Calculation of 14–15 MeV (<Emphasis Type="Italic">n,d</Emphasis>) Reaction Cross Sections Using Newly Evaluated Empirical and Semi-empirical Systematics

In this study, we have investigated the asymmetry term effect for the (n, d) reaction cross sections at 14–15 neutron incident energy. It has been discussed the odd–even effect and the pairing effect considering binding energy systematic of the nuclear shell model for the new experimental data and new cross section formulae developed by Tel et al. for (n, d) reactions. We have determined different parameter groups by the classification of nuclei into even–even, even–odd and odd–even for (n, d) reactions cross sections. The obtained empirical and semi-empirical formulae by fitting two parameters for (n, d) reactions were given. By using the new cross sections formulae for (n, d) reactions the obtained results have been discussed and compared with the available experimental data.     

Theoretical calculation of neutron cross sections for 90,91,92,94,96Zr in the incident energy range between 200 keV and 20 MeV

Neutron cross sections of ^{90,91,92,94,96}Zr were calculated in the incident energy (E_n) range from 200 keV to 20 MeV for the revision of the 4th version of the Japanese Evaluated Nuclear Data Library (JENDL-4.0). The calculation was carried out by using conventional nuclear reaction models such as the spherical optical model, the distorted wave Born approximation, preequilibrium models, and the multi-step statistical model. Parameter values of these nuclear models were adjusted with the aid of experimental cross sections which were published after the JENDL-4.0 evaluation. Cross sections were computed for total, elastic and inelastic scattering, (n, γ), (n, 2n), (n, p), (n, α), (n, nα), and (n, x) = (n, d) + (n, np) reactions, and they were almost consistent with the experimental data. The cross sections were also estimated for the metastable states with the half-life larger than 1 sec. The obtained results well reproduced measured cross sections for the reactions ⁹⁰Zr(n, 2n)^89mZr, ⁹¹Zr(n, x)^90mY and ⁹¹Zr(n, nα)^87mSr.     

Evaluation Methods of Resonance Absorption for System with Pellet Surrounded by Fuel Solution

Abstract

The reaction cross sections of ²⁷Al(n, p)²⁷Mg, ²⁷Al(n, a)²⁴Na, ⁵⁶Fe(n, p)⁵⁶Mn, ⁹⁰Zr(n, 2n)^89m+gZr and ⁹³Nb(n, 2n)^92mNb have been measured by the activation method in an energy range of 13.3–14.9 MeV using the intense D-T neutron source, FNS. Absolute flux was determined by the associated α-particle counting method incorporated with neutron spectra obtained from both a Monte Carlo calculation and a time-of-flight measurement. Corrections were extensively performed not only for the neutron flux determination, but also for the low energy neutron contribution to the reaction rates. The present data were compared with comprehensive evaluations as well as recent experimental data. The measured cross sections of ²⁷Al(n, a)²⁴Na, ⁵⁶Fe(n, p)⁵⁶Mn and ⁹⁰Zr(n, 2n)^89m+gZr are generally in good agreement within experimental errors with the values in both the JENDL Dosimetry File and IRDF-90. It is also shown that there are the overestimation of the cross sections for ⁹³Nb(n, 2n)^92mNb in the JENDL Dosimetry File, and the over- estimation and underestimation of the cross section for ²⁷Al(n, p)²⁷Mg in the JENDL Dosimetry File and IRDF-90, respectively.     

Transient Analysis of Boiling Transition Phenomena Using Liquid Film Flow Model

An evaluation has been made for the covariances of neutron cross sections of ⁵²Cr, ⁵⁶Fe, ⁵⁸Ni and ⁶⁰Ni contained in JENDL-3.2. Reactions considered were the threshold reactions such as (n, 2n), (n, nα), (n, np), (n, p), (n, d), (n, t) and (n, α), the radiative capture reaction above the resonance region, and the inelastic scattering to discrete and continuum levels. Evaluation guidelines and procedures were established during the work.

A generalized least-squares fitting code GMA was used in estimating covariances for reactions of which JENDL-3.2 cross sections had been evaluated by taking account of many measured data. For cross sections that had been evaluated by nuclear reaction model calculations, the KALMAN code, which yields covariances of cross sections and of associated model parameters on the basis of the Bayesian statistics, was used in conjunction with reaction model codes EGNASH and CASTHY.

The evaluated uncertainties of a few percent to 30% in the cross sections look reasonable, and the correlation matrices show understandable trends. Even though there is no strict way to confirm the validity of the evaluated covariances, tools and procedures adopted in the present work are appropriate for producing covariance files based on JENDL-3.2. The covariances obtained will be compiled into JENDL in the near future. Meanwhile, new sets of optical model and level density parameters were proposed as one of byproducts obtained from the KALMAN calculations.     

Neutron Activation Cross Section of Molybdenum Isotopes at 14.8 MeV

The neutron activation cross sections of Mo isotopes have been measured for the 14.8 MeV neutron. The cross sections have been determined with reference to the known ²⁷A1 (n, α)²⁴Na and the ²⁷Al(n, p)²⁷Mg reactions. The cyclic activation method was employed for the γ-ray measurement of short-lived nuclei. A 55 cm³ Ge(Li) detector was used for the measurement of γ-ray spectra. Cross section data are presented for (n, 2n), (n, p) and (n, a) reactions on Mo isotopes. The cross sections of (n, np) reactions on ⁹⁸Mo are also presented. The exponential dependence on (N-Z)/A of the (n, p) reaction cross sections are discussed.     

Evaluation of Neutron Cross Sections of Plutonium-241

The neutron cross sections of ²⁴¹Pu were evaluated in the energy range between 10^?5 eV and 15MeV, and are stored in the Japanese Evaluated Nuclear Data Library Version-1 (JENDL-1). In the energy range below 100eV, the evaluated data contained in ENDE/B-IV and the resonance parameters recommended in BNL-325 were tentatively adopted. The unresolved resonance parameters were determined between 100 eV and 21.5 keV so as to reproduce the experimental data of the fission and capture cross sections. Above 21.5 keV, the fission cross section was evaluated on the basis of the experimental data, most of which were reported as the ratio to the fission cross section of ²³⁵U and then were normalized by the fission cross section of ²³⁵U adopted in JENDL-1. The capture cross section was obtained from the experimental data of a in the energy range up to 250 keV. The capture cross section above 250 keV and the elastic and inelastic scattering, (n, 2n) and (n, 3n) reaction cross sections above 21.5 keV were obtained on the basis of the theoretical calculations. The calculated cross sections are connected smoothly with those obtained from the unresolved resonance parameters at 21.5 keV. This suggests the self-consistency of the present evaluation.     

Activation Cross Sections for (n, 2n) Reaction on Neodymium,Samarium, Gadolinium and Ytterbium at 14.6 MeV

Activation cross sections for the (n, 2n) reaction on Nd, Sm, Gd and Yb have been measured at 14.6 MeV by using a Ge(Li) γ-ray detector. The following cross sections (mb) have been obtained: ¹¹²Nd 1,675±160, ¹⁴³Nd 1,789±147, ¹⁵⁰Nd 1,720±128, ¹⁵⁴Sm 2,010±137, ¹⁶⁰Gd 2,173±152, ¹⁶⁰Yb 2,226 ±152. These (n,2n) cross sections are compared with the theoretical calculations performed by a new model including pre-equilibrium and statistical models. A good agreement between the experimental and calculated cross sections is obtained.     

Measurements of Average Cross Sections for Some Threshold Reactions for Neutrons with Fission-type Reactor Spectrum

The fast neutron spectrum in the core of the Kyoto University Reactor (KUR) was measured by using seven threshold reactions, a ⁶Li sandwich counter and also nuclear emulsion plates, and the results were compared with theoretical calculations by the S_n method. It was found that the shape of the fast neutron spectrum was approximately the same as that of fission neutrons. Making use of these neutrons with fission-type spectrum, measurements were made of the average cross sections for twelve threshold reactions (⁴⁶Ti(n, p)⁴⁶Sc, ⁴⁷Ti(n, p)⁴⁷Sc, ⁴⁶Ti(n, p)⁴⁸Sc, ²⁸Si(n, p)²⁸Al, ²⁹Si(n, p)²⁹Al, ³⁰Si(n, α)²⁷Mg, ⁵¹V(n, α)⁴⁸Sc, ⁶⁴Zn(n, p)⁶⁴Cu, ⁹²Mo(n, p) ^92mNb(n, 2n)_92mNb, ₂₀₄Pb(n, n¹ )^204mPb and ²⁰⁴Pb(n, 2n)²⁰³Pb). For the purpose of comparison, the average cross sections for six among these reactions were measured also with neutrons from a fission plate. The results agreed within experimetal error with those obtained for neutrons in the KUR core. A Ge(Li) counter was mainly used for the measurement of γ-rays emitted from induced activities.     

Evaluation of Photonuclear Reaction Data on Tantalum-181 up to 140MeV

Photonuclear cross sections of ¹⁸¹Ta are evaluated up to an incident photon energy of 140MeV which is the threshold energy for pion production. Re-analyses were performed on the (γ, n) and (γ, 2n) data measured at Saclay and Livermore, and reference data were reconstructed. The absorption cross sections were evaluated with the giant electric dipole resonance (GDR) model below 40MeV. The calculation by the statistical model with preequilibrium correction reproduced the reference data of all the photoneutron cross sections consistently. From 40 to 140 MeV, the quasideuteron model (QDM) was adopted to evaluate photoabsorption cross sections and the results are compared with the measurements. The decaying processes including n, p, d, t, ³He, and α particle emission up to 140MeV were theoretically evaluated by the ALICE-F code.     

Research of Radioisotope Production with Fast Neutrons, (VII)

Production of radioisotopes of high specific activity was studied in the JRR-1 reactor using several (n,p) and (n,α) reactions, such as ²⁴Mg(n,p)²⁴Na, ²⁷A1(n,α)²⁴N_a, ³⁵Cl(n,p)³⁵S, ³⁵C1(n,α)³²P, ⁵⁸Ni(n,p)⁵⁸Co, ⁶⁴Z_n (n,p) ⁶⁴C_u and ⁶⁷Z_n(n,p) ⁶⁷Cu. The target materials for these reactions were irradiated in several experimental holes of JRR-1 and the radioisotopes formed in the target materials were separated. The amount of the radioisotopes produced and the specific activity were determined, and the possibility of producing high specific activity radioisotopes by these reactions was investigated. The specific activity of the radioisotopes produced by the (n,p) and (n,γ) reactions was more than several hundreds times higher than when produced by the corresponding (n,γ)reactions. Although the yield of the radioisotopes by the former two reactions was fairly small, practical production of high specific activity radioisotopes by this method was thought to be possible, at least for elements of lower atomic number such as those studied in the present work.

For each experimental hole, the thermal and the fast neutron fluxes were determined respectively by the reactions ¹⁹⁷Au(n,γ)¹⁹⁸Au and ⁵⁸Ni(n,p)⁵⁸Co. In order to apply these (n,p) and (n,α) reactions effectively to radioisotope production, such basic informations as the dependence of the reactions on neutron energy and the effect of irradiation position on the reaction yield were studied on the basis of the neutron flux distribution, and the cross section of the reactions for fast neutrons in JRR-1 was estimated.     

Current Induced at Conduit Wall by Molten Salt Flowing Across a Magnetic Field

Activation cross sections for mercury isotopes have been measured at neutron energy between 13.4 and 14.9 MeV by means of the activation method using Fusion Neutronics Source (FNS) at Japan Atomic Energy Research Institute (JAERI). Measured cross sections are those of ¹⁹⁶Hg(n, 2n)^195m,^gHg, ¹⁹⁸Hg(n, 2n)^197m,^gHg, ¹⁹⁸Hg(n, p) ¹⁹⁸gAu, ¹⁹⁹Hg(n, p)¹⁹⁹Au, ²⁰⁰Hg(n, p)^200m,gAu, ²⁰¹Hg(n, p)²⁰¹Au, ²⁰²Hg(n, p)²⁰²Au, ²⁰⁴Hg(n, 2n)²⁰³Hg and ²⁰⁴Hg(n, p)²⁰⁴Au reactions. The cross sections of the ²⁰²Hg(n, p)²⁰²Au and ²⁰⁴Hg(n, p)²⁰⁴Au reactions were measured for the first time. For the ¹⁹⁶Hg(n, 2n) ^195m,^gHg, ¹⁹⁸Hg(n, 2n)^197m,^gHg, ¹⁹⁸Hg(n, p)^198gAu and ¹⁹⁹Hg(n, p)¹⁹⁹Au reactions, the cross sections at plural neutron energies were measured for the first time. The present data were compared with the experimental data reported previously and the recent evaluations, and it was shown that some evaluations need to be improved.     

Triton Emission Spectra in Some Target Nuclei Irradiated by Ultra-Fast Neutrons

High-current proton accelerator technologies make use of spallation neutrons produced in (p,xn) and (n,xn) nuclear reactions on high-Z targets. The produced neutrons are moderated by heavy water. These moderated neutrons are subsequently captured on ³He to produce tritium via the (n,p) reaction. Tritium self-sufficiency must be maintained for a commercial power plant. So, working out the systematics of (n,t) reaction cross sections and triton emission differential data are important for the given reaction taking place on various nuclei at different energies. In this study, triton emission spectra by using ultra-fast neutrons (incident neutron energy >50 MeV), the (n,xt) reactions for some target nuclei as ¹⁶O, ²⁷Al, ⁵⁶Fe, ⁵⁹Co, ²⁰⁸Pb and ²⁰⁹Bi have been investigated. In the calculations, the pre-equilibrium and equilibrium effects have been used. The calculated results have been compared with the experimental data taken from the literature.     

Calculation of Neutron Nuclear Data on Molybdenum Isotopes for JENDL-4

Neutron nuclear data on ⁹²,⁹⁴,⁹⁵,⁹⁶,⁹⁷,⁹⁸,⁹⁹,¹⁰⁰ Mo have been calculated for the evaluated nuclear data library JENDL-4. Simultaneously calculated are the total, elastic and inelastic scattering, (n, p), (n, d), (n, t), (n, ³He), (n, α), (n, np), (n, nd), (n; nα), (n, 2n), (n, 3n) reaction cross sections, the angular distributions of emitted particles, and the energy distributions of emitted particles and γrays. The statistical model was applied to calculate these quantities. Coupled-channel optical model parameters were used for neutrons. Preequilibrium and direct-reaction processes were taken into account in addition to the compound process. The present calculations are almost consistent with available experimental data. The calculated results are compiled into JENDL-4.     

The Study of (<Emphasis Type="Italic">n,d</Emphasis>) Reaction Cross Sections for Some Medium Weight Targets up to 30 MeV

In this study, neutron incident reaction cross sections for some medium target nuclei ( ⁴⁴ Ca, ⁶⁵ Cu, ⁵⁴ Fe, ⁵⁶ Fe, ⁵⁷ Fe, ⁵⁸ Ni, ⁶⁰ Ni and ⁶⁷ Zn) have been investigated for the (n,d) reaction cross sections. These new calculations on the excitation functions of ⁴⁴ Ca(n,d) ⁴³ K, ⁶⁵ Cu(n,d) ⁴⁴ Ni, ⁵⁴ Fe(n,d) ⁵³ Mn, ⁵⁶ Fe(n,d) ⁵⁵ Mn, ⁵⁷ Fe(n,d) ⁵⁶ Mn, ⁵⁸ Ni(n,d) ⁵⁷ Co, ⁶⁰ Ni(n,d) ⁵⁹ Co and ⁶⁷ Zn(n,d) ⁶⁶ Cu reactions have been carried out up to 30 MeV incident neutron energy. In these calculations, the pre-equilibrium and equilibrium effects have been investigated. The PEQ calculations involve the new evaluated the Geometry Dependent Hybrid model. Equilibrium effects are calculated according to the Weisskopf–Ewing model. By using the new cross sections formulae for (n,d) reactions developed by Aydin et al., the obtained results have been discussed and compared with the available experimental data taken from EXFOR database.     

Evaluation of Neutron Nuclear Data for Mercury

Neutron nuclear data of stable mercury isotopes (¹⁹⁶Hg, ¹⁹⁸Hg, ¹⁹⁹Hg, ²⁰⁰Hg, ²⁰¹Hg, ²⁰²Hg and ²⁰⁴Hg) have been evaluated in the energy range of 10^?5eV–20MeV. Evaluated quantities are the total, elastic and inelastic scattering, capture, (n, 2n), (n, 3n), (n, p), (n, d), (n, α), (n, np), (n, nα) reaction and γ-ray production cross sections, the resonance parameters, and the angular and energy distributions of emitted neutrons and γ-rays. The evaluation is mainly based on nuclear reaction model calculations. Statistical-model calculation played a significant role in the determination of the reaction cross sections. The evaluated data have been compiled in the ENDF-6 format, and are used for the design study of a mercury target system proposed at the Neutron Science Research Center, Japan Atomic Energy Research Institute.     

Evaluation of Neutron Nuclear Data for Uranium-233

Neutron nuclear data of ²³³U have been evaluated in the energy range from 10-⁵ eV to 20 MeV. Evaluated quantities are the total, fission, capture, elastic and inelastic scattering, (n,2n) and (n,3n) reaction cross sections, and the average numbers of prompt and delayed neutrons emitted per fission. The thermal and resonance cross sections have been evaluated on the basis of the measured data. The resolved resonance parameters are given up to 100 eV and the unresolved resonance parameters between 100 eV and 30keV. The total and fission cross sections have been evaluated in the higher energy region on the basis of the recently measured data, while the theoretical calculation with the optical, statistical and evaporation models has been used for evaluation of the other cross sections. The presently adopted optical potential parameters have reproduced well the experimental total cross section in the entire energy range as well as the measured data of the s-wave strength function. The structure observed in the vp values below 1 MeV is reproduced by the semi-empirical formula based on the fission fragment kinematics. The presently evaluated fission cross section is considerably lower than that of ENDF/B-IV between 10 and 50keV. This low fission cross section is expected to resolve the ^Keff discrepancy pointed out from the benchmark tests in ²³³U critical assemblies.     

Cross Section Calculations of (n,2n) and (n,p) Nuclear Reactions on Germanium Isotopes at 14–15 MeV

Neutron incident reaction cross sections of Germanium isotopes (^70,72,74,76Ge) were investigated for the (n,2n) and (n,p) reactions around 14–15 MeV. Cross section calculations have been presented for ⁷⁰Ge(n,2n)⁶⁹Ge, ⁷²Ge(n,2n)⁷¹Ge, ⁷⁴Ge(n,2n)⁷³Ge, ⁷⁶Ge(n,2n)⁷⁵Ge, ⁷⁰Ge(n,p)⁷⁰Ga, ⁷²Ge(n,p)⁷²Ga, ⁷⁴Ge(n,p)⁷⁴Ga, and ⁷⁶Ge(n,p)⁷⁶Ga reactions. Theoretical calculations were performed with four different computer codes: ALICE/ASH for the Geometry Dependent Hybrid model, TALYS 1.6 for two component Exciton model, EMPIRE 3.2 Malta for Exciton model and PCROSS for Full Exciton model with the incident neutron energy up to 20 MeV. The (n,2n) and (n,p) reaction cross section calculations were compared with empirical formulas derived by several researchers and compared with the experimental data obtained from EXFOR database as well as with evaluated Nuclear data files (ENDF/B-VII.1: USA 2014). Results show good agreement between the theoretical calculations having a major importance in nuclear data evaluation calculations and the experimental data from literature.     

Intranuclear cascade model for 50-MeV-region (p,p′x) reactions over a wide target mass range

In our previous study, the applicable range of the intranuclear cascade model was successfully extended to lower incident energy (p, p′x) reactions by introducing trajectory deflections and low-energy-loss process due to collective excitations. However, the model's validity was confirmed only for a ⁵⁶Fe target. In the present work we widen the applicable range of masses of the target nucleus. First, we derive an expression for the response function, which gives the probability of collective excitation strengths, to fit the distorted-wave Born approximation results as a function of the target mass number and the beam energy. Second, the barrier transmission coefficient was investigated. An expression with a modified Gamow penetration factor was chosen from four phenomenological forms of one-dimensional barrier transmission coefficients. Calculations with the proposed model followed by a generalized evaporation model were carried out for double-differential cross sections of (p, p′x) reactions at 30–60 MeV. Although the response function and the transmission coefficient were only parameterized approximately, the proposed model showed good agreements with experimental observations for a variety of nuclear targets from ¹²C to ²⁰⁹Bi.     

Calculation of Neutron Nuclear Data on Rubidium and Strontium Isotopes for JENDL-4

Neutron nuclear data on ^85,86,87Rb and ^{84,86,87,88,89,90}Sr have been calculated for the evaluated nuclear data library JENDL-4 in the energy region from 10 keV to 20MeV. Simultaneously calculated are the total, elastic, and inelastic scattering, (n,γ), (n, p), (n, d), (n, t), (n,³He), (n,α), (n, np), (n, nd), (n, nα), (n, 2n), (n, 3n) reaction cross sections, angular distributions of emitted particles, and energy distributions of emitted particles and γ-rays. The statistical model was applied to calculate these quantities. Coupledchannel optical model parameters were used for neutrons. Preequilibrium and direct-reaction processes were taken into account in addition to the compound process. The present calculations are consistent with available experimental data. The calculated results are compiled into JENDL-4.     

Evaluation of neutron nuclear data on xenon isotopes

Neutron nuclear data of Xe isotopes have been evaluated in the energy region, including the resolved resonance one, from 1 keV to 20 MeV by using the theoretical nuclear reaction models. The phenomenological optical model potential was employed to calculate the total cross section for natural Xe with the coupled-channels method. The cross sections for channels of capture, (n, 2n), (n, p) and (n, α) reactions were calculated and compared with available experimental results including recently measured data. The elastic scattering angular distributions and particle emission spectra were calculated, although there is no experimental information available. Reaction cross sections of evaluated libraries were considered for comparison with the calculated results. The presently calculated cross sections reproduce better the available experimental data.