Cross-sectional Resonance Research Articles

Modeling of Resonance-Interference Effect in Depleted Fuel Compositions by Pseudo Resonant Isotopes

In order to develop an efficient resonance self-shielding method that can model the complex resonance-interference effects in depleted fuel compositions, an improved Pseudo Resonant Isotope Model (PRIM) has been developed by incorporating a number density–perturbation technique in the resonance cross-section tables for pseudo isotopes. Numerical results for homogeneous mixtures, pin cells, and pressurized water reactor lattice problems show that the new model is able to produce accurate group cross sections for a wide range of depletion states of different types of fuels, comparable to those obtained from online ultra-fine-group slowing-down calculations. Computational cost analysis shows that the improved PRIM is a promising method applicable to the resonance self-shielding calculations for large-scale reactor core analysis with depletion.

Searches for heavy ZZ and ZW resonances in the \u2113\u2113qq and \u03bd\u03bdqq final states in pp collisions at sqrt{s}=13 TeV with the ATLAS detector

This paper reports searches for heavy resonances decaying into ZZ or ZW using data from proton-proton collisions at a centre-of-mass energy of sqrt{s}=13 TeV. The data, corresponding to an integrated luminosity of 36.1 fb−1, were recorded with the ATLAS detector in 2015 and 2016 at the Large Hadron Collider. The searches are performed in final states in which one Z boson decays into either a pair of light charged leptons (electrons and muons) or a pair of neutrinos, and the associated W boson or the other Z boson decays hadronically. No evidence of the production of heavy resonances is observed. Upper bounds on the production cross sections of heavy resonances times their decay branching ratios to ZZ or ZW are derived in the mass range 300-5000GeV within the context of Standard Model extensions with additional Higgs bosons, a heavy vector triplet or warped extra dimensions. Production through gluon-gluon fusion, Drell-Yan or vector-boson fusion are considered, depending on the assumed model.

Incoherent Scatter Spectra Based On Monte Carlo Simulations of Ion Velocity Distributions Under Strong Ion Frictional Heating

AbstractUnder strong electric field conditions often found at high latitudes, the ion velocity distribution of the weakly ionized F region plasma can differ enough from a Maxwellian shape to substantially change incoherent scatter (IS) spectra and thus the analysis of those spectra. With the goal to provide a quantitative and reliable description of the IS spectra, this study directly uses for the first time an advanced Monte Carlo calculation of the ion velocity distribution to derive IS spectra for a range of electric fields and aspect angles. For most cases the spectra associated with NO+ maintains a shape that closely resembles that of a spectrum derived from a Maxwellian distribution with the same line‐of‐sight ion temperature as the equivalent Monte Carlo simulated distribution. This study also fully characterizes the spectral shape as well as the ion temperature and its anisotropy for two different models of the resonant charge exchange between O+ and O. It confirms that the distortions from the Maxwellian shape can be substantial for this particular interaction. The distortions are also such that along the magnetic field direction, the extracted apparent electron temperature is always greater than the real temperature. This work also includes a determination of the stability of the plasma against magnetic field‐aligned electrostatic instabilities. It is found that the NO+ distribution is always stable, whereas the O+ distribution may or may not be stable, depending on the model chosen for the resonant charge exchange cross section in collisions with the background atomic oxygen gas.

Treatment of Double Heterogeneity in the Resonance and Thermal Energy Regions in High-Temperature Reactors

The fuel in high-temperature reactors (HTRs) consists of a large number of tiny (a few hundred microns in size) TRISO-coated particles dispersed randomly in a graphite matrix. At the resonances of the major nuclide (238U or 232Th) of the fuel, the neutron mean free path in the fuel is often comparable to the kernel dimensions, and hence the dispersion of particles in the graphite matrix must be treated as a heterogeneous medium for obtaining self-shielded cross sections in the resonance (epithermal) groups. HTRs containing only plutonium as fuel (as may be the case in reactors designed for burning plutonium) have high concentrations of the isotopes 239Pu and 240Pu in the kernels. This fact together with their rather large resonance cross section in the thermal groups results in a very short neutron mean free path in the fuel that is comparable to the kernel dimensions. In such cases the fuel zone must be treated as a heterogeneous medium in the thermal energy region as well. However, the resonance treatment method in libraries such as the WIMS library does not cover the two large resonances of plutonium lying in the thermal region. Instead, a large number of groups are used to cover the details of cross-section variation in this region.The heterogeneity of the fuel region together with the heterogeneous distribution of fuel region, graphite moderator, and coolant is referred to as the double heterogeneity of HTRs. The paper describes work we carried out for addressing these problems. A new method for generating a random distribution of TRISO particles in the fuel zone of a pebble or fuel compact and Monte Carlo calculation of the Dancoff factor in the heterogeneous random medium, required for calculating the self-shielded resonance group cross sections, is presented. Dancoff factors obtained by our method are compared with values available in published literature on the subject. The paper also discusses a new methodology developed to solve the double-heterogeneity problem at the stage of the multigroup transport theory solution, which is particularly important in the thermal region occurring in high-content Pu-fueled HTRs. These features have been incorporated in the WIMS library–based lattice code BOXER3. An option for handling the spherical geometry of the lattice cell of a pebble bed reactor has been added in the code. Results of analysis of a number of HTR lattice cell benchmark problems are presented.

Resonance self-shielding treatment and analysis of resonance integral tables for Fully Ceramic Micro-encapsulated fuels with the Embedded Self-Shielding Method

A resonance calculation method for Fully Ceramic Micro-encapsulated (FCM) fuels containing stochastically dispersed tri-structural isotropic (TRISO) coated fuel particles has been proposed in this research. The purpose is to obtain effective homogenized resonance cross sections representing the effect of double heterogeneity (DH). The Monte Carlo code MVP is used to solve the heterogeneity in the isolated FCM fuels pin, and to couple with the method of characteristic (MOC) to generate heterogeneous resonance integral (RI) tables for the following Embedded Self-Shielding Method (ESSM) based resonance calculation. The ESSM method is employed to treat the heterogeneity in the lattice (Dancoff effect). Heterogeneous RI tables based on different packing fraction may differ in relationship between background and self-shielded cross sections. Analysis of this distinction’s impact on ESSM calculation has been conducted. Furthermore, resonance interference effect is neglected in ESSM because heterogeneous RI tables are developed for isolated resonant nuclide system. Therefore, Resonance Interference Factor (RIF) Method was applied to correct cross sections from ESSM. To obtain RIF, slowing-down equation need be solved twice for different homogeneous systems. Whereas, the cross section neglecting interference effect could be received by interpolating in homogeneous RI tables to improve efficiency. Evaluation of errors caused by interpolation in RIF method was performed with reference solutions from MVP. Numerical results show that the new method is proved effective in DH capability for resonance self-shielding calculation.

Partial-wave analysis and multipole transition interferences in the breakup of 6Li on 152Sm target

We have performed a detailed partial-wave analysis in order to analyze each partial-wave contribution to the breakup cross-sections as well as multipole interference effects in the [Formula: see text] breakup reaction. The results show that [Formula: see text]-waves contribute up to 67.03% of the overall integrated total breakup cross-section, distributed as follows: 10.43% for the [Formula: see text] partial-wave, 21.94% for the [Formula: see text] partial-wave and 34.66% for the [Formula: see text] partial-wave. A similar trend is observed for both Coulomb and nuclear breakup cross-sections. The importance of [Formula: see text]-waves over the non-[Formula: see text]-waves in the breakup process is mainly due to the higher-order multipole interferences. It is also obtained that the combination of [Formula: see text]-waves and [Formula: see text]-waves accounts for 84.77%, 89.95% and 73.58% of the total, Coulomb and nuclear breakup cross-sections, respectively. Considering the results obtained for the [Formula: see text] and [Formula: see text] partial-waves, we conclude that the [Formula: see text] and [Formula: see text] resonant breakup cross-sections, which can be obtained by integrating over the resonant energy range, could not be negligible compare to the [Formula: see text] resonant breakup cross-section. As far as this reaction is concerned, we can conclude that in the sequential breakup of [Formula: see text], excitations to all its three resonant states should be considered for a fair description of such process.

Resonant Inelastic X-ray Scattering Amplitudes and Cross Sections in the Algebraic Diagrammatic Construction/Intermediate State Representation (ADC/ISR) Approach.

A scheme has been derived and implemented to gain computational access to the full electronic part of the Kramers-Heisenberg-Dirac (KHD) expression for resonant and nonresonant inelastic scattering amplitudes. Our implementation of this scheme is based on the complex polarization propagator in the algebraic diagrammatic construction (ADC) framework and within its intermediate state representation (ISR). The hierarchy of the second- and third-order ADC/ISR computational schemes known as ADC(2), ADC(2)-x, and ADC(3/2) is considered, and the calculated resonant inelastic X-ray scattering (RIXS) amplitudes and transition strengths for water are in excellent agreement with recent experimental data.

Combination of searches for heavy resonances decaying to WW, WZ, ZZ, WH, and ZH boson pairs in proton–proton collisions at [formula omitted] and 13 TeV

A statistical combination of searches is presented for massive resonances decaying to WW, WZ, ZZ, WH, and ZH boson pairs in proton–proton collision data collected by the CMS experiment at the LHC. The data were taken at centre-of-mass energies of 8 and 13 TeV, corresponding to respective integrated luminosities of 19.7 and up to 2.7 fb−1. The results are interpreted in the context of heavy vector triplet and singlet models that mimic properties of composite-Higgs models predicting W′ and Z′ bosons decaying to WZ, WW, WH, and ZH bosons. A model with a bulk graviton that decays into WW and ZZ is also considered. This is the first combined search for WW, WZ, WH, and ZH resonances and yields lower limits on masses at 95% confidence level for W′ and Z′ singlets at 2.3 TeV, and for a triplet at 2.4 TeV. The limits on the production cross section of a narrow bulk graviton resonance with the curvature scale of the warped extra dimension k˜=0.5, in the mass range of 0.6 to 4.0 TeV, are the most stringent published to date.

Generalized equivalence methods for 3D multi-group neutron transport

The process of generating multi-group cross section data to be used in full core 3D transport models requires not only accurate resonance self-shielding methods, but also some form of equivalence method in order to precisely preserve reaction rates of spectral geometry calculations. This paper presents extensions of the traditional concepts of local reaction rate preservation (common in discontinuity factor, SPH, and BBH methods), to derive a new state-of-the-art transport equivalence method that incorporates angular flux jump conditions that provide polar angle neutron current preservation. This method is tested on numerous fixed-source pin-cell problems by condensing fine energy resonance fluxes and cross sections. The method is demonstrated to precisely preserve all spectral geometry multi-group reaction rates as well as polar angle neutron currents for a wide range of cross section resonance heights, fuel pin diameters, coolant densities, and group energy widths.

Erratum: Electric conductivity of a hot hadron gas from a kinetic approach [Phys. Rev. D 93 , 096012 (2016)

We calculate the electric conductivity of a gas of relativistic particles with isotropic cross sections using the Boltzmann equation as the starting point. Our analyses is restricted to elastic collisions. We show the perfect agreement with previously published numerical results for a massless quark- gluon plasma, and give results for the electric conductivity of an interacting hadron gas, employing realistic resonance cross sections. These results for the electric conductivity of a hot hadron gas, as created in (ultra-)relativistic heavy-ion collisions, are of rich phenomenological as well as theoretical interest and can be compared to, e.g., lattice quantum field theory calculations.

Analytical Property of Scattering Matrix:Spectroscopy Phenomena and Sharp Overlapping Autoionization Resonances

An extended atomic data base with sufficiently high precision is required in astrophysics studies and the energy researches. For example, there are “infinite” energy levels in discrete energy region as well as overlapping resonances in autoionization region. We show in this paper the merits of our relativistic eigenchannel R-matrix method R-R-Eigen based on the analytical continuation properties of scattering matrices for the calculations of the energy levels, overlapping resonances and the related transitions. Using Ne+ as an illustration example, the scattering matrices of Ne+ in both discrete and continuum energy regions are calculated by our R-R-Eigen method directly. Based on our proposed projected high dimensional quantum-defect graph (symmetrized), one can readily determine the accuracies of the calculated scattering matrices using the experimental energy levels in a systematical way. The calculated resonant photoionization cross sections in the autoionization region are in excellent agreement with the benchmark high resolution experiments. With the scattering matrices checked/calibrated against spectroscopy data in both discrete and continuum energy regions, the relevant dynamical processes should be calculated with adequate accuracies. It should then satisfy the needs of the astrophysical and energy researches.

Calculation of astrophysical S-factor and reaction rate in 12C(p, γ)13N reaction

The 12C(p, γ)13N reaction is the first process in the CNO cycle. Also it is a source of low-energy solar neutrinos in various neutrino experiments. Therefore, it is of high interest to gain data of the astrophysical S-factor in low energies. By applying Faddeev’s method, we calculated wave functions for the bound state of 13N. Then the cross sections for resonance and non-resonance were calculated through using Breit–Wigner and direct capture cross section formulae, respectively. After that, we calculated the total S-factor and compared it with previous experimental data, revealing a good agreement altogether. Then, we extrapolated the S-factor in zero energy and the result was 1.32 ± 0.19 (keV.b). In the end, we calculated reaction rate and compared it with NACRE data.

Measurements of ep→e′π+π−p′ cross sections with CLAS at 1.40GeV<W<2.0 GeV and 2.0GeV2<Q2<5.0GeV2

This paper reports new exclusive cross sections for $e p \to e' \pi^+ \pi^- p'$ using the CLAS detector at Jefferson Laboratory. These results are presented for the first time at photon virtualities 2.0 GeV^2 < Q^2 < 5.0 GeV^2 in the center-of-mass energy range 1.4 GeV < W < 2.0 GeV, which covers a large part of the nucleon resonance region. Using a model developed for the phenomenological analysis of electroproduction data, we see strong indications that the relative contributions from the resonant cross sections at W < 1.74 GeV increase with $Q^2$. These data considerably extend the kinematic reach of previous measurements. Exclusive $e p \to e' \pi^+ \pi^- p'$ cross section measurements are of particular importance for the extraction of resonance electrocouplings in the mass range above 1.6 GeV.

Practical resolution of angle dependency of multigroup resonance cross sections using parametrized spectral superhomogenization factors

Abstract Based on the observation that ignoring the angle dependency of multigroup resonance cross sections within a fuel pellet would result in nontrivial underestimation of the spatial self-shielding of flux, a parametrized spectral superhomogenization (SPH) factor library (PSSL) method is developed as a practical means of resolving the problem. Region-wise spectral SPH factors are calculated by the normal and transport corrected SPH iterations after ultrafine group slowing down calculations over various light water reactor pin-cell configurations. The parametrization is done with fuel temperature, U-238 number density, fuel radius, moderator source represented by Σ mod V mod , and the number density ratio of resonance nuclides to that of U-238 in a form of resonance interference correction factors. The parametrization is successful in that the root mean square errors of the interpolated SPH factors over the fuel regions of various pin-cells are within 0.1%. The improvement in reactivity error of the PSSL method is shown to be superior to that by the original SPH method in that the reactivity bias of −200 pcm to −300 pcm vanishes almost completely. It is demonstrated that the environment effect takes only about 4% in the reactivity improvement so that the pin-cell based PSSL method is effective in the assembly problems.

On-the-fly Doppler broadening of unresolved resonance region cross sections

Two methods for computing temperature-dependent unresolved resonance region cross sections on-the-fly within continuous-energy Monte Carlo neutron transport simulations are presented. The first method calculates Doppler broadened cross sections directly from zero-temperature average resonance parameters. In a simulation, at each event that requires cross section values, a realization of unresolved resonance parameters is generated about the desired energy and temperature-dependent single-level Breit-Wigner resonance cross sections are computed directly via the analytical ψ−χ Doppler integrals. The second method relies on the generation of equiprobable cross section magnitude bands on an energy-temperature mesh. Within a simulation, the bands are sampled and interpolated in energy and temperature to obtain cross section values on-the-fly. Both of the methods, as well as their underlying calculation procedures, are verified numerically in extensive code-to-code comparisons. Energy-dependent pointwise cross sections calculated with the newly-implemented procedures are shown to be in excellent agreement with those calculated by a widely-used nuclear data processing code. Relative differences at or below 0.1% are observed. Integral criticality benchmark results computed with the proposed methods are shown to reproduce those computed with a state-of-the-art processed nuclear data library very well. In simulations of fast spectrum systems which are highly-sensitive to the representation of cross section data in the unresolved region, k-eigenvalue and neutron flux spectra differences of <10 pcm and <1.0% are observed, respectively. The direct method is demonstrated to be well-suited to the calculation of reference solutions — against which results obtained with a discretized representation may be assessed — as a result of its treatment of the energy, temperature, and cross section magnitude variables as continuous. Also, because there is no pre-processed data to store (only temperature-independent average resonance parameters) the direct method is very memory-efficient. Typically, only a few kB of memory are needed to store all required unresolved region data for a single nuclide. However, depending on the details of a particular simulation, performing URR cross section calculations on-the-fly can significantly increase simulation times. Alternatively, the method of interpolating equiprobable probability bands is demonstrated to produce results that are as accurate as the direct reference solutions, to within arbitrary precision, with high computational efficiency in terms of memory requirements and simulation time. Analyses of a fast spectrum system show that interpolation on a coarse energy-temperature mesh can be used to reproduce reference k-eigenvalue results obtained with cross sections calculated continuously in energy and directly at an exact temperature to within <10 pcm. Probability band data on a mesh encompassing the range of temperatures relevant to reactor analysis usually require around 100 kB of memory per nuclide. Relative to the case in which probability table data generated at a single, desired temperature are used, minor increases in simulation times are observed when probability band interpolation is employed.

L -shell photoionization of Mn5+ to Mn8+ ions

Resonant photoionization cross sections of $\mathrm{M}{\mathrm{n}}^{n+}$ ($n=5$ to 8) ions are measured in absolute values in the photon energy range of the $2p\ensuremath{\rightarrow}3d$ transitions $(645--690\phantom{\rule{0.16em}{0ex}}\mathrm{eV})$ using a merged-beams setup at the SOLEIL synchrotron radiation facility. The experimental cross sections are compared to calculations we performed using a multiconfiguration Dirac-Fock code and the opas code dedicated to radiative opacity calculations of hot and dense plasmas. Both calculations reproduce the measurements well.

Relativistic, correlation, and polarization effects in two-photon photoionization of Xe

Two-photon ionization of xenon was investigated theoretically for exciting-photon energies from 6.7 to 11.5 eV, which results in the ionization of Xe between $5{p}_{1/2}$ (13.43 eV) and $5s$ (23.40 eV) thresholds. We describe the extension of a previously developed computational technique for the inclusion of relativistic effects to calculate energies of intermediate resonance state and cross sections for two-photon ionization. Reasonable consistency of cross sections calculated in length and velocity form was obtained only after considering many-electron correlations. Agreement between calculated and measured resonance energies is found when core polarization was additionally included in the calculations. The presently computed two-photon photoionization cross sections of Xe are compared with Ar cross sections in our previous work. Photoelectron angular distribution parameters calculated here indicate that intermediated resonances strongly influence photoelectron angular distribution of Xe.

Resonances in Electron and Atom Scattering by Molecules. II. Results of Calculations

We describe the main features of the resonant scattering of electrons by molecules and calculate the parameters of the resonances within the framework of two different approaches: (1) the theory of collisions in a two-body system (where it is applicable); (2) the quantum theory of scattering in a fewbody system based on the Faddeev–Yakubovsky equations. We present the results of calculations of the resonant cross sections of electronic and atomic collisions with molecules and compare the obtained results with the available experimental data, as well as with the results of calculations based on other approximations. In addition, we discuss some biological applications (e.g., the properties of biopolymer molecules).

Low- and high-energy spectroscopy of O17 and F17 within a microscopic multiphonon approach

The extension of an equation of motion phonon method to odd nuclei is described step by step. Equations of motion are first constructed and solved to generate an orthonormal basis of correlated $n$-phonon states $(n=0,1,2,\ensuremath{\cdots})$, built of constituent Tamm--Dancoff phonons, describing the excitations of a doubly magic core. Analogous equations are then derived within a subspace spanned by a valence particle coupled to the $n$-phonon core states and solved iteratively to yield a basis of correlated orthonormal multiphonon particle-core states. The basis so constructed is used to solve the full eigenvalue problem for the odd system. The formalism does not rely on approximations but lends itself naturally to simplifying assumptions, as illustrated by its application to $^{17}\mathrm{O}$ and $^{17}\mathrm{F}$. Self-consistent calculations using a chiral Hamiltonian in a space encompassing up to three-phonon basis states generate spectra having a high level density, comparable to that observed experimentally. The spectroscopic properties are investigated at low energy through the calculation of moments, electromagnetic and $\ensuremath{\beta}$-decay transition strengths, and at intermediate and high energy through the computation of the electric-dipole spectra and pygmy and giant dipole resonance cross sections. The analysis of the particle-phonon composition of the eigenfunctions contributes to clarify the mechanism of excitation of levels and resonances and gives unique insights into their nature.

An improved DeCART library generation procedure with explicit resonance interference using continuous energy Monte Carlo calculation

DeCART multi-group cross section library generation procedure based on the KAERI library generation system was improved using the new alternative procedures based on the Monte Carlo slowing down calculations. In the new alternative procedures, the resonance integral tables were generated by solving the slowing down equation with continuous energy Monte Carlo calculations and the new procedures for the library generation were incorporated for the additional improvements. Most of fission product and actinide nuclides are processed as resonant nuclides to reduce the errors which are resulted from the approximate treatment of their resonance cross sections, and the one-group effective FPYs (Fission Product Yield) which are calculated by fission reaction rates are incorporated for improving the accuracy of the burnup calculations. Using the new procedure and ENDF/B-VII.1 evaluated nuclear data library, new DeCART cross section libraries are generated and they are tested for various benchmark calculations for pin-cell, FA, and core depletion problem against the McCARD reference solutions. The results confirmed that the new generated libraries can be used in the PWR SMR (Small Modular Reactor) core design.