Width Fluctuation Correction Research Articles

Theoretical calculation and evaluation of n + 237,241,243,245Pu reactions

Plutonium isotopes are important fuel or radioactive waste loaded to accelerator driven systems and some Generation-IV reactors, so accurate nuclear data of neutron induced reactions on them for the incident energy up to 150 MeV are required for the design of these facilities. The nuclear data on n + 237,241,243,245Pu reactions below 150 MeV are consistently calculated and evaluated by using the optical model, distorted wave Born approximation theory, Hauser-Feshbach theory with width fluctuation correction, fission model, evaporation model, exciton model and the intranuclear cascade model. In the meanwhile, new experimental data are taken into account. Our new evaluated data are compared with the presently existing experimental data and the evaluated data from ENDF/B-VIII, JENDL-4.0/HE and TENDL. In addition, the variation tendency of reaction cross sections related to the target mass numbers is obtained.

Double differential cross sections of light charged particle production for the n+238U reaction**Supported by National Natural Science Foundation of China-NSAF (U1630122), IAEA Coordinated Research Projects (CRPs) on Recommended Input Parameter Library (RIPL) for Fission Cross Section Calculations (20464) and Science Challenge Project (TZ2018005)

Production of light complex particles from the n+238U reaction is analyzed with the exciton model including the improved Iwamoto-Harada pickup mechanism for the preequilibrium process. It is allowed that some of the nucleons forming the complex ejectile come from levels below the Fermi energy, and the intrinsic structure of the emitted particle is taken into account. The equilibrium-state emissions are also considered by using Hauser-Feshbach theory with the width fluctuation correction and the evaporation model. Moreover, all cross sections, angular distributions, energy spectra and double differential cross sections of neutron, proton, deuteron, triton and alpha emissions for the n+238U reaction are consistently calculated and analyzed with nuclear theoretical models in the energy range En ⩽ 150 MeV. ENDF-formatted nuclear data including information about the production of light charged particles are obtained.

Cross sections of α -induced reactions slightly below doubly magic Ca40 from the statistical model

New experimental data for the $^{38}$Ar($\alpha$,n)$^{41}$Ca and $^{38}$Ar($\alpha$,p)$^{41}$K reactions were used to find a best-fit set of parameters for statistical model calculations. The very good agreement between the experimental data and the best-fit calculation confirms the applicability of the statistical model for nuclei in the vicinity of the doubly-magic $^{40}$Ca despite of their relatively low level densities. The present study investigates the sensitivities and finds that the $\alpha$-nucleus and the nucleon-nucleus potentials are the most important ingredients for the calculation of ($\alpha$,n) and ($\alpha$,p) reactions in the statistical model. Furthermore, the width fluctuation correction plays an essential role in the peculiar case of $^{38}$Ar. The best-fit parameters from $^{38}$Ar are applied to the mirror nucleus $^{38}$Ca and the neighboring $^{36}$Ar and $^{40}$Ar nuclei. For $^{38}$Ca this results in an astrophysical reaction rate of the $^{38}$Ca($\alpha$,p)$^{41}$Sc reaction which has a flatter temperature dependence compared to all previous calculations. For $^{40}$Ar a better reproduction of $^{40}$Ar($\alpha$,p)$^{43}$K data from literature is obtained. The disagreement between calculation and an early experimental data point for the $^{36}$Ar($\alpha$,p)$^{39}$K reaction persists.

Modelling Neutron-induced Reactions on 232–237U from 10 keV up to 30 MeV

Comprehensive calculations of cross sections for neutron-induced reactions on 232–237U targets are performed in the 10 keV–30 MeV incident energy range with the code EMPIRE–3.2 Malta. The advanced modelling and consistent calculation scheme are aimed at improving our knowledge of the neutron scattering and emission cross sections, and to assess the consistency of available evaluated libraries for light uranium isotopes. The reaction model considers a dispersive optical potential (RIPL 2408) that couples from five (even targets) to nine (odd targets) levels of the ground-state rotational band, and a triple-humped fission barrier with absorption in the wells described within the optical model for fission. A modified Lorentzian model (MLO) of the radiative strength function and Enhanced Generalized Superfluid Model nuclear level densities are used in Hauser-Feschbach calculations of the compound-nuclear decay that include width fluctuation corrections. The starting values for the model parameters are retrieved from RIPL. Excellent agreement with available experimental data for neutron emission and fission is achieved, giving confidence that the quantities for which there is no experimental information are also accurately predicted. Deficiencies in existing evaluated libraries are highlighted.

Statistical Hauser-Feshbach theory with width-fluctuation correction including direct reaction channels for neutron-induced reactions at low energies

A model to calculate particle-induced reaction cross sections with statistical Hauser-Feshbach theory including direct reactions is given. The energy average of the scattering matrix from the coupled-channels optical model is diagonalized by the transformation proposed by Engelbrecht and Weidenm\"uller [C. A. Engelbrecht and H. A. Weidenm\"uller, Phys. Rev. C 8, 859 (1973)]. The ensemble average of $S$-matrix elements in the diagonalized channel space is approximated by a model of Moldauer [P. A. Moldauer, Phys. Rev. C 12, 744 (1975)] using the newly parametrized channel degree-of-freedom ${\ensuremath{\nu}}_{a}$ to better describe the Gaussian orthogonal ensemble (GOE) reference calculations. The Moldauer approximation is confirmed by a Monte Carlo study using a randomly generated $S$ matrix, as well as the GOE threefold integration formula. The method proposed is applied to the $^{238}\mathrm{U}(n,{n}^{\ensuremath{'}})$ cross-section calculation in the fast-energy range, showing an enhancement in the inelastic scattering cross sections.

Theoretical uncertainty of(α,n)reactions relevant for the nucleosynthesis of lightr-processnuclei in neutrino-driven winds

Background: Neutrino-driven winds following core-collapse supernova explosions have been proposed as a possible site where light $r\text{-process}$ nuclei (between Fe and Ag) might be synthesized. In these events, $(\ensuremath{\alpha},n)$ reactions are key to moving matter towards the region of higher proton number. Abundance network calculations are very sensitive to the rates for this type of reactions.Purpose: The present work aims at evaluating the theoretical uncertainty of these $(\ensuremath{\alpha},n)$ reactions calculated with reaction codes based on the Hauser-Feshbach model.Method: We compared several $(\ensuremath{\alpha},n)$ rates taken from talys and the non-smoker database to determine the uncertainties owing to the existing technical differences between both codes. In addition, we evaluated the sensitivity of talys rates to variations in the $\ensuremath{\alpha}$ optical potentials, masses, level densities, optical potentials, preequilibrium intranuclear transition rates, level structure, radiative transmission coefficients, and width-fluctuation correction factors.Results: The main source of uncertainty at low temperature is mostly attributable to the use of different $\ensuremath{\alpha}$ optical potentials. Differences between talys and non-smoker at high temperatures arise from the energy-binning algorithm used by each code. We have also noticed that the $(\ensuremath{\alpha},n)$ rates from the non-smoker database correspond to the inclusive reaction, instead of the exclusive $(\ensuremath{\alpha},1n)$ channel calculated in the present work and used in network calculations.Conclusions: Theoretical uncertainties in calculated reaction rates can be as high as one to two orders of magnitude and strongly dependent on the temperature of the environment. Besides direct measurements of the inclusive and exclusive $(\ensuremath{\alpha},1n)$ reaction rates, experimental studies of $\ensuremath{\alpha}$ optical potentials are crucial to improve the performance of reaction codes.

Monte Carlo simulation of transfer reactions using extended R-matrix theory picturing surrogate-type WFCF features

This article supplies an overview of issues related to the interpretation of surrogate measurement results for neutron-incident cross section predictions; difficulties that are somehow masked by the historical conversion route based on Weisskopf-Ewing approximation. Our proposal is to handle the various difficulties by using a more rigorous approach relying on Monte Carlo simulation of transfer reactions with extended R -matrix theory. The multiple deficiencies of the historical surrogate treatment are recalled but only one is examined in some details here; meaning the calculation of in-out-going channel Width Fluctuation Correction Factors (WFCF) which behavior witness partly the failure of Niels Bohr’s compound nucleus theoretical landmark. Relevant WFCF calculations according to neutron-induced surrogate- and cross section-types as a function of neutron-induced fluctuating energy range [0 - 2.1 MeV ] are presented and commented in the case of the 240 Pu* and 241 Pu* compound nucleus isotopes.

Calculation of pre-equilibrium effects in neutron-induced cross section on32,34S isotopes using the EMPIRE 3.2 code

In this study, a new version EMPIRE 3.2 code was used in the cross section calculations of (n,p) reactions and in the calculation of proton emission spectra produced by (n,xp) reactions. Exciton model predictions combined with the Kalbach angular distribution systematics were used and some parameters such as those of mean free path, cluster emission in terms of Iwamoto-Harada model, optical model potentials of Morillon for neutrons and protons in the energy range up to 20 MeV, level density for spherical nuclei of Gilbert-Cameron model and width fluctuation correction in terms of compound nucleus have been investigated our calculations. The excitation functions and the proton emission spectra for 32,34S nuclei were calculated, discussed and found in good agreement with available experimental data.

Calculation and analysis for p + 50,52,53,54,natCr reactions

All cross sections, elastic and inelastic scattering angular distributions, energy spectra and double differential cross sections of six outgoing particles (n, p, d, t, helium-3 and α) for p+50,52,53,54,natCr reactions are calculated and analyzed at incident proton energies below 150MeV. The optical model, the intra-nuclear cascade model, evaporation model, Hauser–Feshbach theory with width fluctuation correction, exciton model which includes the improved Iwamoto–Harada model and distorted Born approximation theory are involved in the calculation. The calculated results are compared with existing experimental data.

Neutron capture cross section ofAm241

The neutron capture cross section of $^{241}\mathrm{Am}$ for incident neutrons from 0.02 eV to 320 keV has been measured with the detector for advanced neutron capture experiments (DANCE) at the Los Alamos Neutron Science Center. The thermal neutron capture cross section was determined to be $665\ifmmode\pm\else\textpm\fi{}33$ b. Our result is in good agreement with other recent measurements. Resonance parameters for ${E}_{n}l12$ eV were obtained using an $R$-matrix fit to the measured cross section. The results are compared with values from the ENDF/B-VII.0, Mughabghab, JENDL-3.3, and JEFF-3.1 evaluations. ${\ensuremath{\Gamma}}_{n}$ neutron widths for the first three resonances are systematically larger by 5--15% than the ENDF/B-VII.0 values. The resonance integral above 0.5 eV was determined to be 1553\ifmmode\pm\else\textpm\fi{}7 b. Cross sections in the resolved and unresolved energy regions above 12 eV were calculated using the Hauser-Feshbach theory incorporating the width-fluctuation correction of Moldauer. The calculated results agree well with the measured data, and the extracted averaged resonance parameters in the unresolved resonance region are consistent with those for the resolved resonances.

Improved predictions of nuclear reaction rates with the TALYS reaction code for astrophysical applications

Nuclear reaction rates of astrophysical applications are traditionally determined on the basis of Hauser-Feshbach reaction codes. These codes adopt a number of approximations that have never been tested, such as a simplified width fluctuation correction, the neglect of delayed or multiple-particle emission during the electromagnetic decay cascade, or the absence of the pre-equilibrium contribution at increasing incident energies. The reaction code TALYS has been recently updated to estimate the Maxwellian-averaged reaction rates that are of astrophysical relevance. These new developments enable the reaction rates to be calculated with increased accuracy and reliability and the approximations of previous codes to be investigated. The TALYS predictions for the thermonuclear rates of relevance to astrophysics are detailed and compared with those derived by widely-used codes for the same nuclear ingredients. It is shown that TALYS predictions may differ significantly from those of previous codes, in particular for nuclei for which no or little nuclear data is available. The pre-equilibrium process is shown to influence the astrophysics rates of exotic neutron-rich nuclei significantly. For the first time, the Maxwellian-averaged (n,2n) reaction rate is calculated for all nuclei and its competition with the radiative capture rate is discussed. The TALYS code provides a new tool to estimate all nuclear reaction rates of relevance to astrophysics with improved accuracy and reliability.

Comparisons between various width fluctuation correction factors for compound nucleus reactions

The exact expression for the width fluctuation correction factor, obtained with the Gaussian orthogonal ensemble (GOE) approach, has been implemented computationally to describe a nuclear reaction for any open channel—elastic, inelastic, capture, and fission. This exact expression is compared with various approximate expressions. It turns out that the approximate expression given by Moldauer is the closest to the GOE value. Since comparison between model predictions and experimental data alone cannot provide the answer concerning the correct approximate method, the present comparison indicates that Moldauer’s model is the one to use in reaction models for practical applications.

Neutron Cross-Section Evaluations of Fission Products in the Fast Energy Region

Neutron cross-sections for 19 high priority fission products were evaluated from the unresolved resonance energy region up to 20 MeV. Evaluation procedures included optical model parameter search, followed by complete nuclear reaction model calculations with parameters carefully validated against experimental data. Calculations were done with the code Empire using the following models: spherical optical and coupled-channels deformed optical, multistep direct and multistep compound, preequilibrium exciton, and Hauser-Feshbach with width fluctuation corrections. Results were converted into the ENDF-6 format and detailed graphical comparisons with both CSISRS experimental data and ENDF files was performed. In most cases a considerable improvement over the current ENDF/B-VI library was achieved.

Analysis of 58Ni(n, α) Reaction Cross Sections with the Hauser-Feshbach Statistical Theory and the Bayesian Parameter Estimation Method

Experimental data of 58Ni(n, α) reaction cross sections are analyzed with the Hauser-Feshbach statistical model with the width fluctuation correction by Moldauer. A neutron optical potential which was derived from neutron elastic scattering data is used for an entrance channel in order to fix the total reaction cross sections at reliable values. Global optical potentials are used for the proton and α-particle emission channels, and level density parameters of the residual nuclei are determined from the cumulative plot of discrete levels. These parameters are adjusted to the experimental data of 58Ni(n, α) and (n, p) reaction cross sections, including the angular distribution of the emitted α-particles. The parameters thus obtained yield a good fit to the experimental cross sections of those reactions up to 8 MeV.

Polarisation in 2.9 MeV neutron elastic energy scattering by W, Tl, Bi and U

Simultaneous measurements are presented of the angular dependence of polarisation due to elastic scattering and of the differential cross section for 2.9 MeV neutron scattering by W, Tl, Bi and U. The measurements are compared with the results of combining optical-model and Hauser-Feshbach calculations based on global parameter sets and with the results of searches for optimum optical-model fits to the data. Calculations which take account of the level width fluctuation correction give a better fit to the data. The parameters describing the optimum model potential are considered in relation to others derived from experiments in the 2.9-16 MeV energy range and in relation to the microscopic calculations of the nucleon-nucleus optical-model potential.

Cross sections for fast neutron capture on the Se, Pd, Cd, Os and Pt isotopes

Activation capture cross sections are measured for Se, Pd, Cd, Os and Pt isotopes in the neutron energy range from 0.5 MeV to 1.3 MeV. The results of measurements are tested against the compound nucleus cross sections. The role of the width fluctuation corrections is examined.

Cross sections for the27Al(n,n'γ) reaction from near threshold to 10.0 MeV

Cross sections for the production of the 0.84, 1.01, 2.21, 1.72 and 3.0 MeV deexcitation gamma -rays following inelastic neutron scattering from 27Al from near threshold to 10 MeV are presented. The experimental results are compared with the values calculated using the Hauser-Feshbach formula modified by the Moldauer width-fluctuation correction (1975). A correlation function is evaluated between the total neutron cross section and the 0.84 and 1.01 MeV de-excitation gamma -ray cross sections for neutron energies below 5 MeV. Evidence is found for correlations in structure between the total and inelastic cross sections but not between the inelastic cross sections.

Competition effects in proton-induced reactions on 51V

Absolute cross sections for the reactions 51V(p, γ) 52Cr and 51V(p, n) 51Cr have been measured for laboratory bombarding energies from E p =0.93 MeV to E p = 4.47 MeV. Above the (p, n) threshold ( Q = −1.534 MeV), competition from the neutron decay channel causes the (p, γ) cross section to decrease by a factor of about three. The experimental cross sections for both reactions are described well by current versions of “global” Hauser-Feshbach models, if (i) width fluctuation corrections are included (in the Tepei approximation), (ii) realistic neutron transmission functions which include the effects of size resonances are used and (iii) isospin mixing is assumed to be complete.

Competition cusps in (α, γ) reactions

Absolute cross sections are presented for the reactions 37Cl( α, γ) 41K for 2.90 MeV ≦ E lab α ≦ 5.23 MeV, 62 Ni(α, γ) 66 Zn for 5.07 MeV ≦ E α −2 lab ≦ 8.64 MeV, 62 Ni(α, n) 65 Zn for energies near the ( α, n 0) threshold at E α lab = 6.90 MeV up to 8.76 MeV, 64 Ni(α, γ) 68 Zn for 4.50 ≦ E α lab ≦ 7.45 MeV , and for 64Ni( α, n) 67N from E α lab = 5.30 MeV up to E α = 7.45 MeV. Substantial competition cusps were observed in the excitation function for all three (α, γ) reactions. The data were found to be in reasonable agreement with the predictions of the current versions of global Hauser-Feshbach models used in nucleosynthesis calculations. Including width fluctuation corrections and realistic neutron strength functions generally improves the ability of the models to predict the depth of the (α, γ) competition cusps; the depths of the predicted (α,γ) cusps are insensitive to the degree of isospin mixing. Taken together with studies of competition effects in proton-induced reactions, the present data confirm the importance of width fluctuation and strength function effects, and indicate essentially complete isospin mixing between T < and T > states in the compound nucleus.

The differential cross section and polarization for the elastic scattering of 2.9 MeV neutrons by Fe, Cu, I, Hg and Pb

Simultaneous measurements are presented of the angular dependence of polarization due to elastic scattering and of the elastic differential cross section for 2.9 MeV neutrons. The angular range covered is 20° to 160° for samples of Fe, Cu, I. Hg and Pb. The measurements are compared with the results of combining optical model and Hauser-Feshbach calculations. The optical model calculations were performed using “global fit” parameters as well as with parameters suggested previously for the particular nuclei. The Hauser-Feshbach calculations were performed both with and without the level width fluctuation correction. It is clear that the calculations made without the level width fluctuation correction provide a better fit to the data for Fe, Cu, I and Hg and only for Pb does inclusion of the level width fluctuation correction provide a better fit. These optical model parameter sets are shown not to be very successful in fitting both differential cross-section and polarization data. The results of searches for the parameters which give the best fit for the data are presented. These parameter sets are compared with one another and with the results of 8 and 11 MeV neutron scattering studies for trends in the variation of the parameters.