to continuum states, (2) from continuum states to discrete levels, and (3) from discrete levels to discrete levels. The formula form of the double differential cross section of the first, second particle emission and the residual nucleus are similar, the express are differences and given in Refs. [22,

58

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

27]. The exact Pauli exclusion effect and the Fermi motion of nucleon in the exciton state densities [28,29] and the double differential cross section are taken into account. The fission cross section is an important in n + 230,231,232,233,234 Th reactions. Fission is included as a decay channel, that is, a fission competitive width can be estimated at every step of the cascades. Three uncoupled fission barriers are used to represent the fission system and describe (n, f), (n, nf) and (n, 2nf) channels, respectively. At each barrier a series of transition states characterized by excitation energy above the barrier, spin and parity can be constructed. At higher energies the discrete transition states are replaced by a continuum of such states, using the Gilbert–Cameron level density [30] prescription and appropriate level density enhancement factors. The Hill–Wheeler theory [31] is used in transmission coefficients computed at each barrier. The transmission coefficients of fission channel are defined by the level density ρfJ π (ε) of fissioning nucleus at saddle, TfJ π (U ) =

1 1 J π ρ (U ) 2π h¯

∞ 0

ρfJ π (ε) dε

(12)

1 + exp{−2π(U − Vf − ε)/h¯ ωf }

where U is excited energy of compound nucleus. According to the experimental data of fission cross sections, the adjustment of the height parameters, Vf , the curvature parameters, h¯ ωf of fission barriers, and the saddle level density factors, K1 , is performed to minimize a quantity called χ 2 which represents the deviation of the theoretical calculated fission cross sections from the experimental values. The fission spectrum is calculated by an energy-dependent Watt spectrum. The Kalbach systematical parameter K used in the two-body residual interaction plays an important part in nuclear reaction, which determine the contribution of preequilibrium and equilibrium decay processes. According to the experimental data of reactions and double differential cross sections, K is determined, level densities and giant dipole resonance parameters are adjusted in this work. The fission parameters obtained and level density parameters are given in Table 1. The theoretical model code UNF [22] has been made based on the frame of the optical model, the unified Hauser–Feshbach and exciton model at incident neutron energies below 20 MeV. Since direct inelastic scattering and direct reaction of the outgoing charged particles to low-lying levels is calculated using the coupled channel theory and the distorted wave Born approximation and it is included as input into the UNF calculations, the calculated results will included the effects of the direct reaction processes. To keep the energy balance, the recoil effects are taken into account for all of the reaction processes. Table 1 Level density, pair correction and fission parameters

a ∆ Vf h¯ ω K1

229 Th

230 Th

231 Th

232 Th

233 Th

234 Th

235 Th

28.981 1.000 4.981 1.000 1.000

29.118 0.380 5.350 0.341 0.200

28.936 0.741 5.768 0.741 1.300

29.780 1.018 5.986 1.040 1.950

30.767 0.581 5.135 0.412 1.230

29.087 0.650 5.000 0.500 1.500

29.475 0.780 5.000 0.850 5.500

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

59

3. Theoretical results and analysis The calculated results of neutron total, nonelastic, elastic scattering cross sections and elastic scattering angular distribution are compared with experimental data for n + 232 Th reaction. The calculated results of total cross sections are in good agreement with recent experimental data measured at Los Alamos [1] in Fig. 1, and elastic scattering angular distribution are in agreement with experimental data, while the calculated results of nonelastic cross sections and elastic scattering cross sections pass through existing some experimental data in Fig. 2. Since some experimental data of elastic scattering cross section include inelastic scattering cross sections, calculated results of elastic scattering cross sections are reasonable low experimental data. Based on the above fitting, this set of neutron optical potential parameters is determined for n + 232 Th reaction. The calculated results for total cross sections are similar to evaluated results from ENDF/B6 and JENDL-3 below 7 MeV, there are large difference between them since evaluated data used different experimental data above 7 MeV. Grimes et al. [32,33] have proposed the Ramsaner model to be an excellent tool for fitting available neutron data and for estimating neutron total cross sections where no experimental data are available. The present calculated results of optical potential are similar to those of Grimes et al. for total cross sections of n + 230–234 Th reactions. The comparisons of calculated results of (n, γ ) reaction cross sections with experimental data are given in Fig. 3. The calculated results are in good agreement with recent

Fig. 1. Calculated neutron total cross sections compared with experimental data.

60

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 2. Calculated neutron elastic scattering cross sections compared with experimental data.

Fig. 3. Calculated neutron captures cross section compared with experimental data.

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

61

Fig. 4. Calculated neutron inelastic cross section for the first excited levels compared with experimental data.

measurement data [2–6] and experimental data taken from Refs. [34–39] in the entire energy region. The present results are in agreement with Maslov’s [14] evaluations for energy less 5 MeV. The calculated results of (n, γ ) reaction cross sections are contributions of compound nuclear reaction below 6 MeV, and the direct reaction and semi-direction reaction above 6 MeV. The Oblozinsky model [40] is used in calculation. The cross sections of (n, p), (n, d), (n, t) and (n, α) reactions are less than 10 mb, and have no experimental data. The calculated results of inelastic scattering cross sections and inelastic scattering angular distributions for the first and second excited state are compared with experimental data. The results for the first excited state are given in Figs. 4 and 5. The figures show the compound nuclear reaction is domination for energy below 1.5 MeV, and the direct reaction is domination above 1.5 MeV. The calculated results of inelastic scattering cross sections and inelastic scattering angular distributions of the first excited state are in good agreement with experimental data [41–43]. The calculated results of inelastic scattering angular distributions of the second excited state are in basically agreement with experimental data. The calculated results of inelastic scattering angular distributions and inelastic scattering cross sections for the first and second excited level are lower than the experimental data at energy 3.4 MeV, and since the experimental data of inelastic scattering angular distribution are high for small angular, the experimental data of inelastic scattering cross section deviates from the tendency of all experimental data. Since the first, second and third excited state of 232 Th are 0.0492, 0.1621 and 0.3332 MeV, it is difficult to distinguish between the elastic scattering and inelastic scat-

62

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 5. Calculated neutron inelastic scattering angular distribution for the first excited state compared with experimental data. The results are offset by factors of 10.

tering in experimentally. The experimental data of angular distribution inclusion elastic scattering and inelastic scattering of the first, second and third excited stated were given in Refs. [43,44], respectively. The calculated results of elastic, inelastic scattering angular distribution of the first and second excited stated as well as total angular distribution at energy 2.4 MeV and 5.7 MeV are given in Fig. 6, the results show the contribution of inelastic scattering are important in total angular distribution. The calculated results are in good agreement with experimental data taken from Ref. [43]. Fig. 7 give the comparisons of calculated results with experimental data [44] for elastic, inelastic scattering angular distribution of the first, second and third excited states in energy from 4.5 to 10 MeV, the calculated results fit experimental data very well for all energy. When the contribution of inelastic scattering angular distributions are considered, calculated results are in agreement with experimental data taken from other laboratories as shown in Fig. 8. The present calculated results of optical potential are similar to those of Ignatyuk et al. [13] and Soukhovitskii et al. [15] based coupled-channel optical potential. Fig. 9 gives the comparisons of calculated results with experimental data for (n, n ) reaction. The calculated curves pass through the experimental data within error bars. There are some structures of the evaluation data of ENDF/B6 and JENDL-3, since total inelastic

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

63

Fig. 6. Calculated neutron elastic (doted line) and inelastic scattering angular distribution of the first (dashed line) and second (doted–dashed line) excited state compared with experimental data at energy 2.4 and 5.7 MeV. The solid line represents the total results. The results are offset by factors of 1000.

scattering cross sections are sum of evaluated discrete levels and continuum states cross sections. There are a number of measurements for 232 Th(n, 2n) reaction cross sections. We carried out an exhaustive examination of the measured data, including error analysis and data renormalization, using updated values of appropriated standard and reference data. In most cases the authors used activation technique to measure the 231 Th activity, the activity of the irradiated thorium sample was determined by the weighted average of the values calculated from the intensity of the same gamma peaks using a Ge(Li) detector. The calculated results for (n, 2n) reaction cross sections are in good agreement with the experimental data taken from Refs. [45–49]. The calculated results are in good agreement with new measurements of Karamanis et al. [50] for energy En < 10 MeV, and are not given in Fig. 10. The present theoretical calculated results are similar to Maslov’s [16] results, and are higher than those of ENDF/B6 and JENDL-3. There is a single experimental datum [51] for the (n, 3n) reaction at 14 MeV, the calculated results are basically in agreement with the experimental data as shown in Fig. 11. The fission cross section obtained from theoretical calculations for n + 232 Th reaction are shown in Fig. 12, and the number of neutrons per fission obtained from the systematic formalism which is obtained according to the experimental data of fis-

64

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 7. Calculated neutron elastic and inelastic scattering angular distribution of the first, second and third excited state compared with experimental data. The results are offset by factors of 10.

sion cross sections are modified slightly to better agree with the experimental data. The present results of fission cross section are in good agreement with experimental data [7, 52].

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

65

Fig. 8. Calculated neutron elastic and inelastic scattering angular distribution of the first, second and third excited state compared with experimental data. The results are offset by factors of 10.

The experimental data of fission cross section for n + 232 Th reaction demonstrate strong step-like structures, relevant to the contributions of (n, xnf) reactions to the observed 232 Th(n, tf) fission cross section. It is due to the low fission probability of the 233 Th and the general increase of the fission probabilities of lower mass nuclides for same fissionable element. Fig. 13 gives calculated results of (n, f), (n, nf), (n, 2nf) reactions and total fission cross sections, respectively. The fission probabilities of 231 Th and 230 Th are de-

66

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 9. Calculated neutron inelastic cross sections compared with experimental data.

Fig. 10. Calculated (n, 2n) reaction cross sections compared with experimental data.

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 11. Calculated (n, 3n) reaction cross sections compared with experimental data.

Fig. 12. Calculated neutron fission cross sections compared with experimental data.

67

68

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 13. Calculated neutron fission cross sections for 232 Th.

Fig. 14. Calculated neutron fission cross sections compared with experimental data for 230 Th.

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

69

Fig. 15. Calculated neutron-induced reaction cross sections for 231 Th. The symbols are simulated fission cross section. The (n, f) represents total fission cross section.

fined by the neutron-induced fission data description of 230 Th(n, tf) reaction up to energy about 15 MeV [53–57]. A similar step is predicted in the 230 Th(n, tf) and 234 Th(n, tf) fission cross section around about 9.0 MeV. The results for 230 Th(n, tf) are shown in Fig. 14. The comparison of the calculated fission cross sections of the 231,233 Th(n, f) reactions with the simulated fission cross section data obtained by Younes and Britt [12] show the calculated are in good agreement with simulated fission cross section data [12], and are only given for 231 Th in Fig. 15. The calculated results show the (n, f) reaction competes with the inelastic scattering, the (n, nf) reaction competes with the (n, 2n) reaction and the (n, 2nf) reaction competes with the (n, 3n) reaction. The calculated results for 231 Th(n, n ), (n, 2n) and (n, 3n) reactions are also given in Fig. 15. The present calculated results of fission cross section are similar to those taken from Ref. [16]. The results of (n, nf) and (n, 2nf) reactions are different from those of Ref. [16], since three uncoupled fission barriers are used in present work. Based on the agreement of calculated results with experimental data for all reaction cross section, the fission spectrum, the energy spectrum and double differential cross section of neutron emission are calculated. The fission neutron spectra are compared with experimental data at 1.5, 2.0, 2.9, 4.1 and 14.7 MeV in Fig. 16, and shows the theoretical calculated results are in good agreement with experimental data [8,58–60] for all energy point.

70

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 16. Calculated neutron fission spectra compared with experimental data at 1.5, 2.0, 2.9, 4.1 and 14.7 MeV incident neutron energy. The results are offset by factors of 10.

The neutron-induced double differential emission spectra measurement is that of Baba et al. [9,10] for 1.2, 2.03, 4.25, 6.1, 14.05 and 18.0 MeV incident neutrons. Additionally, Miura et al. [11] gave measurement results at 2.6, 3.6 and 11.8 MeV. Calculated results and experimental data for neutron double differential emission spectra at 1.2 MeV are shown in Fig. 17. Agreement is good over the whole emission energy range. Fig. 17 shows some fluctuations in the calculated results, which are from discrete level contribution in the region of 0.15 to 1.1 MeV. The calculated results are the contribution of the fission channel above neutron emission energy 1.35 MeV. The large peak is mainly contribution of elastic scattering channel and inelastic scattering of the first and second discrete levels. The comparison of calculated results and experimental data for emission neutron double differential cross sections at 2.03 MeV are shown in Fig. 18. The calculated results are in good agreement with experimental data for the position and height of the peak. There are

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

71

Fig. 17. Calculated double differential neutron emission spectra compared with experimental data at 1.2 MeV incident energy. The results are offset by factors of 1000.

some differences between calculated results and experimental data for emission neutron energy below 0.9 MeV, where calculated results are contribution from continuum levels of inelastic scattering channel. Since the energy for the higher discrete level is 1.0787 MeV, levels above 1.0787 MeV are lack of knowledge of spin and parities, and are assumed to be overlapping and level density formalism to be used. If discrete levels above 1.0787 MeV are used, the shortcoming of calculated results may be overcome for emission neutron energy below 0.9 MeV. Fig. 19 is the comparison of calculated results with experimental data at incident energy 2.6 MeV, the calculated results are in good agreement with experimental data for emission neutron energy below 1.0 MeV and above 2.6 MeV, where are contribution from continuum levels of inelastic channel, elastic channel and fission channel. There are some difference between the calculated results and the experimental data for the peak position and height. The comparison of calculated results and experimental data for emission neutron double differential cross sections at 3.6, 4.25 and 6.1 MeV are shown in Figs. 20 and 22, the discrete structures become weaker than for incident neutron below 3.0 MeV, and the continuum component becomes dominant. The calculated results for 3.6 MeV are in good agreement with experimental data. The calculated results for 4.25 and 6.1 MeV are in reasonable agreement with experimental data for emission neutron energy below 4.8 MeV

72

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 18. Calculated double differential neutron emission spectra compared with experimental data at 2.03 MeV incident energy. The results are offset by factors of 10.

and 6.0 MeV, respectively. The experimental data at some angles are higher than calculated results when emission neutron energy are larger than incident neutron energy, where emission neutron double differential cross sections are contribution from elastic scattering and fission channels. It is difficult to understand the experimental data in theoretically. Fig. 23 is the comparison of calculated results with experimental data at incident energy 11.8 MeV, the calculated results are in agreement with experimental data for emission neutron energy below 11.5 MeV. There are some difference between the calculated results

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

73

Fig. 19. Calculated double differential neutron emission spectra compared with experimental data at 2.6 MeV incident energy. The results are offset by factors of 10.

and the experimental data for the elastic scattering peak position, and the elastic scattering peak position for experimental data is at emission neutron energy 12.3 MeV. The calculated results of emission neutron double differential cross sections are from (n, 2n) reaction for emission neutron energy below 5.0 MeV, and inelastic and elastic scattering above 5.0 MeV, respectively. The second chance fission also contributes to fission neutron emission, and the contributions of fission channel are smaller than those of inelastic and (n, 2n) reactions. The experimental data and calculated results of neutron emission double differential cross sections are compared for incident energy 14.05 MeV as shown in Fig. 24. The double differential cross sections are from inelastic, (n, 2n), (n, 3n) and fission reactions.

74

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 20. Calculated double differential neutron emission spectra compared with experimental data at 3.6 MeV incident energy. The results are offset by factors of 10.

The calculated results are in good agreement with experimental data, except the emission neutron energy from 7.0 to 13.0 MeV for some angles, where is the contribution of inelastic scattering channel. Figs. 20–24 also show the calculated results of neutron emission double differential cross sections are lower than experimental data in some range of emission neutron energy for some angles, where the dip structures of experimental data are probable to be produced by statistical error in the subtraction of background data from the foreground one. The elastic scattering peak position of experimental data needs to check in experimentally. The experimental data [10] and calculated results of neutron emission double differential cross sections are compared for incident energy 18.0 MeV as shown in Fig. 25. The

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

75

Fig. 21. Calculated double differential neutron emission spectra compared with experimental data at 4.25 MeV incident energy. The results are offset by factors of 10.

calculated results are in agreement with experimental data above emission neutron energy 10 MeV, and are lower than experimental data below emission neutron energy 10 MeV, where are mainly contribution of (n, 2n), (n, 3n) and fission channels. The experimental data [10] of neutron emission double differential cross sections are inconsistent with experimental data of (n, 2n), (n, 3n) and fission cross sections, since theoretical results and experimental data are in good agreement for (n, 2n), (n, 3n) and fission cross sections at 18.0 MeV. The experimental data [9–11] and calculated results of angle-integrated neutron emission spectra are compared for incident energies 2.03, 2.6, 4.25, 6.1, 14.05 and 18.0 MeV,

76

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 22. Calculated double differential neutron emission spectra compared with experimental data at 6.1 MeV incident energy. The results are offset by factors of 10.

respectively. Our results are in reasonable agreement with experimental data of angleintegrated neutron emission spectra at 2.03, 4.25, 6.1 and 14.05 MeV incident energies as shown in Figs. 26 and 27, except the elastic peak. The experimental data of the spectra at 2.6 MeV were also given in Ref. [11]. There are some difference between the calculated results and the experimental data taken from Ref. [11] for the peak position at energy 2.6 MeV. The comparison of calculated results with experimental data for energy 14.05 and 18.0 MeV is given in Fig. 27. The comparison of calculated results with experimental data at incident energy 18 MeV show the calculated results are not in agreement with experimental data for 5 < En < 11 MeV, where the calculated results are from the contribution of fission and (n, 2n) reaction cross sections. While below emission neutron energy 5 MeV where are mainly contribution of (n, 3n) and fission channels, the calculated results are in

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

77

Fig. 23. Calculated double differential neutron emission spectra compared with experimental data at 11.8 MeV incident energy. The results are offset by factors of 10.

good agreement with experimental data. Figs. 26 and 27 show experimental data of double differential cross sections is inconsistent with those of angle-integrated neutron emission spectra around the elastic peak. Because emission spectra experimental data included prompt fission and scattering neutrons, Figs. 17 to 27 also demonstrate that calculated results of fission neutron spectra are reasonable. Since neutron emission spectra and double differential cross sections provide a complementary information on inelastic scattering for discrete and continuum levels, (n, 2n), (n, 3n) reaction and neutron fission reaction of target nucleus, the agreement of neutron

78

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 24. Calculated double differential neutron emission spectra compared with experimental data at 14.05 MeV incident energy. The results are offset by factors of 10.

emission spectra and double differential cross sections between calculated results and experimental data also shows present calculated results of reaction cross sections are reasonable. Since there are not experimental data up to now, the cross sections, energy spectra and double differential cross sections for neutron, proton, deuteron, triton and alpha emission for n + 230,231,233,234 Th reactions are also calculated and analyzed at incident neutron energies below 20 MeV.

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

79

Fig. 25. Calculated double differential neutron emission spectra compared with experimental data at 18.0 MeV incident energy. The results are offset by factors of 10.

4. Conclusion Based on experimental data of total, nonelastic, elastic scattering cross sections and elastic scattering angular distribution of 232 Th, a set of optimal neutron optical potential parameter is obtained by code APMN. All cross sections of neutron induced reactions, angular distributions, double differential cross sections, the angle-integrated spectra, the prompt fission neutron spectra are consistent calculated using optical model, the unified Hauser–Feshbach and exciton model, the linear angular momentum dependent exciton density model, the coupled channel theory and the distorted wave Born approximation for n + 230,231,232,233,234 Th at incident neutron energies from 0.05 to 20 MeV. Since nuclear model parameters obtained, all channels reaction cross sections and angular distributions

80

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

Fig. 26. Calculated neutron emission spectra compared with experimental data at 2.03, 4.25 and 6.1 MeV incident energies. The results are offset by factors of 100.

Fig. 27. Calculated neutron emission spectra compared with experimental data at 14.05 and 18.0 MeV incident energies. The results are offset by factors of 100.

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

81

are reasonable, the double differential cross section and the angle-integrated spectra for neutron emission are mainly analyzed and compared with experimental data. The present consistent theoretical calculated results are in good agreement with recent experimental data. The successful calculating on all reaction cross sections, angular distributions, the prompt fission neutron spectra, the double differential cross sections and angle-integrated neutron emission spectra also demonstrated the reasonability and dependability of those theoretical models. The calculated results are given in ENDF/B6 format.

Acknowledgements This work is one of Major State Research Development Program that is the physical and technological researches of Accelerator-Driven clean nuclear Power System (ADS), and supported by the China Ministry of Science and Technology under Contract No. G1999022603. This work is IAEA Coordinated Research Projects (CRPs) on Evaluated Nuclear Data for Th-U Fuel Cycle under Contract No. 12484/R0.

References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

W.P. Abfalterer, F.B. Bateman, et al., Phys. Rev. C 63 (2001) 044608. K. Wisshak, F. Voss, F. Kaeppeler, Nucl. Sci. Eng. 137 (2001) 183. D. Karmanis, M. Petit, et al., Nucl. Sci. Eng. 137 (2001) 282. G. Lobo, F. Corvi, et al., Nucl. Sci. Tech. S. 2 (2002) 429. Yu.V. Grigoriev, V.Ya. Kitaev, et al., Nucl. Sci. Tech. S 2 (2002) 350. A. Borella, K. Volev, et al., 2004, private communication. O.A. Shcherbakov, A.Yu. Donets, et al., Nucl. Sci. Tech. S 2 (2002) 230. T. Miura, M. Baba, et al., Nucl. Sci. Tech. S 2 (2002) 409. M. Baba, H. Wakabayashi, T. Ito, et al., Measurements of prompt fission neutron spectra and doubledifferential neutron inelastic scattering cross sections for 238-U and 232-Th, JAERI-M-89-143, 1989. S. Matsuyama, M. Baba, T. Ito, et al., Nucl. Sci. Tech. 27 (1990) 601. T. Miura, M. Baba, et al., Ann. Nucl. Energy 28 (2001) 937. W. Younes, H.C. Britt, Phys. Rev. C 68 (2003) 034610. A.V. Ignatyuk, V.P. Lunev, et al., Nucl. Sci. Eng. 142 (2002) 177. V.M. Maslov, Yu.V. Porodzinskij, et al., Nucl. Sci. Eng. 143 (2003) 177. E.S. Soukhovitskii, S. Chiba, et al., J. Phys. G 30 (2004) 905. V.M. Maslov, Nucl. Phys. A 743 (2004) 236. Q. Shen, Nucl. Sci. Eng. 141 (2002) 78. J. Raynal, Notes on ECIS94, CEA-N-2772, Commissariat a l’Energie Atomique, Saclay, France, 1994, p. 1. G. Vladuca, A. Tudora, M. Sin, Regional phenomenological deformed optical potential for neutron interactions with actinides, Rom. J. Phys. 41 (7–8) (1996) 515–526. P.D. Kunz, Distorted wave code DWUCK4, University of Colorado. J. Zhang, Nucl. Sci. Eng. 114 (1993) 55. J. Zhang, Nucl. Sci. Eng. 142 (2002) 207. H. Feshbach, A. Kerman, S. Koonin, Ann. Phys. (N.Y.) 429 (1980) 429. M.B. Chadwick, P. Oblozinsky, Phys. Rev. C 44 (1991) 1740. A. Iwamoto, K. Harada, Phys. Rev. C 26 (1982) 1821. J. Zhang, Nucl. Sci. Eng. 116 (1994) 35. J. Zhang, Y. Han, L. Cao, Nucl. Sci. Eng. 133 (1999) 218.

82

[28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60]

Y. Han, Z. Zhang / Nuclear Physics A 753 (2005) 53–82

J. Zhang, X. Yang, Z. Phys. A 329 (1988) 69. Z. Sun, S. Wang, J. Zhang, Y. Zhou, Z. Phys. A 305 (1982) 61. A. Gilbert, A.G.W. Cameron, Can. J. Phys. 43 (1965) 1446. D.L. Hill, J.A. Wheeler, Phys. Rev. 59 (1953) 1102. S.M. Grimes, J.D. Anderson, R.W. Bauer, V.A. Madsen, Nucl. Sci. Eng. 130 (1998) 340. R.W. Bauer, J.D. Anderson, S.M. Grimes, D.A. Knapp, V.A. Madsen, Nucl. Sci. Eng. 130 (1998) 348. M. Lindner, R.J. Nagle, J.H. Landrum, Nucl. Sci. Eng. 59 (1976) 381. W.P. Poenitz, D.L. Smith, Fast neutron radioactive capture cross sections, ANL-NDM-42, 1978. K. Kobayashi, Y. Fujita, N. Yamamuro, Measurement of the cross section for the Th-232(n, g) reaction from 1 keV to 450 keV, NEANDC(J)-56/U, 1978. R.P. Anaand, H.M. Jain, et al., Neutron capture cross section of Th-232, BARC-1239, 1984. A.N. Davletshin, E.V. Teplov, et al., Yad. Konstanty 14 (1992). A.N. Davletshin, E.V. Teplov, et al., Yad. Konstanty 13 (1993). P. Oblozinsky, Phys. Rev. C 35 (1987) 407. N.P. Glazkov, Ann. Energy 14 (1963) 400. G. Haouat, J. Lachkar, et al., Nuc. Sci. Eng. 81 (1982) 491. T. Iwasaki, M. Baba, et al., Contribution to the Specialists’ Meeting on Fast Neutron Scattering on Actinide Nuclei, IWASAKI, 1981. A.B. Smith, S. Chiba, Ann. Nucl. Energy 23 (1996) 459. R.J. Prestwood, B.P. Bayhurst, Phys. Rev. 121 (1961) 1438. H. Karius, A. Ackermann, W. Scobel, J. Phys. G 5 (1979) 715. H. Chatani, I. Kimura, Measurement of Th-232 (n, 2n) Th-231 reaction cross section with 14 MeV neutrons, JAERI-M-91-032, 1991, p. 245. H. Chatani, I. Kimura, Ann. Nucl. Energy 19 (1992) 477. P. Paics, S. Daroczy, J. Csikai, et al., Phys. Rev. C 32 (1985) 87. D. Karamanis, S. Andriamonje, et al., Nucl. Instrum. Methods A 505 (2003) 381. M.H. McTaggart, H. Goodfellow, Nucl. Energy, Parts A and B, Reactor Sci. Tech. AB 17 (1963) 437. J.W. Behrens, J.C. Brone, E. Ables, Nucl. Sci. Eng. 81 (1982) 512. J.W. Meadows, ANL-NDM-83, 1983. J.W. Meadows, Ann. Nucl. Energy 15 (1988) 421. D.W. Muir, L.R. Vesser, LA-4648-MS,1971. J.E. Lynn, G.D. James, L.G. Earwaker, Nucl. Phys. A 189 (1972) 225. J. Blons, C. Mazur, D. Paya, et al., Nucl. Phys. A 414 (1984) 1. S.E. Sukhikh, G.N. Lovchikova, et al., Yad. Konstanty 3 (1986) 34. M. Baba, H. Wakabayashi, et al., INDC(NDS)-220, 1989. G.S. Boykov, V.D. Dmitriev, et al., Yad. Konstanty 53 (1993) 628.