Optical Model Potential Research Articles

Energy density functional forαclustering and scattering of lightA=4mnuclei

The energy density functional (EDF) is applied to study $\ensuremath{\alpha}$ clustering and $\ensuremath{\alpha}$ scattering in light $A=4m$ nuclei. Our goal is to study the success of the EDF in predicting the ground-state $\ensuremath{\alpha}$ clustering in $4m$-conjugate nuclei. The $\ensuremath{\alpha}$-cluster density is obtained by optimizing the EDF with the help of the convolution theorem. The obtained cluster density reproduced the experimental binding energy of the considered nuclei. The obtained $\ensuremath{\alpha}$-cluster densities are investigated through the elastic scattering of $\ensuremath{\alpha}$ particles from $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{24}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{32}\mathrm{S}$, and $^{40}\mathrm{Ca}$ in the framework of the optical model. The real part of the optical model potential is calculated using $\ensuremath{\alpha}$-cluster single folding or the conventional double folding models based on the obtained densities. The obtained potentials are used to analyze the elastic scattering of $\ensuremath{\alpha}$-particle from (1) $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{24}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{32}\mathrm{S}$, and $^{40}\mathrm{Ca}$ at 104 MeV, (2) $^{12}\mathrm{C}$, $^{24}\mathrm{Mg}$, and $^{28}\mathrm{Si}$ at 120 MeV, (3) $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, and $^{40}\mathrm{Ca}$ at 130 MeV. The obtained results are very satisfactory and in agreement with experimental data. This success indicates the validity and applicability of the EDF in $\ensuremath{\alpha}$-cluster calculation for $A=4m$ nuclei.

Measurements of Strong-Interaction Effects in Kaonic-Helium Isotopes at Sub-eV Precision with X-Ray Microcalorimeters.

We have measured the 3d→2p transition x rays of kaonic ^{3}He and ^{4}He atoms using superconducting transition-edge-sensor microcalorimeters with an energy resolution better than 6eV (FWHM). We determined the energies to be 6224.5±0.4(stat)±0.2(syst) eV and 6463.7±0.3(stat)±0.1(syst) eV, and widths to be 2.5±1.0(stat)±0.4(syst) eV and 1.0±0.6(stat)±0.3(stat) eV, for kaonic ^{3}He and ^{4}He, respectively. These values are nearly 10 times more precise than in previous measurements. Our results exclude the large strong-interaction shifts and widths that are suggested by a coupled-channel approach and agree with calculations based on optical-potential models.

Dirac partial wave calculation for electron scattering cross section by nucleic acid bases

Differential, total, elastic and inelastic scattering cross sections due to the electron impact on the primary nucleic acid bases, are calculated with relativistic Dirac partial-wave considering a local interaction potential known as spherical complex optical potential model. The electron scattering is modeled by implementing screening-corrected additivity rule, a modified form of independent atom model, over an energy range of 10–20000 eV. Comparisons of results obtained in this work with other theoretical and experimental approaches are also presented.

Analysis of alpha elastically scattered by light nuclei applying different models

This paper reports on 4He elastic scattering by [Formula: see text]Li, 9Be and [Formula: see text]B angular distributions analyzed in the optical model (OM) context using Woods–Saxon (WS) potential form and double folding (DF) with distorted-wave Born approximation (DWBA), while applying the M3Y approach to the real part and a WS shape to describe the imaginary part of the optical model potential (OMP). Cluster folding (CF) with the DWBA model has also been explored for theoretical data analysis. The coupled reaction channels (CRC) method has been applied to all nuclear systems under consideration where both inelastic scattering and the transfer with elastic scattering have been involved in the analysis of experimental data. The study highlights the overall agreement between the data under the study and the concerned theoretical approaches.

Improved version of the α -nucleus optical model potential for reactions relevant to the γ process

The present paper proposes an improved version of the $\ensuremath{\alpha}$-nucleus optical model potential ($\ensuremath{\alpha}$-OMP), in which the real part of the potential is determined by the double-folding calculation using the density-dependent CDM3Y1 interaction plus a repulsive potential. The imaginary part of the $\ensuremath{\alpha}$-OMP is treated by a Woods-Saxon form with energy-dependent depth, while its real part is corrected by including the contribution of the dispersion relation derived from the strong variation of the potential at energies in the vicinity of the Coulomb barrier. The proposed potential is validated by calculating the $(\ensuremath{\alpha},n)$ and $(\ensuremath{\alpha},\ensuremath{\gamma})$ cross sections on different target nuclei and the obtained results are compared with those predicted by the recent $\ensuremath{\alpha}$-OMP suggested by Avrigeanu, as well as the available experimental data. The impacts of the energy-dependent imaginary part and the real dispersive term on the $\ensuremath{\alpha}$-induced cross sections are also investigated. The results obtained show that the proposed $\ensuremath{\alpha}$-OMP together with that of Avrigeanu describe reasonably well the experimental cross sections of all $(\ensuremath{\alpha},n)$ reactions being considered. In addition, the imaginary part of the proposed potential has a strong energy-dependent effect on the $\ensuremath{\alpha}$-induced cross section in the energy region below the Coulomb barrier, in particular for radiative $\ensuremath{\alpha}$-capture reactions. Two potentials also describe well the cross sections of $(\ensuremath{\alpha},\ensuremath{\gamma})$ reactions after rescaling the radiative $\ensuremath{\gamma}$ width. This leads to our conclusion that the present $\ensuremath{\alpha}$-OMP can provide precise $\ensuremath{\alpha}$ widths for the study of reactions relevant to the production of $p$ nuclei, and therefore more intensive theoretical research on the radiative strength functions is required.

Global phenomenological optical model potential for 14N-nucleus elastic scattering

In this paper, a set of global optical model potential parameters of [Formula: see text]N is obtained by fitting the experimental data of the elastic scattering angular distributions for the targets from [Formula: see text]Mg to [Formula: see text]Pb below 200 MeV. The global optical model potential parameters of [Formula: see text]N-nucleus reactions obtained are analyzed and used to describe the experimental data. It is found that the present form of the global optical model potential could reproduce the experimental data. Moreover, the elastic scattering angular distributions for the reactions of [Formula: see text]N inducing on some lighter targets and the elastic scattering observable quantity for the reactions involving [Formula: see text]N projectile are predicted using the obtained global optical model potential, and a reasonable description of the experimental data is obtained by comparing with the existing corresponding experimental data.

Antiproton-nuclei cross sections with Woods-Saxon potential at low energies

The present knowledge of the antinucleons elastic scattering and annihilation processes in matter at low energies is limited to a few nuclei data in a small phase-space. Optical potential models are useful tools for modelling nuclear strong interaction of antinucleons with matter providing predictions at very low energies where data are missing. New calculations of elastic and annihilation cross sections for antiproton with nuclei using an optical potential of Woods-Saxon (WS) shape are presented. Preliminary predictions at low energies for carbon and calcium show clearly-measurable nuclear effects for nuclear elastic cross sections at large angles and momenta greater than 50 MeV/c. Some discrepancies in annihilation cross section comparing predictions and data are present using the same fitting parameters.

LILITA_N21: Updated version of the Monte Carlo fusion–evaporation code

Since the code LILITA was presented in 1981 by Gomez Del Campo and Stockstad (1981)[1] and used to simulate the emission of light particles in the decay of a compound nucleus, relevant improvements have been made. Revisions leading to LILITA_N97 were begun by G. La Rana (Naples), M. Kaplan (CMU, Pittsburgh, PA), J.M. Alexander (Stony Brook, NY) and continued by the Naples Group (Moro et al., 2012) [2]. In this work new key features of the code consisting of the implementation of transmission coefficients based on global parametrization of the optical model potential, a description of the nuclear shape based on the nuclear stratosphere model, the parallelization of the code and a graphical user interface are presented. We expect that the new code version, LILITA_N21, makes it possible a better reproduction of wide data set from literature. In order to illustrate how this could be achieved, the standard statistical model predictions have been compared with those obtained with the new code features. A single set of parameters of the new code simultaneously well reproduces the neutron, proton and α-particle energy spectra, angular distributions, and multiplicities in the fusion–evaporation channel. By way of example, here the calculations are compared with experimental data of the reaction 60Ni+100Mo at the excitation energy of about 280MeV (Charity et al., 2003) [3]. The capability to reduce the execution time by exploiting the code parallelization is also discussed.

Reaction channel contributions to proton scattering at 65 MeV

Background: Well-established coupled channel (CC) and coupled reaction channel (CRC) processes make contributions to elastic scattering that are absent from local density folding models.Purpose: To establish and characterize the contribution to the proton optical model potential (OMP) made by the coupling to neutron pickup channels, in particular the proton OMP for 65 MeV protons on $^{48}\mathrm{Ca}$ and $^{40}\mathrm{Ca}$. Also to relate this contribution to results for ${}^{40}\mathrm{Ca}$ at lower energies; to investigate the dynamical nonlocality of this contribution; to characterize the effect on the OMP of breakup of the deuteron.Methods: CRC calculations of neutron pickup and CC calculations of collective states, provide the elastic channel $S$ matrix ${S}_{lj}$. Inversion of ${S}_{lj}$ produces a local potential that yields, in a single channel calculation, the elastic scattering observables from the CC/CRC calculation. Subtracting the bare potential yields a local and $l$-independent representation of the dynamical polarization potential, DPP. From the DPPs due to a selection of channel couplings the influence of dynamically generated nonlocality can be identified. The effect of coupling to the deuteron breakup continuum is also identified.Results: For $^{40}\mathrm{Ca}$, coupling to pickup channels has an effect on observables somewhat weaker than that at 30 MeV, and much less than for pickup coupling for $^{48}\mathrm{Ca}$. The DPPs have similar general properties in each case, but are much larger in magnitude for $^{48}\mathrm{Ca}$. Subsequent breakup of the deuteron makes a large contribution to the DPP, and hence to the OMP. The formal DPPs due to pickup coupling exhibit dynamical nonlocality.Conclusions: The DPPs challenge local density folding models for elastic scattering. The breakup of the deuteron must henceforth be included in calculations of the DPP due to neutron pickup in proton scattering. Pickup coupling effects are still substantial at 65 MeV. No smoothly varying global OMP could fit proton elastic scattering from both ${}^{40}\mathrm{Ca}$ and ${}^{48}\mathrm{Ca}$.

Optical potential parameters of light nuclear fusion based on precise Coulomb wave functions

Based on precise Coulomb wave functions (CWFs), we attempt to calculate the fusion cross sections of light nuclei in a complex spherical square-well nuclear potential (i.e., optical potential model). Comparing with experimental benchmark cross section data, we can calibrate optical potential parameters associated with D+D, D+T, D+He3, p+D, p+Li6 and p+Li7 fusion reactions. Surprisingly, we find that our calculated optical potential parameters are quite different from those of many previous results (e.g., Li et al. (2000) [9], Singh et al. (2019) [14], etc.), in which approximate Coulomb wave functions (ACWFs) with only retaining the leading terms are exploited for the continuity conditions at the radius of nuclear potential. Furthermore, with the obtained optical potential parameters, we compare the fusion cross sections and astrophysical S-factors with that formulated from ACWFs approach, and also find apparent deviations especially for the fusion reactions with resonance peaks such as D+T and D+He3 fusion reactions. We then calculate the phase diagrams of the fusion cross sections with respect to the optical potential parameters and demonstrate several narrow shape resonance belts. It implies that a small deviation of ACWFs from the exact CWFs at nuclear radius might lead to fall off the resonance regimes and therefore causes the big difference on the optical parameters as well as the cross sections.

A Brief Review on the Development of Theories of Deuteron Stripping Reactions

As one type of single nucleon transfer reactions, deuteron stripping reaction has been playing an important role in the study of the single particle structure of atomic nuclei. Also, as a typical three-body nuclear reaction, deuteron stripping reaction is also an important subject in the development of direct nuclear reaction theories. We briefly review the history of the study of deuteron stripping reactions, focusing on the evolution of its theoretical descriptions, and the differences and the relations of the Plane Wave Born Approximation(PWBA), the distorted wave Born approximation(DWBA), the Continuum Discretized Coupled Channel method(CDCC), the Adiabatic Wave Approximation(ADWA), and the approach based on the Faddeev equations. Some important problems being currently addressed in deuteron stripping reaction theories and those should be addressed in near future are also discussed, including deuteron strippings at intermediate and high energies, theory for transfer to continuum states of the residue nuclei, applications of dispersive optical model potentials and non-local potentials, etc. Some preliminary results of our theoretical calculations for deuteron stripping at intermediate and high energies are presented.

Description of elastic scattering induced by the unstable nuclei 9,10,11,13,14C * *Supported by the National Natural Science Foundation of China (11405099, 11575291, 12065003), Scientific and Technological Innovation Programs of Higher Education Institutions (STIP) in Shanxi of China (2019L0743) and Science Foundation for General in Shanxi of China (201901D111317). This work is also supported by the Open Project of Guangxi Key

The elastic-scattering angular distributions and total reaction cross sections of projectiles were predicted using the obtained and global optical model potentials, respectively. The predictions were analyzed in detail by comparison with the available experimental data. The results indicate that the and global optical model potentials provide a satisfactory description of the elastic scattering data for the reactions induced by the . For the neutron-rich carbon isotope , the elastic scattering can be well described by changing the real part radius parameter of the global optical model potential. Possible physical explanations for the observed differences are further discussed.

Activation thick target yield measurement of Mo100(α,n)Ru103 for studying the weak r -process nucleosynthesis

Background: Light ($30\ensuremath{\le}Z\ensuremath{\le}45$) neutron-rich isotopes are thought to be synthesized in the neutrino-driven ejecta of core-collapse supernovae explosions via the weak $r$ process. Recent nucleosynthesis studies have demonstrated that $(\ensuremath{\alpha},xn)$ reactions play a particularly important role in the production of these isotopes. $\ensuremath{\alpha}$-nucleus optical model potentials ($\ensuremath{\alpha}$-OMPs) are used to model this nucleosynthesis scenario.Purpose: The different $\ensuremath{\alpha}$-OMP model parameters can affect the calculated cross sections by more than an order of magnitude in the relevant energy regions, which affects the production of light neutron-rich isotopes. Consequently, to constrain the astrophysical conditions characterizing the supernovae ejecta, the uncertainty of the nuclear physics input has to be reduced.Methods: The cross section of the $^{100}\mathrm{Mo}(\ensuremath{\alpha},n)^{103}\mathrm{Ru}$ reaction was measured by means of the activation method. 0.5 mm thick molybdenum disks were irradiated with ${E}_{\ensuremath{\alpha}}$ = 7.0 to ${E}_{\ensuremath{\alpha}}$ = 13.0 MeV $\ensuremath{\alpha}$ beams. Thick target yields and reaction cross sections were determined via $\ensuremath{\gamma}$-ray spectroscopy.Results: Cross sections at several energies below the Coulomb barrier were measured, reaching the astrophysically relevant energy region. Large discrepancies between the experimental values and statistical model predictions calculated using the well-known $\ensuremath{\alpha}$-OMPs were found. The measured cross section data could be excellently described by the Atomki-V2 potential. Therefore, this $\ensuremath{\alpha}$-OMP was used to derive the astrophysical reaction rates as a function of temperature.Conclusions: The successful reproduction of the measured cross sections in a wide energy region confirm the reliability of the Atomki-V2 potential. The usage of the new $^{100}\mathrm{Mo}(\ensuremath{\alpha},n)^{103}\mathrm{Ru}$ experimental data along with the Atomki-V2 potential reduces the nuclear uncertainties of the weak $r$-process production yields of nuclei with $36\ensuremath{\le}Z\ensuremath{\le}50$ to a marginal level.

Systematic Low-Energy Optical Model Potential for $$\alpha$$-Nucleus Elastic Scattering

Systematic Low-Energy Optical Model Potential for $$\alpha$$-Nucleus Elastic Scattering

Cross section measurements of proton capture reactions on Sr isotopes for astrophysics applications

Background: Abundance calculations of a certain class of proton-rich isotopes, known as $p$ nuclei, require knowledge of the cross sections of thousands of nuclear reactions entering a reaction network. As a result, the solution of the latter relies on the predictions of the Hauser-Feshbach (HF) theory and, hence, on the reliability of the models describing the nuclear parameters entering the HF calculations, notably the optical model potential (OMP), the nuclear level density (NLD) and the $\ensuremath{\gamma}$-ray strength function ($\ensuremath{\gamma}\mathrm{SF}$).Purpose: The present work reports on a systematic study of proton capture reactions on Sr isotopes at energies relevant to the $p$ process which is responsible for the production of the $p$ nuclei at explosive stellar sites. The purpose of the work reported here is to perform a validity test of the different OMP, NLD, and $\ensuremath{\gamma}\mathrm{SF}$ models through extensive and detailed comparisons between HF calculations and experimental cross section data. This test is necessary to understand the origin of discrepancies between the $p$-nuclei abundances observed in the solar system and those predicted by the different astrophysical models, known as $p$-process models, aiming at describing the nucleosynthesis of the $p$ isotopes.Method: Cross sections were determined from $\ensuremath{\gamma}$-angular distribution measurements and from angle-integrated $\ensuremath{\gamma}$ spectra taken with the $4\ensuremath{\pi}\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$-summing technique. Cross-section data and the resulting astrophysical $S$ factors were compared with Hauser-Feshbach calculations obtained with the latest version 1.95 of the nuclear reaction code talys using combinations of global semi-microscopic and phenomenological models of optical potentials (OMPs), nuclear level densities (NLDs), and $\ensuremath{\gamma}$-ray strength functions ($\ensuremath{\gamma}\mathrm{SFs}$).Results: Total cross sections as well as cross sections to the ground and metastable states were determined for the reactions $^{86}\mathrm{Sr}(p,\ensuremath{\gamma})^{87}\mathrm{Y}$, $^{87}\mathrm{Sr}(p,\ensuremath{\gamma})^{88}\mathrm{Y}$, and $^{88}\mathrm{Sr}(p,\ensuremath{\gamma})^{89}\mathrm{Y}$ at incident proton-beam energies from 2.5 to 3.6, 2 to 5, and 1.5 to 5 MeV, respectively.Conclusions: The experimental data reported in the present work are in very good agreement with the talys 1.95 calculations obtained with the default combination of OMP, NLD, and $\ensuremath{\gamma}\mathrm{SF}$ models. This combination is based on purely phenomenological models. A semimicroscopic proton-nucleus optical model potential was optimized at low energies leading to an equally good agreement between experimental data and theoretical calculations based solely on combinations of fully semimicroscopic models of OMP, NLD, and $\ensuremath{\gamma}\mathrm{SF}$. Our results highlight the need for a continued effort on the systematic study of proton-capture reactions to reduce the range of uncertainties arising from global nuclear models for as wide a range of relevant nuclei as possible. In this regard, new ($p,\ensuremath{\gamma}$) data at the lowest possible energies below the opening of the neutron channel are of key importance to improve global proton-nucleus optical model potentials.

Three-body model of the d+A system in an antisymmetrized, translationally invariant many nucleon theory

This paper concerns the theory of direct $A(d,p)B$ reactions and how practical three-body models of them are related to the optical model potentials describing the interaction of the deuterons constituents and the target $A$. A new definition of the nucleon optical potential is introduced which necessitates a careful examination of the boundary conditions involved in the associated coupled-channel formalism. The new definition turns out to be very convenient for making a connection with the theory of the $A(d,p)B$ reaction. The analysis is carried out within an antisymmetrized, translationally invariant formalism and provides a firm basis from a many-body point of view for the three-body force effects calculated in [Phys. Rev. C 99, 064612 (2019)].

Electron-impact excitation of the (4d105s)S1/22→(4d95s2)D3/22 and (4d105s)S1/22→(4d106s)S1/22 transitions in silver: Experiment and theory

We present angle-differential and angle-integrated cross sections for electron-impact excitation of the ($4{d}^{10}5s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}(4{d}^{9}5{s}^{2})\phantom{\rule{0.16em}{0ex}}^{2}D_{3/2}$ and $(4{d}^{10}5s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}\ensuremath{\rightarrow}(4{d}^{10}6s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ transitions in atomic silver. Experimental data for four incident electron energies between 10 and 60 eV are compared with predictions from our relativistic distorted wave (RDW) and nonrelativistic atomic optical potential models. Agreement between our measured and calculated data is only fair, although in the case of the RDW it is seen to improve with increasing incident electron energy. However, only for the $(4{d}^{10}6s)\phantom{\rule{0.16em}{0ex}}^{2}S_{1/2}$ excitation process, agreement of our measured data with earlier relativistic convergent close coupling results from McNamara et al. [J. Phys. B 51, 085203 (2018)] was, with a few exceptions, typically observed to be very good, to within the uncertainties on the data.

Theoretical Calculations and Evaluations of Neutron-Induced Reactions on 121Sb, 123Sb, and Natural Sb

An optical model potential for neutron-antimony isotopes collision systems is obtained at the incident energies up to 200 MeV. Cross sections, angular distributions, energy spectra and double differential cross sections for neutron-induced reactions on 121Sb, 123Sb and natural Sb are consistently calculated and analyzed at incident energies below 20 MeV by using theoretical nuclear models for nuclear energy applications. The calculated results are compared with experimental data and the evaluated data from CENDL-3 and JENDL-4.

Reduction of the neutron imaginary potential off the stability line and its possible impact on neutron capture rates

The effect of the isovector imaginary optical potential has been studied experimentally by using the particle-evaporation technique for the $^{11}\mathrm{B}+^{48}\mathrm{Ca}$ reaction with a 21.8 MeV $^{11}\mathrm{B}$ beam. Spectra of neutron, proton, and $\ensuremath{\alpha}$ particles emitted from the neutron-rich compound nucleus $^{59}\mathrm{Mn}$ have been measured and analyzed with traditional optical model potentials with their original parametrizations as well as with adjusted isovector imaginary components. It is shown that the isovector component of the imaginary potential is indispensable in the reproduction of proton and $\ensuremath{\alpha}$-particle yields from this reaction and even needs to be enhanced compared with the suggestions of the original model parametrizations. This can lead to important consequences for astrophysical reaction-rate calculations.

Study of total, absorption, and 3He and 3H production cross sections in 4He-proton collisions

Light ion breakup cross sections are important for studies of cosmic ray interactions in the inter-stellar medium or radiation protection considerations of energy deposition in shielding and tissues. Abrasion cross sections for heavy ion reactions have been modeled using the Glauber model in the large mass limit or Eikonal form of the optical potential model. Here we formulate an abrasion model for 4He fragmentation on protons using the Glauber model avoiding the large mass limit and include a model for final state interactions. Calculations of energy dependent total, absorption, elastic and breakup cross sections for 4He into 3He or 3H with proton targets are shown to be in good agreement with experiments for energies from 100 to 100,000 MeV/u. The Glauber model for light nuclei with and without a large mass limit approximation is shown to be in fair agreement above 300 MeV/u, however important differences occur at lower energies.