A Two-Dimensional Benchmark Experiment for Neutron Transport in Water

For the purpose of providing standard data for checking two-dimensional neutron penetration calculations, fast neutron spectra as well as thermal and epithermal neutron fluxes were measured over a two-dimensional (R, Z) space in water shield using an activation method. Threshold reaction rates were converted to fast neutron scalar flux spectra with the aid of the SAND-II code. These results agree within a factor of 2 with the calculations by a two-dimensional discrete ordinates code PALLAS-2D. Thermal and epithermal neutron fluxes obtained with the Westcott's method agree quite well with the calculated values by the PALLAS-2D code in which the diffusion equation was adopted for dealing with low energy neutrons to reduce the computing time. All experimental results are given in the absolute values.     

Measurement of Thermal Neutron Spectra in High Temperature Graphite Bulk Poisoned with Boron

Thermal neutron spectra in the graphite bulk of slab geometry with boron carbide were measured at temperatures from 20 to -800°C by the time-of-flight method, using a 100 MeV electron linear accelerator. The results were compared with calculation based on the multi-group S ₈ method using Young-Koppel's scattering law. Fairly good agreement is obtained between the calculated and measured spectra except in a limited range of energy just above the peak of the thermal spectra. Considering the uncertainty in the spectrum calculations, the scattering kernel of graphite based on the scattering law will be accurate sufficiently to evaluate the infinite multiplication factor of a graphite moderated reactor within an error of about 0.15%. It is also emphasized from the two-dimensional S ₄ calculations that the effect of reentrant hole perturbation should be so significant in the graphite bulk as to decrease the peak of the thermal spectra by 10-12%.     

Fast Neutron Transport through Laminated Iron-Water Shield

Reaction rates were measured in a laminated iron-water shield by threshold detectors, from which the neutron spectra were obtained with the aid of the SAND-II code. The error analysis for the unfolding of the spectra proved that the spectra obtained satisfactorily in the energy range of 1–10.5 MeV. One-dimensional calculations were made by the discrete ordinates transport codes ANISN-JR and PALLAS in a spherical geometry. Agreements within a factor of 1.6 for the spectra and 1.31 for the reaction rates were obtained between the measurements and calculations, though rather large discrepancies were found in the spectra at the energy range of 3–7 MeV. All experimental data in absolute value and detailed specifications for source, detector and the experimental geometry are given for a fast neutron transport benchmark calculation.     

Thermal Neutron Spectra in Light Water Poisoned with Cadmium and/or Indium

The thermal neutron spectra in light water of slab geometry poisoned with Cd and/or In were measured by the time of flight method, using a 20-MeV electron linear accelerator. The thermal spectra were simulated to those in the Pu built-up core of a commercial light water reactor corresponding to a fuel burnup of about 15,000 MWD/T. The results of measurements were compared with calculations based on the S ₄ method using the Haywood scattering law. Fairly good agreement was obtained between the calculated and measured results except in a limited range of energy above the 0.176 eV resonance of Cd. It is concluded that the P ₁ components of the source neutrons as well as the neutron scattering kernel play a significant role in the calculation of the thermal neutron spectra with large flux gradients, and that the scattering kernel of light water based on the Haywood model will be accurate enough to evaluate the infinite multiplication constant k_∞ of light water reactor cores with high fuel burnup within an error of about — 0.17%, as estimated from the uncertainty in the spectrum calculation in the region above the Cd resonance. It is also emphasised from the two- dimensional S ₄ calculations that the effect of reentrant hole perturbation should be evaluated quantitatively in the interpretation of the measured angular neutron spectra produced within finite media.     

Measurement of Neutron Flux Distribution in Critical Assembly with Position-Sensitive Helium-3 Proportional Counter

Neutron flux distributions in the Kyoto University Critical Assembly were measured with a position-sensitive ³He proportional counter. The authors examined the results of the first attempt to apply the position-sensitive counter for such measurement in the critical assembly. Some problems to be solved were drawn from the present examination for the further development of this type of counters. The counter had a sensitive length of 118 cm and an outer diameter of 2.5 cm. The counting gas was a mixture of ³He (270 Pa) and CF₄ (3×10⁴Pa). The observed distribution was very similar to that measured with the conventional gold wire activation method. The position resolution was 2.7 cm in the experimental condition. The measurable neutron flux (at peak position) was limited to the order of 10⁴ n-cm^?2-s^?1 due to the pileup of signal pulses. The counter was a useful tool to quickly measure the flux distribution in the assembly.     

Moderator Temperature Coefficient in BWR Core

Temperature dependences of infinite multiplication factor k∞ and neutron leakage from the core must be examined for estimation of moderator temperature coefficient. Temperature dependence on k∞ has been investigated by many researchers, however, the dependence on neutron leakage of a BWR with cruciformed control rods has hardly been done. Because there are difficulties and necessity on calculations of three space dimensional and multi-energy groups neutron distribution in a BWR core.

In this study, moderator temperature coefficients of JPDR-II (BWR) core were obtained by calculation with DIFFUSION-ACE, which is newly developed three-dimensional multi- group computer code. The results were compared with experimental data measured from 20 to 275°C of the moderator temperature and the good agreement was obtained between calculation and measurement.

In order to evaluate neutron leakage from the core, the other two calculations were carried out, adjusting criticality by uniform absorption rate and by material buckling. The former underestimated neutron leakage and the latter overestimated it. Discussion on the results shows that in order to estimate the temperature coefficient of BWR, neutron leakage must be evaluated precisely, therefore the calculation at actual pattern of control rods is necessary.     

Measurements and Calculations of Neutron Energy Spectra Behind Polyethylene Shields Bombarded by 40- and 65-MeV Quasi-Monoenergetic Neutron Sources

Measurements of neutron energy spectra behind 30.5-, 61.0-, 122.0-, 183.0-cm-thick polyethylene shields bombarded by 40- and 65-MeV quasi-monoenergetic neutrons are performed at the 90-MeV AVF cyclotron of the TIARA (Takasaki Ion Accelerator for Advanced Radiation Application) at JAERI (Japan Atomic Energy Research Institute). Source neutrons are produced at 3.6- and 5.2-mm-thick⁷ Li targets bombarded by 43- and 68-MeV protons, respectively. A BC501A organic liquid scintillator and multi-moderator spectrometer with a ³He counter (Bonner ball) are used for spectrometry of transmitted neutrons and their energy spectra are obtained with the unfolding technique. The energy spectra from a few MeV up to a peak energy are obtained by the BC501A scintillator measurement and those below a few MeV down to thermal energy are obtained by the Bonner ball measurement. The measurements are performed on the neutron beam axis and at off-center positions, and attenuation profiles of neutron fluxes along the beam axis are obtained. The MORSE Monte Carlo calculations are performed with the DLC119/HIL086 multi-group cross section library for comparison with the measured data. The calculation generally gives a little overestimated fluxes, and a few % longer attenuation lengths of peak flux and dose equivalent.     

Kinetic Parameter βeff/ℓ Measurement on Low Enriched Uranyl Nitrate Solution with Single Unit Cores (600𝛗;, 280T, 800𝛗;)of STACY

The kinetic parameter β_eff/? of low enriched (10% EU) uranyl nitrate solution was measured by the pulsed neutron source (PNS) method in STACY This measurement was repeated systematically over several uranium concentrations from about 195 gU/l to about 430 gU/l. Used core tanks were two cylindrical tanks whose diameters are 600 mm and 800 mm and one slab tank which has 280 mm thickness and 700 mm width. In this report, experimental data such as solution conditions, critical solution level for each solution condition, subcritical solution levels where measurements were conducted, measured decay time constants of prompt neutron and extrapolated β_eff/? values are described as well as basic principle of the PNS method. The kinetic parameter β_eff/? values were evaluated also by computation with the diffusion code CITATION in SRAC and the nuclear data library JENDL 3.2. Strong linear correlation has been found between kinetic parameter β_eff/? and uranium concentration regardless of differences of reflecting conditions or core tank conditions. Experimentally or computationally evaluated β_eff/? value is about 90 s^-1 at 195 gU/l and about 170 s^-1 at 430 gU/l and both experimental and computational values show good agreement within an error of 3% which is comparable to about 2% uncertainty of measurement.     

Calculational Study of Time-Dependent Neutron Spectra in Ice at Low Temperature

Calculations on the time-dependent neutron spectra in an ice block are reported for the temperature range of 86–16 K.

Three models for the lattice vibrational frequency distributions were applied to calculate scattering kernels. Calculated spectra were compared with measured spectra. It was found that the calculation with the Debye model agrees well with the experiment.

From the present analysis, it was suggested that the Debye temperature θ_D of the low temperature ice can be expressed as θ_D = 208 + 0.3T ₀ where T ₀ is the medium temperature.     

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.     

Design concept of a small nuclear reactor for large-diameter NTD-Si using a conventional PWR full-length fuel assembly

A design concept for a small nuclear reactor dedicated to large-diameter neutron transmutation doping silicon (NTD-Si) is proposed. Conventional PWR (Pressurized Water Reactor) full-length fuel assembly is used to assure stable and reliable supply of fuel. Criticality, neutron transportation, and core burn-up calculations are performed using the MVP/GMVP II code and MVP-BURN code. The calculation results show that the proposed reactor can be critical over 18 years, and excess reactivity can be suppressed by a combination of Gd₂O₃ burnable poison and soluble boron. Preliminary steady-state single-channel thermal hydraulic analysis showed that heat removal from core is possible under 1 atm operating pressure. Si ingots up to 30 cm in diameter can be irradiated in the reactor irradiation channels, and the uniform irradiation condition can be achieved for a large-diameter Si ingot.     

Analysis of Cavity Effect on Space- and Time-Dependent Fast and Thermal Neutron Energy Spectra

The effects of the presence of a central cavity on the space- and time-dependent neutron energy spectra in both thermal and fast neutron systems are analyzed theoretically with use made of the multi-group one-dimensional time-dependent S_n method. The thermal neutron field is also analyzed for the case of a fundamental time eigenvalue problem with the time-dependent P₁ approximation. The cavity radius is variable, and the system radius for graphite is 120 cm and for the other materials 7 cm.

From the analysis of the time-dependent S_n calculations in the non-multiplying systems of polythene, light water and graphite, cavity heating is the dominant effect for the slowing-down spectrum in the initial period following fast neutron burst, and when the slowing-down spectrum comes into the thermal energy region, cavity heating shifts to cavity cooling. In the multiplying system of ²³⁵U, cavity cooling also takes place as the spectrum approaches equilibrium after the fast neutron burst is injected.

The mechanism of cavity cooling is explained analytically for the case of thermal neutron field to illustrate its physical aspects, using the time-dependent P₁ approximation. An example is given for the case of light water.     

Estimate of (n,p) Cross Section for Unstable Nuclide 60Co by Multi-Step Hauser-Feshbach Model with Pre-Equilibrium Correction

Abstract

The cross section of the (n, p) reaction for unstable target nuclide ⁶⁰Co was estimated by a multi-step Hauser-Feshbach model code with pre-equilibrium correction. Parameters used in the model calculations were determined from the fitting of the cross sections to existing experimental data of (n, p), (n, α) and (n, 2n) cross sections and particle emission spectra for the adjacent stable nuclide ⁵⁹Co. The present result for ⁶⁰Co(n, p)⁶⁰Fe was compared with the values estimated from semi-empirical formulae around 14 MeV, The prediction accuracy of the present calculation is considered to satisfy the requirement for the fusion reactor applications. The theoretical model calculations with a reliable parameter set are recommended rather than the semi-empirical formulae for the important activation cross sections of exotic target nuclei including unstable ones.     

Comparison of measured and calculated neutron and gamma ray energy spectra behind an in-line shielded duct

Integral experiments that measure the transport of 14 MeV neutrons through a 0.30-m-diameter duct having a length-to-diameter ratio of 2.83 that is partially plugged with a 0.15 m diameter, 0.51 m long shield comprised of alternating layers of stainless steel type 304 and borated polyethylene have been carried out at the Oak Ridge National Laboratory. Measured and calculated neutron and gamma ray energy spectra are compared at several locations relative to the mouth of the duct. The measured spectra were obtained using an NE-213 liquid scintillator detector with pulse shape discrimination methods used to simultaneously resolve neutron and gamma ray events. The calculated spectra were obtained using a computer code network that incorporates two radiation transport methods: discrete ordinates (with P₃ multigroup cross sections) and Monte Carlo (with continuous point cross sections). The two radiation transport methods are required to account for neutrons that singly scatter from the duct to the detectors. The calculated and measured neutron energy spectra above 850 keV agree within 5–50% depending on detector location and neutron energy. The calculated and measured gamma ray energy spectra above 750 keV are also in favorable agreement, 5–50%, depending on detector location and gamma ray energy.     

Development of a Fine and Ultra-Fine Group Cell Calculation Code SLAROM-UF for Fast Reactor Analyses

A cell calculation code SLAROM-UF has been developed for fast reactor analyses to produce effective cross sections with high accuracy in practical computing time, taking full advantage of fine and ultra-fine group calculation schemes.

The fine group calculation covers the whole energy range in a maximum of 900-group structure. The structure is finer above 52.5 keV with a minimum lethargy width of 0.008. The ultra-fine group calculation solves the slowing down equation below 52.5 keV to treat resonance structures directly and precisely including resonance interference effects. Effective cross sections obtained in the two calculations are combined to produce effective cross sections over the entire energy range.

Calculation accuracy and improvements from conventional 70-group cell calculation results were investigated through comparisons with reference values obtained with continuous energy Monte Carlo calculations. It was confirmed that SLAROM-UF reduces the difference in k-infinity from 0.15 to 0.01% for a JOYO MK-I fuel subassembly lattice cell calculation, and from ?0.21 % to less than a statistical uncertainty of the reference calculation of 0.03% for a ZPPR-10A core criticality calculation.     

Measurement of α particle energy loss in biological tissue below 2 MeV

The energy loss of α particles crossing biological tissue at energies between 0.8 and 2.2 MeV has been measured. This energy range is very important for boron neutron capture therapy, based on the ¹⁰B(n,α)⁷Li reaction, which emits α particles with energies of 1.78 and 1.47 MeV. One of the methods used for the measurement of the boron concentration in tissue is based on the deconvolution of the α spectra obtained from neutron irradiation of thin (70 μm) tissue samples. For this technique, a knowledge of the behaviour of the energy loss of the particles in the irradiated tissue is of critical importance. In particular, the curve of the residual energy as a function of the distance travelled in the tissue must be known. In this paper, the results of an experiment carried out with an ²⁴¹Am source and a series of cryostatic sections of rat-lung tissue are presented. The experimental measurements are compared with the results of Monte Carlo calculations performed with the MCNPX code.     

Fission Spectrum Averaged Cross Sections of Some Threshold Reactions Measured with Fast Reactor “YAYOI”

Abstract

Fission spectrum averaged cross sections of twenty one threshold reactions were measured in the core center of YAYOI which was a fast neutron source reactor. Fast neutron spectrum in the core was experimentally determined by using a set of activation foils and micro-fission counters, prior to the cross section measurement. It was found that the shape of the fast neutron spectrum was approximately the same as that of fission neutrons above about 2MeV. This fact was also supported by theoretical calculation.

Since this neutron field has scarce thermal and epithermal neutrons, measurement of nuclei produced by threshold reactions is not affected by (n, γ) reactions which are induced by thermal and epithermal neutrons. Moreover, considerably high fast neutron flux (about 5 x 10¹¹n/cm²·sec) enables to measure cross sections of small values.

The results in general agreed with the previous values obtained in a reactor core or with a fission plate within an experimental error, while they were systematically smaller by about 10% than those recommended by Fabry. The measured values are also compared with the results calculated by Pearlstein based on a statistical model.     

A Practical Method for Evaluating the Neutron Dose Equivalent Rate

A practical method applicable to field monitoring with survey instruments is presented, which permits evaluation of the dose equivalent rate for neutrons, the spectrum of which is unknown but with energy ranging from epithermal to fast. The detectors employed consist of a BF₃ proportional counter with paraffin moderators 6.5 cm and I.Ocm thick, sheathed in 0.5 mm thick Cd, and a scintillation (ZnS and plastic) counter.

The dose equivalent rate Z)(mrem/hr) of neutrons with a broad spectrum is determined from the equation D=D_B+D_S , where D _B is dose equivalent rate determined from the effective neutron flux and the effective neutron energy through the counting rates obtained with the BF₃ proportional counter with paraffin moderators, and Ds the dose measured with the scintillation counter, the sensitivity of which is nearly proportional to the dose equivalent rate for neutrons above 2 MeV.

The error in evaluating the dose equivalent rate by the present method has been calculated to be at most 60% for typical neutron spectra, in the energy range from epithermal to 10 MeV.     

Development of Discrete Ordinates SN Code in Three-Dimensional (X,Y, Z) Geometry for Shielding Design

A discrete ordinates transport code ENSEMBLE in (X, Y, Z) geometry has been developed for the purpose of shielding calculations in three-dimensional geometry. The code has some superior features, compared with THREETRAN which is the only code of the same kind so far developed. That is, the code can treat higher order anisotropic scattering and employs a coarse mesh rebalancing method. Moreover it has a negative flux fix-up routine using a variable weight diamond difference equation scheme and has a ray-effect fix-up option using a fictitious source based on S_N→P_N-1 conversion technique. Formulations for these advanced features in three-dimensional space have been derived.

As the demonstration of the capabilities of the code, several numerical analyses and an analysis of an annular duct streaming experiment in JRR-4 at Japan Atomic Energy Research Institute, have been performed.

As a result of these analyses, confirmation has been obtained for the prospect of applicability of ENSEMBLE to practical shielding design.     

Ep≤200 MeV能区p+58Ni反应的计算与分析

以现有质子诱发⁵⁸Ni的各种核反应截面、能谱、双微分截面、弹性散射角分布等实验数据为基础，利用自行研制的大型核模型计算程序MEND计算质子能量在200MeV能区内⁵⁸Ni(p,x)反应的截面、能谱、角分布和n、p、α、d、t、³He6种出射轻粒子的双微分截面。MEND程序的理论框架基于球形光学模型、核子的核内级联发射模型、以激子模型为基础的预平衡发射理论、蒸发模型和带宽度涨落修正的Hauser Feshbach统计理论。光学模型中的势参数由APMN程序通过符合p+⁵⁸Ni反应的去弹截面和弹性散射角分布获得。出射粒子的双微分截面则利用MEND程序输出的能谱再通过Kalbach系统学公式计算。将计算结果与实验数据及ENDF/B6评价库进行了比较，计算结果与实验数据基本一致，与ENDF/B6相比，增加了³He的计算，且将能区上推至200MeV。 