Narrow Resonance Approximation Research Articles

Radiative Neutron Capture Rate of 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B(n,γ)12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n,\\gamma )^{12}$$\\end{document}B Reaction from the Coulomb Dissociation of 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{12}$$\\end{document}B

We calculate the 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B(n,γ)12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n,\\gamma )^{12}$$\\end{document}B reaction rate which is an important constituent in nucleosynthesis networks and is contributed by resonant as well as non-resonant capture. For the resonant rate, we use the narrow resonance approximation whereas the non-resonant contribution is calculated with the Coulomb dissociation method for which we use finite-range distorted wave Born approximation theory. We then compare our calculated rate of 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B(n,γ)12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n,\\gamma )^{12}$$\\end{document}B reaction with those reported earlier and with other charged particle reactions on 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B.

Extension of SARAX code system for reactors with intermediate spectrum

The fast reactor code system SARAX, which was developed at Xi’an Jiaotong University, has recently been extended for wider energy range in order to meet the requirements of new reactor designs with intermediate spectrum. The extension efforts mainly included three parts. First, the new pointwise and multigroup cross-section libraries considering the thermal scattering law were generated by the Atlas code and GESALIB interface. Second, the energy-partitioned resonance self-shielding treatment was used to consider the distinct resonance phenomena in the fast and intermediate energy range. The one-dimensional hyperfine group method was integrated for wide resonance self-shielding in the intermediate energy range, while the Tone’s method with narrow resonance approximation was used for resonance self-shielding in the fast energy range. Third, the pointwise energy-collapsing super-homogenization technique was proposed to obtain the reaction rate conservation in the pointwise-multigroup equivalence. The new SARAX system was verified against several problems with different neutron-moderating materials. Results showed that for the heterogeneous subassembly calculation, the eigenvalue error was less than 100 pcm, and the relative error of multigroup self-shielded cross-sections of major actinides was less than 3.1% compared to the results of Monte-Carlo code OpenMC. For the lead-cooled small modular reactor with beryllium reflector, the results of eigenvalue, Doppler constant, power distribution all agreed well with the OpenMC results.

Three-body scattering: ladders and resonances

We discuss unitarity constraints on the dynamics of a system of three interacting particles. We show how the short-range interaction that describes three-body resonances can be separated from the long-range exchange processes, in particular the one-pion-exchange process. It is demonstrated that unitarity demands a specific functional form of the amplitude with a clear interpretation: the bare three-particle resonances are dressed by the initial- and final-state interaction, in a way that is consistent with the considered long-range forces. We postulate that the resonance kernel admits a factorization in the energy variables of the initial- and the final-state particles. The factorization assumption leads to an algebraic form for the unitarity equations, which is reminiscent of the well-known two-body-unitarity condition and approaches it in the limit of the narrow-resonance approximation.

The SCALE/AMPX multigroup cross section processing for fast reactor analysis

The SCALE/AMPX multigroup (MG) cross section processing procedure has been updated to minimize reactivity differences for fast reactor designs and boiling water reactors (BWRs) with very high void fractions to provide excellent agreement with continuous-energy reference calculations. SCALE MG calculations are widely applied to thermal spectrum light-water reactor (LWR) systems as well as fast spectrum metallic systems of interest to National Nuclear Security Administration. With growing interest from industry and regulators in applying SCALE for the design of fast spectrum reactors, both sodium and molten salt, and in the licensing of power up rates for BWRs, it is desirable to review the SCALE/AMPX procedure for unresolved resonance self-shielded data and high energy neutron spectra. The data were improved by generating MG unresolved resonance data based on the analytic probability table method with the narrow resonance approximation as well as the use of a very fine group structure typically used in fast system analysis. This study focused on verifying the probability table and the SCALE/AMPX MG cross section processing procedure by performing reaction rate analysis and benchmark calculations for various fast reactor and high void BWR systems. Results indicate that the improved SCALE/AMPX MG cross section processing provides excellent results for the fast reactor analysis.

Error analysis of approximations and treatments commonly made in multi-group library and self-shielding calculation based on NECP-X

Approximations and treatments commonly applied in multi-group library and self-shielding calculation of conventional neutronics calculation codes are analyzed based on a numerical nuclear reactor physics code NECP-X. The numerical results show that the approximations and treatments introducing largest errors for UO2 pin cell problems are narrow resonance (NR) approximation, ignorance of multi-group (MG) equivalence effect, Bondarenko iteration method and using average fission spectra. For MOX pin cell problems, the approximations and treatments introducing largest errors are ignorance of thermal resonance, NR approximation, resonance interference factor method, ignorance of MG equivalence effect and in-flow transport correction. These analysis provide references and help to improve the conventional methods and legacy codes.

A new Tone's method in APOLLO3 ® and its application to fast and thermal reactor calculations

Abstract This paper presents a newly developed resonance self-shielding method based on Tone's method in APOLLO3® for fast and thermal reactor calculations. The new method is based on simplified models, the narrow resonance approximation for the slowing down source and Tone's approximation for group collision probability matrix. It utilizes mathematical probability tables as quadrature formulas in calculating effective cross-sections. Numerical results for the ZPPR drawer calculations in 1,968 groups show that, in the case of the double-column fuel drawer, Tone's method gives equivalent precision to the subgroup method while markedly reducing the total number of collision probability matrix calculations and hence the central processing unit time. In the case of a single-column fuel drawer with the presence of a uranium metal material, Tone's method obtains less precise results than those of the subgroup method due to less precise heterogeneous–homogeneous equivalence. The same options are also applied to PWR UOX, MOX, and Gd cells using the SHEM 361-group library, with the objective of analyzing whether this energy mesh might be suitable for the application of this methodology to thermal systems. The numerical results show that comparable precision is reached with both Tone's and the subgroup methods, with the satisfactory representation of intrapellet spatial effects.

MC2-3: Multigroup Cross Section Generation Code for Fast Reactor Analysis

This paper presents the methods and performance of the MC2-3 code, which is a multigroup cross-section generation code for fast reactor analysis, developed to improve the resonance self-shielding and spectrum calculation methods of MC2-2 and to simplify the current multistep schemes generating region-dependent broad-group cross sections. Using the basic neutron data from ENDF/B data files, MC2-3 solves the consistent P1 multigroup transport equation to determine the fundamental mode spectra for use in generating multigroup neutron cross sections. A homogeneous medium or a heterogeneous slab or cylindrical unit cell problem is solved in ultrafine (2082) or hyperfine (~400 000) group levels. In the resolved resonance range, pointwise cross sections are reconstructed with Doppler broadening at specified temperatures. The pointwise cross sections are directly used in the hyperfine group calculation, whereas for the ultrafine group calculation, self-shielded cross sections are prepared by numerical integration of the pointwise cross sections based upon the narrow resonance approximation. For both the hyperfine and ultrafine group calculations, unresolved resonances are self-shielded using the analytic resonance integral method. The ultrafine group calculation can also be performed for a two-dimensional whole-core problem to generate region-dependent broad-group cross sections. Verification tests have been performed using the benchmark problems for various fast critical experiments including Los Alamos National Laboratory critical assemblies; Zero-Power Reactor, Zero-Power Physics Reactor, and Bundesamt für Strahlenschutz experiments; Monju start-up core; and Advanced Burner Test Reactor. Verification and validation results with ENDF/B-VII.0 data indicated that eigenvalues from MC2-3/DIF3D agreed well with Monte Carlo N-Particle5 MCNP5 or VIM Monte Carlo solutions within 200 pcm and regionwise one-group fluxes were in good agreement with Monte Carlo solutions.

Total sensitivity and uncertainty analysis for LWR pin-cells with improved UNICORN code

In this paper, improvements to the multigroup cross-section perturbation model have been proposed and applied in the self-developed UNICORN code, which is capable of performing the total sensitivity and total uncertainty analysis for the neutron-physics calculations by applying the direct numerical perturbation method and the statistical sampling method respectively. The narrow resonance (NR) approximation was applied in the multigroup cross-section perturbation model, implemented in UNICORN. As improvements to the NR approximation to refine the multigroup cross-section perturbation model, an ultrafine-group cross-section perturbation model has been established, in which the actual perturbations are applied to the ultrafine-group cross-section library and the reconstructions of the resonance cross sections are performed by solving the neutron slowing-down equation. The total sensitivity and total uncertainty analysis were then applied to the LWR pin-cells, using both the multigroup and the ultrafine-group cross-section perturbation models. The numerical results show that the NR approximation overestimates the relative sensitivity coefficients and the corresponding uncertainty results for the LWR pin-cells, and the effects of the NR approximation are significant for σ(n,γ) and σ(n,elas) of 238U. Therefore, the effects of the NR approximation applied in the total sensitivity and total uncertainty analysis for the neutron-physics calculations of LWR should be taken into account.

An Improved Resonance Self-Shielding Calculation Method Based on Equivalence Theory

The deviation of the effective resonance cross section obtained by conventional equivalence theory for a heterogeneous system is analyzed. It is shown that several approximations commonly adopted in conventional equivalence theory account for the deviation at different levels, with the narrow resonance (NR) approximation being the main source of deviation. Based on the analysis, an improved method based on equivalence theory is proposed. It utilizes the resonance fine flux integral table to minimize the deviation caused by NR approximation. The validity of the method is confirmed by test calculations of effective resonance cross sections in different geometries and different energy group structures. The results of eigenvalue calculations on typical fuel pin cells show that the proposed improvement is effective in reducing the error of infinite multiplication factors of the pin cell. Since the resonance fine flux integral used in this method has already been obtained in calculating the resonance integral table and can be pre-tabulated in the process of generating the library, the implementation of the proposed method is simple and requires no additional calculations. It is useful for improving the accuracy of lattice physics codes based on the equivalence theory.

The cosmological 7Li problem from a nuclear physics perspective

The primordial abundance of 7Li as predicted by Big Bang Nucleosynthesis (BBN) is more than a factor 2 larger than what has been observed in metal-poor halo stars. Herein, we analyze the possibility that this discrepancy originates from incorrect assumptions about the nuclear reaction cross sections relevant for BBN. To do this, we introduce an efficient method to calculate the changes in the 7Li abundance produced by arbitrary (temperature dependent) modifications of the nuclear reaction rates. Then, considering that 7Li is mainly produced from 7Be via the electron capture process 7Be+e− → 7Li+νe, we assess the impact of the various channels of 7Be destruction. Differently from previous analysis, we consider the role of unknown resonances by using a complete formalism which takes into account the effect of Coulomb and centrifugal barrier penetration and that does not rely on the use of the narrow-resonance approximation. As a result of this, the possibility of a nuclear physics solution to the 7Li problem is significantly suppressed. Given the present experimental and theoretical constraints, it is unlikely that the 7Be+n destruction rate is underestimated by the 2.5 factor required to solve the problem. We exclude, moreover, that resonant destruction in the channels 7Be+t and 7Be+3He can explain the 7Li puzzle. New unknown resonances in 7Be+d and 7Be+α could potentially produce significant effects. Recent experimental results have ruled out such a possibility for 7Be+d. On the other hand, for the 7Be+α channel very favorable conditions are required. The possible existence of a partially suitable resonant level in 11C is studied in the framework of a coupled-channel model and the possibility of a direct measurement is considered.

Towards Quantum Field Theory of D-Particles

§1. Remarks on string field theory from a historical perspective In the first part of the present written report, I would like to review the early history of string theory from the viewpoint of its connection to field theory as well as string field theory, including my personal recollections. I feel somewhat reluctantly that this may be justified, in view of the fact that among the participants of this conference I belong to the eldest generation, starting my research career four decades ago almost simultaneously with the birth of string theory. A hope is that these remarks from a personal point of view tell us something about the nature of string field theory, and also that reflections on the historical side are of some help for conveying to the reader the background and motivations for my recent singular attempt toward a ‘field theory’ of D0-branes. String theory started with the Veneziano amplitude which was originally proposed to be a mathematical model for a duality between Regge-pole and resonance behaviors, being established in the late 1960s experimentally as the characteristics of the scattering of hadrons. The Regge-pole behavior corresponds to the exchange of composite states of hadrons exchanged in t-channel, while the resonance behavior corresponds to the formation of resonating states composed of scattering hadrons in s-channel. The duality meant that a single scattering amplitude can be described either by summation over the Regge pole contributions or over the resonances, but not both simultaneously. The Veneziano formula was regarded as an ideal realization of this duality in the limit of narrow resonance approximation, ignoring finite life times of hadronic states.

Influence of resonance parameters' correlations on the resonance integral uncertainty; 55Mn case

For nuclides with a large number of resonances the covariance matrix of resonance parameters can become very large and expensive to process in terms of the computation time. By converting covariance matrix of resonance parameters into covariance matrices of background cross-section in a more or less coarse group structure a considerable amount of computer time and memory can be saved. The question is how important is the information that is discarded in the process. First, the uncertainty of the 55Mn resonance integral was estimated in narrow resonance approximation for different levels of self-shielding using Bondarenko method by random sampling of resonance parameters according to their covariance matrices from two different 55Mn evaluations: one from Nuclear Research and Consultancy Group NRG (with large uncertainties but no correlations between resonances), the other from Oak Ridge National Laboratory (with smaller uncertainties but full covariance matrix). We have found out that if all (or at least significant part of the) resonance parameters are correlated, the resonance integral uncertainty greatly depends on the level of self-shielding. Second, it was shown that the commonly used 640-group SAND-II representation cannot describe the increase of the resonance integral uncertainty. A much finer energy mesh for the background covariance matrix would have to be used to take the resonance structure into account explicitly, but then the objective of a more compact data representation is lost.

Broad sub-continuum resonances and the case for finite-energy sum-rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension $> 6$ condensates containing at least one $\bar{q}q$ pair. We extract the direct single-instanton contribution to the $F_1$ sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel.

Self-shielding and energy dependence of dilution cross-section in the resolved resonance region

In the calculation of flux weighted multigroup neutron cross-sections of a nuclide present in a homogeneous mixture of several nuclides, by the well known Bondarenko approach, the contributions from the other nuclides to the flux weighting function, are contained in a parameter called ‘dilution’. Under the narrow resonance approximation and with assumed non-overlap of resonances, the energy fluctuations of the dilution are usually ignored within an energy group. The ‘self-shielding factor’ (SSF), which is the ratio of the group cross section for a given dilution to that at infinite dilution, is a smooth function of dilution. A conventional multigroup cross section set, apart from the infinite dilution cross-sections, gives SSF over a dilution grid, from which the effective SSF for any dilution could be obtained by interpolation. The effective SSF multiplied by the infinite dilution cross-section then gives the effective cross-section to be used in the neutronic analyis. Though this conventional procedure works well, the accuracy of this procedure depends on the interpolation scheme used and on the fineness of the dilution grid. The effect of fineness of the dilution grid and the effect of energy dependence of the dilution on the effective SSF are observed, for a specific case, and the results presented in this paper. The JENDL-2 basic nuclear data was used and the benchmark fast critical assembly ZPR-6-7 analysed for a temperature of 300K. The study was restricted to the resolved resonance regions of the nuclides involved. The results appear significant with respect to the target accuracies demanded for the SSF.

QCD sum-rule consistency of lowest-lying [formula omitted] scalar resonances

We investigate lowest-lying scalar meson properties predicted from QCD Laplace sum rules based upon isovector and isoscalar non-strange qq currents. The hadronic content of these sum rules incorporates deviations from the narrow resonance approximation anticipated from physical resonance widths. The field theoretical content of these sum rules incorporates purely perturbative QCD contributions to three-loop order, the direct single-instanton contribution in the instanton liquid model, and leading contributions from QCD-vacuum condensates. In the isovector channel, the results we obtain are compatible with a 0(1450) being the lowest-lying q q resonance, and are indicative of a non-q q interpretation for a 0(980). In the isoscalar channel, the results we obtain are compatible with the lowest lying q q resonance being f 0(980) or a state somewhat lighter than f 0(980) whose width is less than half of its mass. A linear sigma-model interpretation of the lowest-lying resonance's coupling, when compared to the coupling predicted by sum rules, is indicative of a renormalization-group invariant light-quark mass between 4 and 6 MeV.

Broad sub-continuum resonances and the case for finite-energy sum-rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We first discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We then show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension > 6 condensates containing at least one q-bar q pair. We extract the direct single-instanton contribution to the F_1 sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass resonance contributions within the pseudoscalar channel.

Beyond the narrow resonance approximation: Decay constant and width of the first pion-excitation state

We consider the first pion excitation as a sub-continuum resonance in the pseudoscalar channel, and we obtain parameters characterizing this resonance through a global fit of the Borel-parameter dependence of the field-theoretical pseudoscalar Laplace sum rule to its hadronic (pion + pion-excitation + QCD-continuum) content. Our analysis incorporates finite-width deviations from the narrow resonance approximation, instanton effects, and higher-loop perturbative contributions to the pseudoscalar correlator. We obtain the following values (uncertainties reflect 90% confidence levels): mass $M_\Pi = 1.15 \pm 0.28 GeV$, width $\Gamma_\Pi = < 0.48 GeV$, decay constant $r \equiv [F_\Pi M_\Pi^2 / f_\pi m_\pi^2]^2 = 4.7 \pm 2.8$.

Evaluation methods of resonance absorption for system with pellet surrounded by fuel solution.

KEYWORDS: uranium dioxidebenchmarkscriticalityfuel pelletsfuel solutionsresonance absorptionMonte Carlo methodcalculation methodsDancoff factor methodTone's methodPEACO methodcomparative evaluations

Electron-electron interactions and resonant tunneling in heterostructures

A Hartree–Fock approach [Z. Physik 61, 126 (1930)] is used to analyze electron-electron interactions in heterostructures. The analysis includes estimates of the effect of electron-electron interactions on localized states in quantum wells and resonant tunneling. Resonant tunneling is treated in a self-consistent narrow resonance approximation. The Hartree–Fock approach yields an explicit exchange interaction subband energy shift which is completely omitted in Poisson equation treatments. Exchange effects are found to be of the same order of magnitude but opposite in sign to direct interactions at typical electron densities.

Combined Monte Carlo Narrow Resonance-Intermediate Resonance Method for Testing Resonance Integral Calculations in Complex Geometries

The narrow resonance (NR) approximation has, in the past, been applied mainly to regular lattices with fairly simple unit cells. Attempts to use the NR approximation to deal with fine details of th...