Elastic Angular Distributions Research Articles

Density and energy dependent semi-microscopic optical potential of nucleon–nucleus elastic scattering

A nonlocal velocity-dependent optical potential was used to study the angular distribution of the differential cross section of nucleon–nucleus elastic scattering. The potential parameters were calculated by fitting elastic angular distributions over a wide range of energy (10-65 MeV) and mass (12-208). The real part of the local optical potential was calculated using the CDM3Y6-Paris interaction, whereas the imaginary part was a Woods-Saxon form factor and its derivative.

Effects of correlations in uncertainties of total cross section and elastic angular distribution for a deep penetration of 14-MeV neutrons in Cu

ABSTRACT Uncertainty in neutron reaction rates after penetrating a thick copper benchmark assembly was estimated based on two different kinds of Total Monte Carlo methods under random sampling methodology. Five hundred random nuclear data files were generated for 63Cu by Bayesian Monte Carlo method by perturbing the underlying nuclear model parameters. In the first method, these files were used directly to generate processed libraries, preserving all the correlations among different physical quantities. In the second method, the random files generated in the first method were used, but the angular distributions of elastic scattering were kept fixed to those of the non-perturbed nominal one. It was found that the two methods have the same neutron reaction rate after 608 mm penetration of copper. However, the uncertainty of the first method was smaller than that of the second method. It shows that the correlation between angular distribution of elastic scattering at 0 degrees and total cross section, which stems from Wick’s inequality, affects uncertainty of the calculated neutron reaction rate. It could be concluded that the uncertainty obtained by using the covariance files given in the ENDF-6 format may not give correct results for the uncertainty of neutron penetration calculations.

Behavior of 6Li + 144Sm elastic and inelastic angular distributions in the region of the Coulomb barrier

Behavior of 6Li + 144Sm elastic and inelastic angular distributions in the region of the Coulomb barrier

Velocity dependent potential for alpha 40Ca-elastic scattering

Angular distribution of the differential cross section of α40Ca elastic scattering has been investigated in the anomalous large angle scattering (ALAS) region by a nonlocal velocity dependent optical potential with surface term. The geometrical potential parameters were fixed and the depths of the potential were determined by fitting elastic angular distribution over the energy range (23–53.9 MeV). The real and the imaginary parts of the optical potential used here are of Woods–Saxon form factors. An energy dependence of the potential depths has been investigated at fixed geometrical potential parameters.

Analysis of nucleon-nucleus scattering data using a density-dependent semi-microscopic optical model with channel coupling

Background: The neutron scattering data was previously analyzed using a semi-microscopic optical model with channel coupling to inelastic excited states [Phys. Rev. C 100, 014603 (2019)]. The real part of the potential was constructed by single folding the density-independent M3Y-Paris bare nucleon-nucleon ($NN$) interaction, with zero-range knock-on exchange term, over the density of the target nucleus. The model reproduced the overall features of the inelastic angular distributions and polarization data. The elastic angular distributions were well reproduced.Purpose: In this work we test the effectiveness of the semi-microscopic optical model with channel coupling, but we employ a density-dependent BDM3Y1-Paris bare ($NN$) interaction, with the finite-range form of the knock-on exchange term, in describing the scattering observables, particularly, the inelastic distributions and polarization data.Method: The real volume term of the semi-microscopic model is constructed by single folding the density-dependent BDM3Y1-Paris bare ($NN$) interaction, over the matter distribution of the target nucleus. The ground state is coupled to low-lying inelastic excitation levels. The potential parameters are determined by fitting the elastic, inelastic, and polarization data corresponding to nucleon scattering off a wide range of mass numbers in the range $7\ensuremath{\le}A\ensuremath{\le}208$ for various energies from 10--95 MeV.Results: The density-dependent model resulted in significant improvements in the description of the inelastic angular distributions and analyzing power. In addition, the potential depths showed systematic linear dependence on incident energy, and one set of geometrical parameters is obtained for each nuclear target. We used our best-fit potential parameters to calculate the total cross sections corresponding to nucleon scattering off the considered nuclei. The calculated cross sections are in good agreement with the measured data.Conclusions: In a semi-microscopic optical model, construction of the real volume term by single folding the density-dependent BDM3Y1-Paris bare ($NN$) interaction, with finite form of the knock-on exchange term, results in significant improvements in reproducing the inelastic angular distributions and polarization data as compared to the case of using the density-independent M3Y-Paris bare nucleon-nucleon ($NN$) interaction, with either zero-range or finite-range exchange term.

Elastic, inelastic, and one-neutron transfer angular distributions of Li6+Sn120 at energies near the Coulomb barrier

The elastic scattering, first ${2}^{+}$ and ${3}^{\ensuremath{-}}$ target inelastic excitation and one neutron pickup angular distributions for the $^{6}\mathrm{Li}+^{120}\mathrm{Sn}$ reaction have been measured for three bombarding energies (19, 24, and 27 MeV). Data have been analyzed through coupled-channel calculations and continuum-discretized coupled-channel calculations extended to include target excitation. In general, both theoretical models give a reasonable description of the data. For the elastic and inelastic angular distributions taken at ${E}_{\mathrm{lab}}=24$ and 27 MeV, the continuum-discretized coupled-channel results are slightly better in comparison to the coupled-channel predictions. For the elastic and inelastic angular distributions measured at ${E}_{\mathrm{lab}}\phantom{\rule{4pt}{0ex}}=19$ MeV, the effect of the break-up channel seems to be quite important. At this energy, the elastic scattering data can be well explained by coupled channel calculations in which a strong absorptive optical imaginary potential is considered. In particular, the continuum-discretized coupled-channel theoretical results provided the best description of the ${3}^{\ensuremath{-}}$ excitation data at 19 MeV.

Iterative Bayesian Monte Carlo for nuclear data evaluation

In this work, we explore the use of an iterative Bayesian Monte Carlo (iBMC) method for nuclear data evaluation within a TALYS Evaluated Nuclear Data Library (TENDL) framework. The goal is to probe the model and parameter space of the TALYS code system to find the optimal model and parameter sets that reproduces selected experimental data. The method involves the simultaneous variation of many nuclear reaction models as well as their parameters included in the TALYS code. The ‘best’ model set with its parameter set was obtained by comparing model calculations with selected experimental data. Three experimental data types were used: (1) reaction cross sections, (2) residual production cross sections, and (3) the elastic angular distributions. To improve our fit to experimental data, we update our ‘best’ parameter set—the file that maximizes the likelihood function—in an iterative fashion. Convergence was determined by monitoring the evolution of the maximum likelihood estimate (MLE) values and was considered reached when the relative change in the MLE for the last two iterations was within 5%. Once the final ‘best’ file is identified, we infer parameter uncertainties and covariance information to this file by varying model parameters around this file. In this way, we ensured that the parameter distributions are centered on our evaluation. The proposed method was applied to the evaluation of p+^{59}Co between 1 and 100 MeV. Finally, the adjusted files were compared with experimental data from the EXFOR database as well as with evaluations from the TENDL-2019, JENDL/He-2007 and JENDL-4.0/HE nuclear data libraries.

Nucleon-nucleus velocity-dependent optical model: revisited

In this work we study nucleon-nucleus elastic scattering using a nonlocal, velocity-dependent optical potential. The potential parameters are determined by fitting elastic angular distributions and polarization data for nucleon scattering off a wide range of nuclei falling in the mass range 12 ⩽ A ⩽ 208 and over the energy range 10–60 MeV. Our potential parameters lead to smoothly varying local equivalent potentials and, unlike previous works, the potential depths corresponding to the real volume, imaginary surface, and imaginary volume terms show systematic linear dependences on energy. In addition, for each nuclear target, we determined constant sets of geometric parameters. Including the polarization data in the fitting procedure helped in reducing the large variations in the depths of the spin–orbit term. Our best-fit angular distributions and polarization data are in very good agreement with measured data, and are either as good as the cross sections obtained with widely-used systematics or better.

Statistical tools for a better optical model

Background: Modern statistical tools provide the ability to compare the information content of observables and provide a path to explore which experiments would be most useful to give insight into and constrain theoretical models.Purpose: In this work we study three such tools in the context of nuclear reactions with the goal of constraining the optical potential.Method: The three statistical tools examined are (i) the principal component analysis, (ii) the sensitivity analysis based on derivatives, and (iii) the Bayesian evidence. We first apply these tools to a toy-model case, comparing the form of the imaginary part of the optical potential. Then we consider two different reaction observables, elastic angular distributions and polarization data for reactions on $^{48}\mathrm{Ca}$ and $^{208}\mathrm{Pb}$ at two different beam energies.Results: For the toy-model case, we find significant discrimination power in the sensitivities and the Bayesian evidence, showing clearly that the volume imaginary term is more useful to describe scattering at higher energies. When comparing between elastic cross sections and polarization data using realistic optical models, sensitivity studies indicate that both observables are roughly equally sensitive but the variability of the optical model parameters is strongly angle dependent. The Bayesian evidence shows some variability between the two observables, but the Bayes factor obtained is not sufficient to discriminate between angular distributions and polarization.Conclusions: From the cases considered, we conclude that, in general, elastic scattering angular distributions have similar impact in constraining the optical potential parameters compared with the polarization data. The angular ranges for the optimum experimental constraints can vary significantly with the observable considered.

Microscopic Analysis of Elastic Scattering Angular Distributions for Five Different Density Distribution of 9Be Nucleus

Microscopic Analysis of Elastic Scattering Angular Distributions for Five Different Density Distribution of 9Be Nucleus

Probing proton halo effects in the 8B+64Zn collision around the Coulomb barrier

Proton halo effects in the 8B+64Zn reaction at an energy around 1.5 times the Coulomb barrier have been studied at HIE-ISOLDE CERN using, for the first time, the only existing postaccelerated 8B beam. This, together with the use of a high granularity and large solid angle detection system, allowed for a careful mapping of the elastic angular distribution, especially in the Coulomb-nuclear interference region. Contrary to what is observed for the one-neutron halo nucleus 11Be on the same target in a similar energy range, the analysis of the elastic scattering angular distribution shows only a modest suppression of the Coulomb-nuclear interference peak, with no remarkable enhancement of the total reaction cross-section. Inclusive angular and energy distributions of 7Be produced in direct reaction processes have also been measured. The comparison of these data with the results of theoretical calculations for the elastic and non-elastic breakup contributions indicate that both processes are important. Overall, the experimental data suggest a 8B collision dynamics at the barrier very different from the one of neutron halo nuclei, showing only modest effects of coupling to continuum. This behaviour can be interpreted as due to the presence of the additional Coulomb interactions halo-core and halo-target together with the presence of the centrifugal barrier felt by the valence proton of 8B.

Understanding the mechanisms of nuclear collisions: A complete study of the B10+Sn120 reaction

Background: Reactions involving exotic and stable weakly bound nuclei have been extensively studied in recent years. Although several models have been successfully used to explain particular reaction outcomes, the answers to many questions remain elusive. In previous works, we presented elastic, inelastic, and transfer angular distributions for the $^{10}\mathrm{B}+^{120}\mathrm{Sn}$ system measured at ${E}_{\mathrm{Lab}}=31.5$, 33.0, 35.0, and 37.5 MeV. The data set was analyzed through coupled reaction channels calculations in the context of the double-folding S\~ao Paulo potential.Purpose: We investigate nuclear reaction mechanisms for systems involving weakly bound projectiles.Method: Angular distributions for several nuclear reaction processes were measured for the $^{10}\mathrm{B}+^{120}\mathrm{Sn}$ system at ${E}_{\mathrm{Lab}}=39.70$ MeV.Results: The new data set involves angular distributions for elastic scattering, projectile and target inelastic excitations, one-neutron pickup transfer, one-proton stripping transfer, deuteron pickup transfer, and $^{3,4}\mathrm{He}$ stripping transfer. We have also observed $^{10}\mathrm{Be}$ nuclei. The effect of the couplings to some nonelastic states on the angular distributions is discussed.Conclusion: The theoretical calculations within the coupled reaction channels formalism provide an overall good agreement with the corresponding inelastic, one-neutron stripping, one-proton pickup, one-deuteron pickup, and $^{3}\mathrm{He}$ stripping transfer data. However, to improve the description of the elastic scattering angular distribution, the inclusion of additional channels in the coupling scheme might be necessary.

An Analysis of Elastic Scattering Angular Distributions of $$^{17}$$F on a $$^{208}$$Pb Target at Different Energies

This study investigated the elastic scattering of a $$^{\mathrm {17}}$$ F $$+^{\mathrm {208}}$$ Pb system at different energies using the Continuum-Discretized Coupled Channels (CDCC) method. A microscopic optical model was selected and double-folding potential was used for the $$^{\mathrm {16}}$$ O $$+$$ target interaction. The real part of the optical model was determined as folding potential and the imaginary part of the optical model was taken as standard volume Woods–Saxon shape. Single-channel and multi-channel CDCC calculations were performed to determine the effect of excited channels. An elastic scattering cross section of the $$^{\mathrm {17}}$$ F $$+^{\mathrm {208}}$$ Pb system was calculated and its compatibility with experimental data was determined.

Determination of the asymmetry term strength in the n–A elastic scattering process using a nonlocal optical model

In previous works, the imaginary surface and (or) the imaginary volume depths of the optical potential were parametrized as linear functions of the projectile’s incident energy and neutron-proton asymmetry (N – Z)/A of the target nucleus. However, the obtained asymmetry strength parameters were not robust nor unique. In this work, we determine values for the strength parameters by simultaneously fitting 38 angular distribution data sets corresponding to neutron elastic scattering off chains of isotopes. For each isotopic chain, we considered the data sets that are measured at the same energy. This minimises the effect of the known energy dependence of the optical model and projects the dependence on the asymmetry term, which in turn leads to more reliable values of the strength parameters. To demonstrate the significance of the obtained strength values, we use the model to predict elastic angular distributions for neutron scattering off nuclei not considered in the χ2 analysis. Our theoretical angular distributions are in good agreement with the measured data and are also comparable to the predictions of local global models. In addition, our predicted total elastic and total reaction cross sections are in fair overall agreement with experiment. An additional result of this work is the determination of a global set of nonlocal parameters that describe neutron elastic scattering off nuclei that fall in the mass range 24 ≤ A ≤ 208 corresponding to incident neutron energies between ≈10–30 MeV.

Elastic scattering of nucleon by the lightest mirror nuclei 3H and 3He using the optical model potential

The angular distribution of the nucleon elastic scattering on the lightest mirror nuclei 3H and 3He at incident energies of 6 and 9[Formula: see text]MeV has been analyzed. A new set of phenomenological optical potential parameters has been obtained. A comparison of differential cross-sections has been performed for both elastic scatterings of neutron and proton on the mirror nuclei. The contribution of individual volume, surface, and spin-orbit terms in the optical model potential for the projectiles at different energies was studied. The predicted elastic angular distributions results compared well with the experimental data.

A nonlocal optical potential with a Gaussian nonlocality for proton elastic scattering off light 1p-shell nuclei

In a recent work we used the nonlocal optical model of Perey and Buck (Nucl Phys A 32:353, 1962) to fit the angular distribution data corresponding to neutron elastic scattering off light nuclei from $$^6\hbox {Li}$$ to $$^{18}\hbox {O}$$ over the 9–35 MeV energy range. Although such nuclei posses diffuse edges that complicate the scattering process, the model resulted in improved angular distribution fits compared to those obtained using local optical models. In this work we extend the treatment to the case of proton elastic scattering off light 1p-shell nuclei, but consider the wider 10–70 MeV energy range. No single global set of nonlocal parameters adequately described the measured data across the entire energy range. Instead, we obtained two global sets of fixed nonlocal parameters; one corresponds to the 10–39 MeV range, the other is for the higher 40–70 MeV incident energies. Each set resulted in angular distribution fits which are in very good agreement with experimental data even in the large-angle scattering region, which is usually endowed by nonlocal effects. The fits were improved even further by expressing the imaginary volume and imaginary surface depths as linear functions of energy and the $$(N-Z)/A$$ asymmetry term. This indicates that there is still need for energy-dependent parameters even when nonlocality is explicitly included in the potential. We also used the model to predict elastic angular distributions for proton scattering off nuclei not included in the fitting procedure. The theoretical predictions showed very good agreement with experiment. As a further test of the nonlocal model, we calculated total reaction cross sections for proton scattering off light 1p-shell nuclei. Our predictions are in fair overall agreements with the experimental data.

Energy dependence of the optical potential of the weakly bound 9Be projectile on the 197Au target

In this work we measured elastic and inelastic angular distributions of the weakly bound 9Be projectile on the 197Au target at several bombarding energies from 84% up to 140% of the Coulomb barrier. The elastic angular distributions were analyzed using a phenomenological Woods-Saxon potential and a double folding São Paulo potential and the energy dependence was extracted. Angular distributions from two inelastic peaks were compared with coupled channel calculations using reduced transition probabilities available in the literature. The energy dependence of the two interaction potential models show a similar trend in the region of the Coulomb barrier. Dispersion relation calculation demonstrates the presence of the breakup threshold anomaly proposed for weakly bound systems.

Theoretical analysis of double-differential cross sections of proton, deuteron, and triton emission in the p+Li7 reaction at 14 MeV

Based on the statistical theory of light nucleus reactions (STLN), the description of the complicated emission processes of proton and light composite charged particles are further improved through considering the effects of Coulomb barriers both in incident and different outgoing reaction channels. And the analysis of the reaction channels including the sequential and simultaneous emission processes for $p + ^7$Li reaction is performed in detail. So the partial spectra of all of outgoing particles are also obtained for different reaction processes. The calculated double differential cross sections of total outgoing proton, deuteron and triton at $E_p = 14$ MeV agree well with the available experimental data for different outgoing angles. The ENDF-6 formatted data, which includes all of the reaction cross sections, elastic angular distributions, double differential cross sections of nucleon and light composite charged particles for $p + ^7$Li reaction, are also obtained by PUNF code.

New 23Na evaluation in the resolved resonance range taking into account both differential and double differential experiments

In 2012 CEA produced a entire new evaluation of sodium nuclear data for the release of the JEFF-3.2 evaluated nuclear data library. During the evaluation process performed with the CONRAD code, several differential measurements (total and discrete inelastic cross-sections) have been used. However double differential data (elastic angular distribution) that were yet available in the EXFOR database were not incorporated in the analysis at that time. The experimental elastic angular distribution were discarded because of it was impossible to obtain a good agreement for both angle-integrated cross-sections and double differential ones. The underlying cause of this disagreement is expected to be due to the attribution of quantum numbers to resonance and related channel amplitudes. Indeed these numbers are imposed during the analysis but impact differently angular distributions and angle-integrated cross-sections. An automated search for an accurate set of quantum numbers has been implemented in order to produce a reliable quantum numbers set. In this paper we present a new evaluation of Na-23 taking into account both differential and double differential measurements. The analysis performed with the CONRAD code reached the level of agreement with experimental data for the total and inelastic cross-sections but this time with a significant improvement for the elastic angular distributions. This new evaluation produced in the ENDF-6 format has then been tested and validated on critical facilities calculation (MASURCA and ZPPR) in different configurations (nominal and voided) in order to assess its performances.

Ne20+Ge76 elastic and inelastic scattering at 306 MeV

Background: Double charge exchange (DCE) nuclear reactions have recently attracted much interest as tools to provide experimentally driven information about nuclear matrix elements of interest in the context of neutrinoless double-beta decay. In this framework, a good description of the reaction mechanism and a complete knowledge of the initial and final-state interactions are mandatory. Presently, not enough is known about the details of the optical potentials and nuclear response to isospin operators for many of the projectile-target systems proposed for future DCE studies. Among these, the 20Ne + 76Ge DCE reaction is particularly relevant due to its connection with 76Ge double-beta decay. Purpose: We intend to characterize the initial-state interaction for the 20Ne + 76Ge reactions at 306 MeV bombarding energy and determine the optical potential and the role of the couplings between elastic channel and inelastic transitions to the first low-lying excited states. Methods: We determine the experimental elastic and inelastic scattering cross-section angular distributions, compare the theoretical predictions by adopting different models of optical potentials with the experimental data, and evaluate the coupling effect through the comparison of the distorted-wave Born approximation calculations with the coupled channels ones. Results: Optical models fail to describe the elastic angular distribution above the grazing angle (9.4{\deg}). A correction in the geometry to effectively account for deformation of the involved nuclear systems improves the agreement up to about 14{\deg}. Coupled channels effects are crucial to obtain good agreement at large angles in the elastic scattering cross section.