Measurements and Calculations of Angular Flux Spectra Emitted from Lithium and Graphite Slabs with D-T Neutron Source

Angular dependent flux spectra from slab assemblies (lithium and graphite) were measured to test nuclear data and calculational methods for D-T fusion reactor neutronics. The collimated 14 MeV neutron source could be applied by the use of an associated particle method and the neutron spectra from 14 to 2 MeV were observed with TOF technique. The measured spectral pattern was dependent on the anisotropy of secondary neutrons emitted from both the elastic and the non-elastic scattering for 14 MeV neutrons. As for the numerical calculations, one-dimensional discrete ordinates transport codes (ANISN and NITRAN) were used. The multigroup cross sections processed with SPTG4Z from ENDF/B-IV were used as common nuclear data base. The problems of calculational methods and nuclear data were discussed in comparison with the experimental data and it was clarified that sufficient nuclear data of angular dependent cross sections for the non-elastic scattering have not been available in ENDF/B-IV and that the anisotropy of the scattering could not be calculated with ANISN which utilized the scattering kernel generated by incorrect treatment of scattering kinematics in the processing code. However, good agreement between the measurements and calculations was obtained by the use of NITRAN system with the appropriate processing codes of inelastic scattering anisotropies. It was shown that the NITRAN system was useful for anisotropic neutron transport calculations.     

中子与58,60Ni反应的理论计算

根据中子与天然Ni及其同位素反应的总截面、去弹截面和弹性散射角分布的实验数据，得到中子的光学模型势参量。应用得到的光学模型势参量，根据光学模型、统一的Hauser-Feshbach和激子模型理论以及扭曲波玻恩近似理论，系统计算和分析了中子与^58,60Ni反应的非弹散射角分布和双微分截面，理论结果与实验很好地一致。     

Cross Section Assessment by Measurement of Time Dependent Neutron Spectra from Lithium Assemblies

Time dependent neutron spectra from lithium assemblies were measured to assess the neutron cross sections of ⁷Li in ENDF/B-IV, which is important nuclide for the D-T fusion reactor blanket material. Pulsed neutrons produced by D-D or D-T reaction were used to measure leakage neutron spectra from cubical lithium assemblies as a function of time by the use of NE213 liquid scintillator. Calculations of time dependent neutron spectra were carried out by the Monte Carlo code SIMON, which was prepared for this study. The group constants used in these calculations were processed from ENDF/B-IV data. The calculated and the measured neutron spectra were compared for the following three; a stationary spectrum, spectra at each time interval and decay curves for specified energy groups. Discrepancies between the measured and the calculated neutron spectra were found in these comparisons. In order to assure the cause of these discrepancies, some calculations were carried out with recently measured cross sections of inelastic scattering which excite 0.478 and 4.63 MeV level of ⁷Li. It was concluded that some of the neutron cross section data of ⁷Li in ENDF/B-IV should be ameliorated.     

Measurement of Double-Differential Neutron Emission Spectra from Uranium-238

We have performed the measurement of neutron emission spectra from ²³⁸U using a time-of-flight technique, and deduced the following data; (1) the prompt fission neutron spectra for 2 MeV incident neutrons at two emission angles of 90° and 135°, (2) the double-differential neutron emission cross sections at the incident energies of 1.2, 2.0, 4.2, 6.1 and 14.1 MeV. The emission spectra and the cross sections for scattering process were also deduced by subtracting the fission neutrons from the experimental spectra. The experimental results were compared with other experiments and the evaluations of JENDL-3 and ENDF/B-IV.

From the fission spectrum data ranging from 2 to 12 MeV, we have derived the best fit parameters for the Maxwellian and Watt type distribution functions. The experimental spectra are described with the Maxwellian spectrum with temperature of 1.24–1.26 MeV and are softer than both evaluations.

The spectra and cross sections for inelastic-scattering showed substantial disagreement with the evaluations concerning the discrete levels between 0.5 and 1.2 MeV, and continuum neutrons due to evaporation and pre-equilibrium processes. The secondary neutron angular distributions at 14 MeV incident energy were reproduced fairly well with the systematics.     

Numerical Solution to Space-Angle Energy-Dependent Neutron Integral Transport Equation

A numerical approach to the steady-state, space-, angle- and energy-dependent neutron transport equation is presented for neutron shielding calculations. The scattering integral, with anisotropic treatment of elastic scattering and isotropic treatment of inelastic scattering, is evaluated by the use of Gaussian and straightforward quadratures. A system of coupled one-group integral equations for all the energy meshes of interest, converted from the energy-dependent integral transport equation, is calculated by performing a line integration along the neutron path in the direction of motion. For this purpose the direction of neutron motion is represented by discrete-ordinate directions Ω_pq on the unit sphere.

The final presentation of the integral transport equation is derived in a difference form convenient for machine computation. A computation program PALLAS has been written in Fortran IV for IBM 360-75 computer to perform neutron transport calculations based on this approach.

Comparisons are given of the numerical solutions with analytical solutions for unscattered fluxes in various geometries such as plane, spherical and two-dimensional cylindrical, for volume sources with self absorption, and with experimental spectra for angular neutron fluxes in graphite-, polyethylene- and water-shield. Excellent agreement is obtained between the present calculations and analytical or experimental results.     

Total Neutron Cross Sections of Magnesium,Aluminum, Silicon,Zirconium, Niobium and Molybdenum in Energy Range from 0.001 to 0.3 eV

Total neutron cross sections of Mg, Al, Si, Zr, Nb and Mo at room temperature have been measured in the energy range of 0.001–0.3 eV using a chopper and TOF facility of the Musashi Institute of Technology Research Reactor. The experiments were performed for solid and powdered samples. For these samples inelastic and elastic scattering cross sections were respectively calculated with the THRUSH code assuming Debye-type frequency spectrum and with the UNCLE-TOM code using crystal structure and lattice constants of each sample.

For solid samples the measured cross sections agreed well with the calculations below the Bragg cut-off energies. For the powdered samples there were good agreements above the Bragg cut-off, and the measurements were larger than the calculations below the Bragg cut-off.

The experimental cross section, adopting the results of powdered and solid samples for energy ranges above and below the Bragg cut-off respectively, agreed well with the calculation which was performed for the samples in perfect polycrystalline state.     

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.     

139La全套中子数据理论计算及评价

利用已有光学模型参数,基于光学模型、扭曲波玻恩近似、统一的Hauser-Feshbach以及角动量宇称相关的激子模型等核反应理论,计算了20 MeV能量范围内,中子与¹³⁹La反应的全套数据,包括反应截面、弹性及非弹性散射角分布、中子及带电粒子出射的能谱及双微分截面等。对模型计算结果进行了评价和统调,加入了共振参数,并将评价结果与实验数据及已有评价数据进行了比对,所有数据均以ENDF-6标准格式输出。     

A Numerical Method for Solving the Neutron Transport Equation in Finite Cylindrical Geometry

A method is presented which provides a numerical solution to the steady state, energy dependent neutron transport equation for finite cylindrical geometry, with anisotropic treatment of elastic scattering and isotropic treatment of inelastic scattering. The main characteristic features of the method are the use of quasi-cartesian coordinates and the application of discrete ordinate numerical integration. A difference form of the Boltzmann equation is derived as the final expression for machine computation.

Comparisons are given of the numerical solutions with an analytical solution for a constant source distribution, and with NIOBE calculations and experimental spectra for neutron transport in water, with good agreement obtained between them.     

Neutron elastic scattering angular distribution in the resolved and unresolved resonance regions

We derive a simple relationship between observed total cross sections and elastic scattering angular distributions for neutron-induced reactions in the fast energy range by combining resonance theory and the optical model (OM). This relationship enables us to estimate the anisotropy in the scattering angular distribution when experimental total cross-section data are available. We apply this method to the angular distributions of ⁵⁸Ni and ⁵⁶Fe and compare with the evaluated values which are based on the experimental data. We also explore the method with ⁹⁰Zr for which the multi-level Breit-Wigner resonance parameters are given.     

Evaluation of Neutron Nuclear Data for Z>88 Minor Nuclides

Neutron nuclear data for 15 minor nuclides (Z>88) have been evaluated in the energy range of 10^?5 eV–20 MeV. Since only few experimental data are available, the present evaluation was mainly based on the systematics of the data from neighboring nuclides and also optical and statistical model calculations. The evaluations have been carried out for neutron cross sections of total, elastic scattering, inelastic scattering, (n, 2n), (n, 3n), (n, 4n), fission and capture reactions. In addition, angular and energy distributions of the emitted neutrons and average number of the emitted neutrons per fission were also evaluated. The results were compiled in the ENDF/B-V format and stored in the JENDL-3.     

Angular distribution of elastic and inelastic scattering of 2.34 Mev neutrons from chromium,iron, and lead

Spectra are obtained for neutrons with initial energy E₀=2.34 Mev scattered by chromium, iron, and lead nuclei, and the corresponding differential cross sections for elastic and inelastic scattering are measured for angles from 30 ° to 135 °. The neutrons were obtained from the D (d, n) He³ reaction with an initial deuteron energy of 1 Mev and a neutron emission angle of 110 °. Nuclear photographic emulsion was used as the detectorspectrometer and as the monitor of the incident neutron flux. The scatterers were 2.8 cm diameter spheres. In calculating the cross sections for elastic and inelastic scattering, corrections for self-absorption and multiple scattering were introduced to the incident neutron flux in the scatterer. The angular distribution of inelastically scattered neutrons from chromium and iron, as well as from lead when the 0.53 Mev level was excited, was found to be isotropic within the limits of the experiment. Inelastic scattering from lead when the 0.805 and 0.890 Mev levels are excited cannot be considered isotropic.     

Investigation of ortho↔para hydrogen conversion by collisions with neutrons

Liquid hydrogen (LH) is constituted by para hydrogen (pH) and ortho hydrogen (oH) molecules. We analyzed the neutron scattering cross sections for pH→oH, pH→pH, oH→pH, and oH→oH reactions in LH. Results show that incident neutron energy lower than 14.7 meV is not sufficient to achieve pH→oH conversion. As energy increases, the cross section of pH→oH reaction increases sharply. If incident neutron energy is larger than 30 meV, branching fraction of pH molecules being converted into oH molecules upon inelastic scattering with the neutrons approaches 100%. As for the opposite process, branching fraction of oH→pH conversion is 10%–20% when incident neutron energy is lower than 30 meV. This conversion fraction oscillates with increasing incident neutron energy, eventually stabilizing at 30%. Based on the cross sections of the four reaction channels, we calculated the corresponding conversion rates based on a reactor cold neutron source model. There is 0.12% pH molecules of LH moderator would be converted to oH for one month operation . If neutron flux increased by 2 orders of magnitude, more than 10% pH would be transformed into oH, which means relative conversion rate of pH→oH induced by neutron inelastic scattering is not negligible.     

Scattering of 14.1 MeV Neutrons by 6Li, 7Li, 9Be, 10B and 11B

Using a time-of-flight spectrometer, the differential cross sections were measured for the elastic and inelastic scattering of 14.1 MeV neutrons by ⁶Li, ⁷Li, ⁹Be, ¹⁰B and ¹¹B. In the case of elastic scattering by ⁷Li and ¹⁰B, correction was applied to subtract the contribution of inelastic scattering from the unresolved first excited state, after which, the elastic scattering data were compared with predictions based on the optical model. The potential parameters derived with a seven-parameter search yielded angular distributions agreeing with the present experimental data. The expressions for these parameters are presented as a function of mass number.

The experimental data on inelastic scattering were analyzed with the distorted wave Born approximation. The deformation parameters were estimated to be nearly equal to or larger than unity for these nuclei.     

Calculation and analysis of proton-induced reactions on Ni at incident energies from threshold to 200 MeV

Proton-induced reactions on ⁵⁸Ni have been studied in the energy range from threshold to 200 MeV. Based on experimental data of elastic scattering angular distributions and nonelastic cross section, an optimal set of proton optical potential parameters for ⁵⁸Ni has been obtained. All cross sections, elastic and inelastic scattering angular distributions, energy spectra and especially double differential cross sections for neutrons, protons, deuterons, tritons, helium particles and alpha particles emission have been calculated, using nuclear models theory. Theoretical calculations have been compared with existing experimental data, in most cases, the calculated results are in good agreement with the experimental data.     

氘核中子反应截面的法捷耶夫方程理论计算

中子引起的轻核反应是核数据研究的重要内容。当前我国核数据库中氘核中子反应截面的计算结果局限于采用s 波可分离势,且入射能量在20 MeV以下。需要发展三体核反应的法捷耶夫方程理论方法,采用超出s 波的核子 核子相互作用,从而对更高能量范围内氘核全套中子反应截面做出准确的描述。本文介绍了利用法捷耶夫方程计算n+d三核子反应体系的弹性散射微分截面、破裂反应、破裂反应出射中子和质子的双微分截面的理论框架及数值计算结果,同时计算了弹性散射总截面和破裂反应总截面的激发函数。计算结果与实验数据及CENDL 32、ENDF/B Ⅷ.0、JENDL 5、JEFF 33等数据库中的评价数据符合较好。     

Elastic Removal Self-Shielding Factors for Light and Medium Nuclides with Strong-Resonance Scattering

The self-shielding factors for elastic removal cross sections of light and medium weight nuclides were calculated for the parameter, σ_o within the conventional concept of the group constant sets. The numerical study were performed for obtaining a simple and accurate method. The present results were compared with the exact values and the conventional ones, and shown to be remarkably improved. It became apparent that the an-isotropy of the elastic scattering did not affect to the self-shielding factors though it did to the infinite dilution cross sections. With use of the present revised set, the neutron flux were calculated in an iron medium and in a prototype FBR and compared with those by the fine spectrum calculations and the conventional set. The present set showed the considerable improvement in the vicinity of the large resonance regions of sodium, iron and oxygen.     

Theoretical calculation and analysis of the p+Co reaction

All cross sections, elastic and inelastic scattering angular distributions, energy spectra, and double differential cross sections of neutron, proton, deuteron, triton, helium and alpha particle emission for the p+⁵⁹Co reaction have been calculated and analyzed at incident energies from threshold to 200 MeV. The optical model, the intra-nuclear cascade model, direct, pre-equilibrium and equilibrium reaction theories are used. It is found that the theoretical calculated results are in good agreement with experimental data.     

Measurement and Analysis of Neutron Spectra in Lithium Fluoride and Polytetrafluoroethylene Piles

For the assessment of neutron cross section data for fluorine, angular neutron spectra in the lithium fluoride (LiF) and polytetrafluoroethylene ((CF₂)n) piles were measured in the energy range from a few keV to a few MeV by the time-of-flight method with an electron linac, and the results were compared with those calculated by using nuclear data from JENDL-2 and ENDF/B-IV. Spatial distributions of neutron and X-ray fluxes were also measured in the test piles by the activation method, and the influence of photoneutrons generated in the sample material on the neutron spectrum in each pile was estimated. As a result, it was found that their influence on the neutron spectrum shape below 1 MeV was not so large as was necessary to be taken into account for the present assessment.

The calculated spectra using the JENDL-2 data and the ENDF/B-IV data show generally good agreement with those measured in both piles. However, both calculations underestimate the neutron fluxes around several 100 keV, and overestimate those below 100 keV, when they are normalized in the energy range of 10 keV～1 MeV. Large discrepancies are found between the shapes of the measured and calculated spectra around the resonances of fluorine cross section below 100 keV. The present measurements and analyses suggest that the reevaluations of the inelastic and elastic scattering cross sections below 1MeV and the resonance cross sections below 100 keV are necessary to reduce the observed discrepancies.