Optical Model Potential Research Articles

Uncertainty-quantified phenomenological optical potentials for single-nucleon scattering

Optical-model potentials (OMPs) continue to play a key role in nuclear reaction calculations. However, the uncertainty of phenomenological OMPs in widespread use---inherent to any parametric model trained on data---has not been fully characterized, and its impact on downstream users of OMPs remains unclear. Here we assign well-calibrated uncertainties for two representative global OMPs, those of Koning-Delaroche and Chapel Hill '89, using Markov-chain Monte Carlo for parameter inference. By comparing the canonical versions of these OMPs against the experimental data originally used to constrain them, we show how a lack of outlier rejection and a systematic underestimation of experimental uncertainties contributes to bias of, and overconfidence in, best-fit parameter values. Our updated, uncertainty-quantified versions of these OMPs address these issues and yield complete covariance information for potential parameters. Scattering predictions generated from our ensembles show improved performance both against the original training corpora of experimental data and against a new ``test'' corpus comprising many of the experimental single-nucleon scattering data collected over the last twenty years. Finally, we apply our uncertainty-quantified OMPs to two case studies of application-relevant cross sections. We conclude that, for many common applications of OMPs, including OMP uncertainty should become standard practice. To facilitate their immediate use, digital versions of our updated OMPs and related tools for forward uncertainty propagation are included as Supplemental Material.

Additional reaction mechanisms to statistical α-emission and the related optical-potential validation

The major role of consistent parameter sets within analysis of neutron-induced α-particle emission, for the assessment of a possible difference between the optical model potentials (OMPs), which describe either alpha-particle elastic scattering and induced reactions or alpha-emission from excited compound nuclei, is shown. They are involved at variance with use of either empirical rescaling factors of the γ and/or neutron widths or even combinations of all options of a computer code for main input parameters. Suitable description of all competitive reaction channels, confirmed by a careful uncertainty analysis in order to avoid parameter ambiguities and/or error compensation, supports further consideration of additional direct processes.

Neutron-induced inelastic γ-production cross sections on 58,60,64Ni

This paper reports partial results of a (n, n’γ) measurement on nickel. The inelastic channel was measured using the Gamma Array for Inelastic Neutron Scattering (GAINS) spectrometer at the 100-m measurement cabin of the Geel Electron Linear Accelerator (GELINA) neutron source of the European Commission’s Joint Research Centre (EC-JRC) in Geel, Belgium. Using γ spectroscopy, we were able to extract angle-integrated production cross sections for several γ rays but we report here only the results for the main transition in 58Ni. We discuss however in detail the observed discrepancy between our data and other experiments (especially the work of Voss et al.). We also shortly comment on the quality of the neutron-target optical model potential in describing the inelastic data in this mass region. The calculations were performed using the talys 1.9 code in the default settings.

Calculation of nucleon scattering on <sup>40</sup>Ca based on dispersive optical model

Spherical nucleus <sup>40</sup>Ca is important structural and alloy material nucleus. Based on important theoretical value and application prospect of nuclear data of calcium isotopes, nucleon-nucleus scattering data on <sup>40</sup>Ca nucleus, the main isotopes of natural calcium, are calculated by using dispersive optical model (DOM). The dispersive optical model potential is defined by energy-dependent real potentials, imaginary potentials, and also by the corresponding dispersive contributions to the real potential which are calculated analytically from the corresponding imaginary potentials by using a dispersion relation that follow from the requirement of causality. By fit simultaneously scattering experimental data for neutron and proton, an isospin-dependent dispersive optical model potential containing a dispersive term is derived. This derived potential in this work considers the nonlocality in the real “Hartree-Fock” potential <inline-formula><tex-math id="M5">\begin{document}$ V_{\rm{HF}} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231054_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="22-20231054_M5.png"/></alternatives></inline-formula> and introduces the shell gap in the definition of nuclear imaginary volume, surface and spin-orbit potentials near the Fermi energy. This dispersive optical model potential shows a good description of nucleon-nucleus scattering data on <sup>40</sup>Ca nucleus up to 200 MeV including neutron total cross sections, neutron elastic scattering angular distributions, proton elastic scattering angular distributions, neutron analyzing powers and proton analyzing powers. In addition, the energy dependencies of calculated real volume integrals of dispersive optical model potential is shown, and a typical dispersive hump is seen around the Fermi energy. This dispersive hump behavior naturally obtained from dispersion relations, and allows the dispersion optical potential to get rid of energy dependent geometry, thus avoiding the use of a radius dependent on energy.

Fermi Function and Its Applications

In this paper, we give a definition of the Fermi function, or the so-called Woods-Saxon potential, a well-known potential in nuclear physics; then, we give a few of its applications as examples. Some important integrals, which involve this function, are computed discussing the integrability and convergence of these integrals. Following, we derive formulae that encounter the above-mentioned function to get nuclear and generalized moments; the radial Fourier transformation is also exposed. Some related applications are then given that use such important integrals; in particular, we give the computation in conjunction with the problem of getting the optical-model potential for heavy-ion interactions at intermediate energies. Finally, we conclude with important remarks to do with the evolution of the subject.

Effects of Deuteron and Alpha Optical Model Potentials on the Production Cross–Section Calculations of Some Radiobromine Isotopes

The extensive use of radioisotopes in diverse fields, particularly in medical studies for diagnosis and treatment, is one of the outcomes of evolving technology and improved scientific research. Among the various radioisotopes used for medical purposes, an example that can be highlighted considering their properties and utilization possibilities is radiobromine isotopes. It is obvious that both experimental and theoretical studies make significant contributions to the literature on medically relevant radioisotopes. The cross–section, which is the data connected with the occurrence of a reaction, is one of the theoretical metrics that may provide information to researchers. The framework of this study was constructed by taking into account the importance of radiobromine isotopes in medical applications as well as the effects of some parameters that might have an impact on their production cross–section calculations. In this context, the impact of five deuteron and eight alpha optical model potentials, which are available in the 1.95 version of the TALYS code, on the production cross–section calculations of 75-77Br radioisotopes through some (d,x) and (α,x) reactions have been studied. The obtained calculation results were compared visually and numerically with the experimental data available in the literature for each reaction, and the outputs were interpreted.

Energy density functional for α+12C elastic scattering

In this work, the α-particle elastic scattering from 12C is studied using three different 12C densities based on the cluster model. This work aims to extend our previous analysis of α+12C system to study the energy dependence of the real double folded (DF) potential deduced from the energy density functional (EDF) α-cluster model over a wide energy range. In addition, The EDF α-cluster model is compared with other cluster models to see how reliable is this cluster model for 12C nucleus. The two α-cluster models used for comparison are based on the antisymmetrized molecular dynamics (AMD) and a cubic approximation of the nuclear equation of state (liquid drop type density-LD) models. The 12C densities based on these cluster models are used in the double folding procedure to obtain α+12C real part of the optical model potential (OMP). The imaginary part of the OMP is considered in conventional Wood-Saxon (WS) form. The obtained elastic scattering results show the reliability of the EDF α-cluster model in reproducing the experimental data on equal footing with the other two considered cluster models. Thus the EDF is reliable for studying the ground state α-cluster of the light 4mα-conjugate nuclei.

Reaction channel contributions to the proton +Pb208 optical potential at 40 MeV

Background: Reaction channel coupling substantially modifies the real and imaginary nucleon-nucleus interactions for nuclei of $Z=20$ or less in ways that cannot be represented as uniform renormalizations of folding model potentials. For such nuclei coupling to inelastic channels also contributes. This raises the question of the effect of these couplings for heavier target nuclei.Purpose: To establish and characterize the contribution to the proton-nucleus interaction generated by coupling to neutron pickup (outgoing deuteron) channels for 40 MeV protons on the heavy closed shell nucleus $^{208}\mathrm{Pb}$. To identify and evaluate the consequent dynamical non-locality.Methods: Coupled reaction channel (CRC) calculations provide the elastic channel $S$-matrix ${S}_{lj}$ due to the included processes. Inversion of ${S}_{lj}$ will produce the local potential that would yield, in a single channel calculation, the elastic scattering observables from the CRC calculation. Subtracting the bare potential of the CRC calculations gives a local and $l$-independent representation of the dynamical polarization potential (DPP). From the DPPs due to various combinations of channel couplings, the influence of dynamically generated nonlocality can be identified.Results: Coupling to deuteron channels generates a repulsive component for the real potential and an absorptive component for the imaginary term. The radial shapes of both terms were modified in ways that could not be represented by uniform renormalization; the rms radius of the real part was substantially altered. Evidence of the dynamical nonlocality of the DPP due to pickup is provided by the nonadditivity of contributions of different couplings and other effects. For the doubly closed shell $^{208}\mathrm{Pb}$ coupling to low-lying (nongiant) collective states has a very small effect on elastic scattering, making a negligible contribution compared with pickup, and was not included.Conclusions: The DPPs established here strongly challenge the notion that folding models, in particular local density models, provide a satisfactory description of elastic scattering of protons from heavy nuclei. Coupling to neutron pickup channels induces dynamical nonlocality in the proton optical model potential with implications for direct reactions.

Analyses of α–nucleus interaction on the 28Si(α, d)30P reaction at 40 and 50 MeV

The angular distributions of the 28Si(α, d)30P reaction at 40 and 50 MeV incident energies have been analyzed using the full finite-range (FFR) distorted-wave Born approximation (DWBA) method. Three forms of the optical model potentials namely, Woods-Saxon, Michel, and molecular potentials are used to analyze the bound states of the 30P nucleus for 8 and 21 transitions at 40 and 50 MeV, respectively. The two-nucleon spectroscopic factors that have been obtained for the three optical model potentials are compared with the previous experimental and theoretical calculations. The χN2 values have been calculated for the optical model potentials to estimate the quality of fits for the α+28Si elastic scattering and the 28Si(α, d)30P reaction at two different incident energies. These analyses show that the Michel and the molecular potentials describe the elastic scattering data more satisfactorily than the Woods-Saxon potential at 40 and 50 MeV incident energies, but for the reaction analyses at 40 MeV the Woods-Saxon potential takes over the other two forms of potential. These investigations also show that the direct two nucleons transfer reaction mechanism with the angular distributions of the admixture of L transfers in most of the states of 30P is seemingly sufficient for all forms of the optical model potential at these incident energies.

Validation of an optical potential for incident and emitted low-energy alpha –particles in the Asim 60 mass range

The assessment of an alpha -particle optical model potential for nucleon–induced alpha -emission within the Asim 60 mass-number range [Avrigeanu and Avrigeanu (Eur. Phys. J. A 57:54, 2021)] is completed by analysis of neutron–induced reactions on stable Ni isotopes. The same consistent set of nuclear–model input parameters as well as first uncertainty analysis of calculated cross sections related to the accuracy of independent data formerly used within parameter setting up have been concerned. Description of absorption and emission of alpha -particles by the same potential is validated, while the pickup direct reaction and Giant Quadrupole Resonance (GQR) alpha -emission beyond the statistical predictions are confirmed by recent data around the GQR energies.

Effects of deuteron optical model potentials on the production cross-section calculations of 66-68Ga from natZn and natGe

Since it was reported that several radioisotopes might be advantageous for different medical uses in diagnostics and therapeutics, they have gained significance. Theoretical and experimental researches on such radioisotopes have contributed to the literature on a wide variety of topics, including production route research, getting activation and yield values, optimum production method analysis, clinical effects and production cross-section calculations. This study was motivated by the studies described in this domain as well as those published in the literature. The primary purpose of this study is to investigate the effects of deuteron optical model potentials in various reactions where [Formula: see text] radioisotopes, which are known to be medically important, have been generated with deuteron induced particles on [Formula: see text] and [Formula: see text] targets. The experimental data from the literature and the calculation results generated using the five deuteron optical model potentials accessible in the TALYS code (version 1.95) were compared in line with the objective of this study. The experimental results in the literature and the data obtained as an outcome of the computations are graphically illustrated in order to comprehend these comparisons. Furthermore, to perform a numerical assessment, mean weighted deviation and relative variance calculations were also performed.

Charged-particle optical potentials tested by first direct measurement of the Cu59(p,α)Ni56 reaction

Due consideration of proton optical--model potential (OMP) anomalies at sub-Coulomb energies for medium--weight nuclei is shown to be critical for the analysis of the unprecedented measurement of $^{59}$Cu$(p,\alpha)^{56}$Ni reaction cross section at an energy of $\sim$6 MeV [Phys. Rev. C {\bf 104}, L042801 (2021)]. The variation in predicted cross sections from standard statistical--model calculations and the cross--section range corresponding to the anomalous proton imaginary--potential depth, for target nuclei off the line of stability, are distinct and well separated. Consequently, the new measurement provides, under unique conditions, tests of proton isoscalar and isovector real--potential components, the anomalous imaginary potential, as well as previous alpha-particle OMP, for nuclei off the line of stability.

Scattering of e± from CF3I Molecule

Theoretical investigation of the scattering of electrons and positrons from the plasma etching gas trifluoroiodomethane (CF3I) is presented in the present work. The investigation is carried out by taking into account the screening correction arising from a semiclassical analysis of atomic geometrical overlapping of the scattering cross-sections calculated in the independent atom approximation. The scattering system e±-CF3I is studied through the calculations of the observable quantities, namely, absolute differential, Sherman function, total elastic and inelastic, momentum transfer, viscosity, ionization and total cross sections over the energy range 1 eV–1 MeV. Energy dependency of the differential cross section and Sherman function are also picturized in this work. A comparative study is carried out between scattering observables for electron impact with those for positron impact to get a better understanding of the interaction and dynamics of the collision process. The corresponding scattering quantities of the constituent atoms are calculated employing a complex optical model potential by solving the Dirac relativistic wave equations in the framework of partial wave analysis. The comparison of our results with the available experimental and theoretical data shows a reasonable agreement.

SPECTRIOSCOPY AND DYNAMICS OF HEAVY EXOTIC PIONIC ATOMIC SYSTEMS: ADVANCED RELATIVISTIC THEORY

An advanced relativistic approach is presented to studying spectroscopy and photodynamics of the exotic (pionic) atomic systems based on the Klein-Gordon-Fock equation approach and relativistic many-body perturbation theory with accounting for the fundamental electromagnetic and strong pion-nuclear interactions. The strong pion-nuclear interactions are taken into account by means of using the generalized strong pion-nuclear optical potential model with the effective Ericson-Ericson potential. The nuclear finite size effect is taken into consideration within the Fermi model. In order to take the nuclear quadrupole deformation effects on pionic processes into account we have used the model by Toki et al. The radiative corrections are effectively taken into account within the generalized Uehling-Serber approximation to treat the Lamb shift vacuum polarization part. The advanced data for the energy and spectral parameters for pionic atoms of the 173Yb, 175Lu, 197Au, 208Pb, 238U with accounting for the radiation (vacuum polarization), nuclear (finite size of a nucleus ) and the strong pion-nuclear interaction corrections are listed.

Constraining Nucleosynthesis in Neutrino-driven Winds: Observations, Simulations, and Nuclear Physics

A promising astrophysical site to produce the lighter heavy elements of the first r-process peak (Z = 38 − 47) is the moderately neutron-rich (0.4 < Y e < 0.5) neutrino-driven ejecta of explosive environments, such as core-collapse supernovae and neutron star mergers, where the weak r-process operates. This nucleosynthesis exhibits uncertainties from the absence of experimental data from (α, xn) reactions on neutron-rich nuclei, which are currently based on statistical model estimates. In this work, we report on a new study of the nuclear reaction impact using a Monte Carlo approach and improved (α, xn) rates based on the Atomki-V2 α optical model potential. We compare our results with observations from an up-to-date list of metal-poor stars with [Fe/H] < −1.5 to find conditions of the neutrino-driven wind where the lighter heavy elements can be synthesized. We identified a list of (α, xn) reaction rates that affect key elemental ratios in different astrophysical conditions. Our study aims to motivate more nuclear physics experiments on (α, xn) reactions using the current and new generation of radioactive beam facilities and also more observational studies of metal-poor stars.

Theoretical study of e ±-NH3 scattering

The theoretical investigation of differential, integrated elastic, momentum transfer, viscosity, inelastic, grand total and total ionisation cross sections along with the Sherman functions for the scattering of electrons and positrons by polar NH3 molecule in the energy range 1 eV–1 MeV are reported in the present work. We carry out calculations using the independent atom model (IAM) and IAM with screening correction. The scattering observables are calculated using a complex optical model potential in the framework of the Dirac partial wave analysis. The application of screening correction to the IAM substantially improves the cross sections particularly at lower incident energies. The results obtained from the present study are compared with the available experimental and theoretical works found in the literature.

On the separability of microscopic optical model potentials and emerging bell-shape Perey–Buck nonlocality

After nearly sixty years since its introduction, the phenomenological bell-shape Perey-Buck spatial nonlocality in the optical model potential for nucleon-nucleus scattering has remained unaccounted for from a microscopic standpoint. In this article we provide a quantitative account for such nonlocality considering fully nonlocal optical potentials in momentum space. The framework is based on a momentum-space in-medium folding model, where infinite nuclear matter $g$ matrices in Brueckner-Hartree-Fock approximation are folded to the target one-body mixed density. The study is based on chiral next-to-next-to-next-to-leading order (N3LO) as well as Argonne $v_{18}$ nucleon-nucleon bare interaction models. Applications focus on $^{40}$Ca($p,p$) scattering at beam energies in the range 11-200 MeV, resulting in the identification of a separable structure of the momentum-space optical potential of a form we coin as $JvH$, with a nonlocality form factor as one of its terms. The resulting nonlocaliy form factor features a bell-shape with nonlocality range $\beta$ between 0.86 and 0.89 fm, for both proton and neutron beams at energies below 65 MeV. An analytic toy model is introduced to elucidate the underlying mechanism for the nonlocality in the optical model, providing an estimate of its range based on the Fermi motion of the target nucleons and the long-range part of the $NN$ interaction.

Determination of Differential Cross-Section of (n+89Y) Elastic and Inelastic Scattering using Eikonal Approximation

Neutron differential-elastic and inelastic scattering cross-sections of Yttrium-89 isotope were calculated at energies 8,10,12,14, and 17 MeV, at angles distributed between 20o and 180o in the center of mass frame. The obtained results data were interpreted using a spherical optical potential model and Eikonal approximation, to examine the effect of the first-order Eikonal correction on the effective potential. The real and imaginary parts of optical potential were calculated. It was found that the nominal imaginary potential increase monotonically while the effective imaginary one has a pronounced minimum around r = 6fm and then increases. The analysis of the relative energy of the projectile and reaction product was taken into account. The main results were compared with available experimental data at EXFOR.

Positron impact elastic scattering by calcium atom using first order distorted wave born approximation with a complex potential

Precise positron scattering cross section data are essential for the development of a wide range of technological fields such as astrophysics, plasma sciences, material sciences and bio-medicine. Thus, lack of complete agreement among the available theoretical data, unavailability of experimental data and the first-order distorted wave born approximation with a complex potential at impact energy range 10-200 eV not having been utilized in such a study; are the reasons that informed this investigation. After formulating the complex potential, with positronium formation channel proficiently incorporated, the radial equation was solved numerically. The extracted phase shifts were used to compute the transition matrix. The Roothaan-Hartree-Fock ground state wavefunctions of calcium were utilized in evaluation of the distorting potential and the transition matrix. The transition matrix was then used to determine the differential cross sections while the optical theorem was used to compute total cross sections. With only static potential, the present distorted wave Born approximation and optical potential models yield results that are in close agreement while the effect of positronium formation channel on the cross sections is insignificant at impact energies beyond 150 eV.

Effects of combining some theoretical models in the cross-section calculations of some alpha-induced reactions for natSb

In cases where it is not possible to obtain the cross-section values experimentally due to various factors, the importance of obtaining them with theoretical models has been explained in many studies available in the literature. In this context, the comparison of the cross-section values obtained by using the theoretical models with the experimental data will also be very beneficial for updating and developing these models. Existing studies, which also serve this purpose, have given inspiration to this study and it is aimed to examine the effects of the simultaneous use of the alpha optical model potentials and the level density models on the cross-section calculations for some alpha-particle-induced reactions on natural antimony. The effects of theoretical models on the cross-section calculations were investigated by comparing the obtained calculation results with the experimental data taken from the literature. The TALYS code, which is frequently preferred in the literature, was used in all calculations within the scope of this study. For the comparison of the calculated results with the experimental data, not only a visual analysis by graphing the outcomes, but also a mean-weighted-deviation calculation was used, and the findings were interpreted by accounting for both of them.