Effective Resonance Integral Research Articles

Determination of the Neutron Flux at the IREN Facility

The IREN complex for neutron physics research was constructed at the Frank Laboratory of Neutron Physics based on a linear accelerator of electrons up to an energy of 50 MeV. Measurements of the neutron flux density in a wide range of energies (from thermal to fast) are required in various experiments. This is done by neutron activation analysis with high-resolution gamma spectroscopy. In order to determine the flux of resonant neutrons more accurately, one needs to calculate the effective resonance integrals with specific features of the real neutron spectrum and the thermal motion and absorption of neutrons in the sample taken into account. A program for computation of effective resonance integrals has been developed for this purpose. The effective resonance integrals for 197Au, 95Zr, 97Zr, and 63Cu are calculated using this program. The values differ considerably from the ones given in reference literature. These results are used to more accurately determine the flux density of neutrons.

Neutron capture cross sections of130,132,134,136,138Ba

Cross sections for radiative capture of neutrons have been measured by the activation technique for stable isotopes of Ba with mass numbers 130, 132, 134, 136, and 138. From separate irradiations using thermal and epithermal neutrons, independent values for the thermal cross sections and effective resonance integrals have been determined. Improved values for the radioactive decay half-lives of ${}^{131}$Ba${}^{g}$, ${}^{131}$Ba${}^{m}$, ${}^{133}$Ba${}^{m}$, ${}^{135}$Ba${}^{m}$, and ${}^{139}$Ba were also obtained. Results of a new measurement of the energies and intensities of the \ensuremath{\gamma} rays in the decay of ${}^{139}$Ba are reported, along with \ensuremath{\beta} feedings and energies for the excited states in the daughter ${}^{139}$La.

Neutron capture by Ru: Neutron cross sections ofRu96,102,104andγ-ray spectroscopy in the decays ofRu97,103,105

Cross sections for radiative capture of neutrons have been measured for stable isotopes of Ru with mass numbers $96,102$, and $104$. From separate irradiations using thermal and epithermal neutrons, independent values for the thermal cross section and effective resonance integral have been determined. Spectroscopic studies of the $\ensuremath{\gamma}$ rays emitted in the decays of $^{97,103,105}\mathrm{Ru}$ have enabled improvements in the precision of the energies and intensities of the radiations along with corresponding improvements in the $\ensuremath{\beta}$-decay feeding intensities and the energies of the levels in the respective daughter nuclei. Similar spectroscopic measurements of the decays of $^{105}\mathrm{Rh}$ (daughter of $^{105}\mathrm{Ru}$) and $^{96}\mathrm{Tc}$ (produced from $n,p$ reactions on $^{96}\mathrm{Ru}$) have resulted in improved $\ensuremath{\gamma}$-ray energies and intensities in those decays.

R-Matrix Analysis of 238U High-Resolution Neutron Transmissions and Capture Cross Sections in the Energy Range 0 to 20 keV

The neutron resonance parameters of 238U were obtained from a SAMMY analysis of high-resolution neutron transmission measurements and high-resolution capture cross-section measurements performed at the Oak Ridge Electron Linear Accelerator (ORELA) in the years 1970–1990 and from more recent transmission and capture cross-section measurements performed at the Geel Linear Accelerator. Compared with previous evaluations, the energy range for this resonance analysis was extended from 10 to 20 keV, taking advantage of the high resolution of the most recent ORELA transmission measurements. The experimental database and the method of analysis are described in this paper. The neutron transmissions and the capture cross sections calculated with the resonance parameters are compared with the experimental data. A description is given of the statistical properties of the resonance parameters and of the recommended values of the average parameters. The new evaluation results in a slight decrease of the effective capture resonance integral and improves the prediction of integral thermal benchmarks by 70 to 200 pcm.

Neutron capture cross section ofPd102

The cross sections for radiative neutron capture by $^{102}\mathrm{Pd}$ have been deduced from a measurement of the \ensuremath{\gamma} rays emitted by 17.0-d $^{103}\mathrm{Pd}$. The thermal cross section has been determined to be $\ensuremath{\sigma}=1.82\ifmmode\pm\else\textpm\fi{}0.20$ b, and the effective resonance integral is $I=23\ifmmode\pm\else\textpm\fi{}4$ b. We also report thermal and resonance capture cross sections for $^{108}\mathrm{Pd}$ and note possible inconsistencies with the presently accepted values of the $^{110}\mathrm{Pd}$ cross sections.

Resonance Self-Shielding in the Actinides

The calculated self-shielding coefficient of the group cross sections for 235U, 239Pu using the evaluated nuclear data files from ENDF/B-6 and JENDL 3.2 are obtained in the energy region bellow 1 keV. The results for the ratios of effective resonance integrals of neutron capture and fission (α) in the groups are presented. The significant difference in the self-shielding factors from the previous evaluations is illustrated. For non-fissile nuclei (e.g. 232Th) the self-shielding factors are calculated by the method of the characteristic function and the results are compared with the available experimental data.

Adjoint neutron spectrum calculation for heterogeneous cells

Forward spectrum weighting has been used to generate broad-group cross sections. However, for some applications of perturbation theory, the adjoint spectrum is needed. Recently an approximate method has been proposed for the adjoint spectrum in a lattice cell, based on an equivalence principle. The approximations made can be avoided if the neutron energy dependence is treated in detail, and the neutron transport through the regions of a lattice cell is adequately represented. In this paper the neutron balance adjoint equations are derived for a heterogeneous unit cell based on the collision probabilities method, and the adjoint spectrum is calculated from this system of equations for different intervals of energy. Forward and adjoint spectra comparisons are done for a unit cell having in its inner region. In the numerical applications of the neutron balance adjoint equations the most important resonances of were considered. The results show significant variations between the forward and adjoint spectra, leading to remarkable differences in the effective resonance integrals.

A New Self-Shielding Method Based on a Detailed Cross-Section Representation in the Resolved Energy Domain

The calculation of a dilution cross section {bar {sigma}}{sub e} is the most important step in the self-shielding formalism based on the equivalence principle. If a dilution cross section that accurately characterizes the physical situation can be calculated, it can then be used for calculating the effective resonance integrals and obtaining accurate self-shielded cross sections. A new technique for the calculation of equivalent cross sections based on the formalism of Riemann integration in the resolved energy domain is proposed. This new method is compared to the generalized Stamm`ler method, which is also based on an equivalence principle, for a two-region cylindrical cell and for a small pressurized water reactor assembly in two dimensions. The accuracy of each computing approach is obtained using reference results obtained from a fine-group slowing-down code named CESCOL. It is shown that the proposed method leads to slightly better performance than the generalized Stamm`ler approach.

An electronic mechanism for electron pairing in antiferromagnetic bridged mixed-valence systems

One- and two-dimensional bridged mixed-valence systems consisting of metal atoms M and polarizable ligands L are discussed. It is argued that when the valence state of the metal atom is changed, the energy gap and the effective resonance integral between M and L orbitals are also changed. The former is due to electron–electron repulsion and the latter to ligand polarization. A Hubbard model Hamiltonian with an occupation-dependent resonance integral is adopted to describe these systems. Approximate solutions are obtained by the Hartree–Fock method. One-dimensional chains and two-dimensional nets are studied, in which metal ions are joined together by bridging ligands. The fully oxidized system is taken to have one electron per metal orbital, with the ligand orbitals vacant. The electron spin vectors are aligned in an antiferromagnetic fashion. Upon the addition of extra electrons, low-lying vacancies can be formed under certain conditions, which can lead to interesting p-type conductive properties in one or two dimensions. In the one-dimensional system, the formation of such a low-lying vacancy requires that the regional orbitals which contain the added electron are delocalized over seven units or more. (If the bridging ligands are monatomic and the metal–ligand bond distance is about 2 Å, then the delocalization length is about 12 Å.) This phenomenon is unlikely to be realizable in one dimension for the present type of system since it only occurs in parts of parameter space with an unrealistically small value for the electron–electron repulsion U. However, in two dimensions, low-lying vacancies are sometimes predicted by the present model for reasonable values for U. Furthermore, the minimum delocalization radius required for the generation of low-lying vacancies is somewhat smaller in two dimensions than in one. The relative stability of one isolated versus two paired excess electrons is also explored, although some crude assumptions about the delocalization lengths of two vs one excess electrons had to be made. When a single excess electron is delocalized over three units or more, the total energy for two paired excess electrons may be lower than that for two isolated excess electrons. Possible superconductivity by such an electronic mechanism is discussed.

Generalization of the Livolant-Jeanpierre method of resonance self-shielding

In the formulation of resonance self-shielding of Livolant and Jeanpierre, the case of a single fuel region surrounded by a single moderator region is considered. Also a constant macroscopic flux distribution as a function of energy is adopted. This is far from validity in the case of undermoderated systems or in the case of fast reactor spectra. In the present work we started from the original formulation of Livolant-Jeanpierre, but consider that the fuel is surrounded by several moderating regions. It is found that the structure of the fine flux distribution in the resonance can be described using a series of functions which was found to be rapidly convergent. The method is applied for the calculation of multigroup effective cross-sections of 238U for pin cell rods at different moderating ratios and for annular fuel rods as well as for fast reactor lattices. Results were compared with those obtained by Livolant formalism. It has been found that the discrepancies between the two methods depend on the case treated and they reach more than 2% in the case of the effective cross-section and 1.6% in the case of the effective resonance integral.

Effective resonance levels

A method based on the use of effective resonance integrals or group cross sections with resonance self-shielding factors has come into extensive use in calculations of resonance absorption in homogeneous systems. An attempt is made to extend the subgroup treatment, which was initially formulated for the region of forbidden resonances, to the allowed region as applicable to heterogeneous media. A method based on the model of equidistant levels with identical parameters has been developed for the region of the forbidden resonances. Two models are presented; one is based on the theory of intermediate resonances with a temperature dependence. Both models are suitable for describing resonance absorption in both homogeneous and heterogeneous media. Test calculations were made for eight uranium-water cells which demonstrated that by using effective resonance levels for U 238 one can attain the accuracy that is at present attainable in calculations according to the parameters of levels and determined by the error of measurement of the parameters and the error of integrated experiments. The method considered can find application in calculations of resonance absorption in the cells of a reactor according to programs oriented for the use of universal constants, which the parameters are.

Improved Intermediate Resonance Approximation in Heterogeneous System

An improvement of the IR (Intermediate Resonance) approximation is proposed. The effective resonance integrals of the infinite cylindrical fuel lattices are calculated by the analytical method, efficiently and with reasonably good accuracy. The fuel escape probability Pf(E) is based on the two-term rational approximation with an accurate Bell factor [Abar]. The IR parameters λ, κ and μ are determined taking into account the interference between the resonance and potential scatterings, and the effect of the fuel temperature. The effective resonance integrals of the main resonance levels of 238U were calculated using the improved IR approximations, and the accuracy of the method was ascertained by comparing the results with those obtained by the RICM code, which solves the neutron slowing-down equations numerically. Simple approximate expressions for J(ξ β) and J(ξ, σ, β) functions, which are useful in the IR approximations, are also given together with a table of J(ξ, β) and the errors of the simple approximation.

Instrumental neutron activation analysis of geological and pedological samples. Further investigation of epithermal neutron activation analysis using monostandard method

A comparative study is presented on neutron activation analysis of rock and soil samples using whole reactor neutron spectrum and epithermal neutrons with both relative and monostandard procedures. The latter procedure used with epithermal neutron activation analysis of soil samples necessitated the use of the “effective resonance integrals” which were determined experimentally. The incorporation of the β factor, representing deviation of reactor epithermal neutron flux from 1/E law, is developed in the present work. The main criteria for the choice of one or more of the procedures studied for a given purpose are also indicated. Analysis of 15 trace elements, Ca and Fe in the standard Japanese granite JC-1 using monostandard epithermal neutron activation gave results in good agreement with the average literature values.

Resonance absorption calculations in thermal reactors

Publisher Summary The calculation of resonance absorption rates in nuclear reactor cores has long been recognized as one of the most complicated parts of reactor analysis on account of the large number of nuclides with pronounced resonances that are present in the fuel and the drastic cross-section changes that occur in each resonance, sometimes over very narrow energy ranges. The difficulties arise both from the mathematical complexity involved in the accurate description of the cross-section shapes and their changes with temperature, and from the flux changes produced by the resonance absorption. The resonance absorption depends on the fine structure of the flux that has pronounced dips near the energies of the cross-section peaks. An accurate calculation aims at evaluating the resonance reaction rates directly after the energy dependence of the flux has been determined in sufficient detail, particularly at energies in the vicinity of the resonance peaks. Such calculations are quite feasible at present on large computers, for cases in which the material composition and geometrical description of the problem under investigation are not too complicated. This chapter discusses a number of different practical methods in which the resonance absorption problem has been handled in the case of thermal reactor lattices. Lattice heterogeneity effects lead to several practical methods for the calculation of effective resonance integrals that are utilized in a number of core physics analysis codes. They are also required in codes that evaluate the resonance reaction rates directly.

Measurement of the effective resonance integral of thorium metal

Measurement of the effective resonance integral of thorium metal

Grain Structure of High-Temperature Gas-Cooled Reactor Fuel and Its Influence on the Effective Resonance Integral

Calculations taking into account the influence of grain structure on the effective resonance integral of high-temperature reactor fuel assemblies caused by the use of coated particles are checked b...

Direct and adjoint Monte Carlo sampling with reference to a resonance integral problem in a small phase element

Different Monte Carlo methods for estimation of effective resonance integral in small phase element have been studied and compared with each other.

Self-Limiting Power Excursion Characteristics of Light Water Reactor, (V)

The Doppler effect and its influence on the shape of the power burst are studied by analyzing the experimental data from self-limiting power excursion tests on the HTR (Hitachi Training Reactor)-P core (UO2 ceramic fuel, water moderated, enriched to 10% in 235U). Uniform temperature distribution in the fuel element has usually been assumed hitherto for evaluating the Doppler reactivity feedback during a power excursion. In the HTR experiment, however some discrepancy is found in the power transient curve between the experimental results and the calculation with uniform temperature model. It is shown that most of this discrepancy can be explained as being due to the influence of the transient variation of the non-uniform temperature distribution in the fuel element, and also to the large contribution of the surface term of the effective resonance integral.

Self-Limiting Power Excursion Characteristics of Light Water Reactor, (V)

The Doppler effect and its influence on the shape of the power burst are studied by analyzing the experimental data from self-limiting power excursion tests on the HTR (Hitachi Training Reactor)-P core (UO2 ceramic fuel, water moderated, enriched to 10% in 235U). Uniform temperature distribution in the fuel element has usually been assumed hitherto for evaluating the Doppler reactivity feedback during a power excursion. In the HTR experiment, however some discrepancy is found in the power transient curve between the experimental results and the calculation with uniform temperature model. It is shown that most of this discrepancy can be explained as being due to the influence of the transient variation of the non-uniform temperature distribution in the fuel element, and also to the large contribution of the surface term of the effective resonance integral.

Massenspektrometrische bestimmung der neutroneneinfangsquerschnitte von isotopen der seltenen erden

For the determination of neutron capture cross sections of rare earth isotopes, the corresponding elements were electromagnetically separated and the highly enriched isotopes were irradiated with and without Cd-shielding in the ASTRA-reactor to an integrated neutron flux of about 10 20n cm −2. Before and after irradiation, the isotopic abundances were measured by mass spectrometry. The pile capture cross section, the thermal capture cross section and the effective resonance integral for ▪ were obtained, the results are given in the text.