Dispersive Optical Model Potential Research Articles

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.

Dispersive optical model description of nucleon scattering on Pb and Bi isotopes

A recently derived dispersive optical model potential (DOMP) for $^{208}$Pb is extended to consider the non-locality in the real potential and the shell-gap in the definition of the nuclear imaginary potentials near the Fermi energy. The modified DOMP improves the simultaneous description of nucleon scattering on $^{208}$Pb and of the $^{208}$Pb particle-hole bound states. The new potential is shown to give a very good description of nucleon scattering data on near-magic targets $^{206,207}$Pb and $^{209}$Bi.

Analysis of neutron bound states of 208Pb by a dispersive optical model potential

A Lane-consistent dispersive spherical optical model potential (DOMP) was derived in EPJ Web of Conferences 146, 12010 (2017) to describe the nucleon scattering on 208Pb by fitting scattering data at positive energies. The real part of this dispersive potential, representing the shell-model potential, is used to calculate the energies of the bound single-particle states of the target nucleus. The effect of dispersive correction terms on the calculation of the bound-state energies is discussed. A set of re-adjusted optical potential parameters, in particular of the spin–orbit potential, is fitted to measured energies of the bound single-particle states of 208Pb. Derived 208Pb root mean square radius shows good agreement with the measured data. This new set of optical model parameters is also shown to improve the agreement with the polarization scattering data for proton induced reactions on 208Pb.

Calculation of neutron cross-sections on copper-63 and -65

ABSTRACT Toward the development of the next version of Japanese Evaluated Nuclear Data Library (JENDL) general-purpose file, we calculate neutron cross-sections on 63, 65Cu from 50 keV to 20 MeV, which is the incident energy range above the resolved resonance region in JENDL-4.0. A dispersive optical model potential is adopted with a coupled-channel method for interaction between neutron and 63, 65Cu. Direct, pre-equilibrium, and compound processes are taken into account in the calculation. All cross-sections, differential and double-differential cross-sections are consistently calculated with a single set of model parameters. The calculation results reproduce the measured data very well. In addition, disagreement between the calculated and experimental values seen in an integral test for the 63Cu(n, α)60Co reaction is improved by using the cross-section data obtained from the present work.

Evaluation of the neutron induced reactions on235U from 2.25 keV up to 30 MeV

An evaluation of fast neutron induced reactions on 235 U is performed in the 2.25 keV–30 MeV incident energy range with the code EMPIRE–3.2 Malta, combined with selected experimental data. The reaction model includes a dispersive optical model potential (RIPL 2408) that couples seven 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. EGSM nuclear level densities are used in Hauser-Feshbach calculations of the compound-nuclear decay. The starting values for the model parameters are retrieved from the RIPL-3 data-base. Excellent agreement is achieved with available experimental data for neutron emission, neutron capture and fission, which gives confidence that the quantities for which there is no experimental information are also predicted accurately. In the fast neutron region of the evaluated file, the fission cross section is taken from Neutron Standards, and neutron capture includes fluctuations observed in recent experiments. Other channels are taken directly from model calculations. New evaluation is validated against ICSBEP criticality benchmarks with fast neutron spectra with excellent results.

The single-particle characteristics of Pb isotopes near the drip lines calculated within the dispersive optical model

The neutron and proton dispersive optical potential for the 208Pb nucleus has been determined for the energy region from–70 to +60 MeV and used to calculate the differential elastic scattering, the total interaction and reaction cross sections, as well as the single-particle characteristics, the neutron and charge densities, rms radii, and the thickness of the nucleus skin. The calculated results are in good agreement with the experimental data. The proton dispersive optical model potential for the spherical and close to spherical Pb isotopes within the neutron and proton drip lines has been obtained by a similar method. The calculation predicts a trend towards the growth of the proton particle-hole gap, which corresponds to Z = 82 shell closure as Z approaches the proton drip line.

A Fully Lane-consistent Dispersive Optical Model Potential for Even Fe Isotopes Based on a Soft-rotator Model

A fully Lane-consistent dispersive coupled-channel optical model (DCCOM) potential is derived that describes nucleon induced reactions on even iron isotopes. Low-lying structure of excited levels in iron even-even isotopes is described by a soft-rotator model that allows for dynamical deformation around the spherical shape. Soft-rotator Hamiltonian parameters are adjusted to reproduce the experimental energies of the low-lying collective levels of these isotopes. The comprehensive experimental database used in the fitting process included all scattering data for neutron and proton scattering up to 200 MeV. Employed Lane-consistent formalism allows deriving a potential fully symmetric for neutrons and protons. Lane consistency of the derived potential was validated by describing the quasi-elastic (p,n) scattering with excitation of IAS states. An exact approach for calculation of inelastic analyzing powers is derived. Calculated elastic and inelastic analyzing powers both for neutron and proton induced reactions were shown to be in good agreement with experimental data demonstrating the reliability of dispersive spin-orbit potential.

A dispersive optical model potential for nucleon induced reactions on238U and232Th nuclei with full coupling

A dispersive coupled-channel optical model potential (DCCOMP) that cou- ples the ground-state rotational and low-lying vibrational bands of 238 U and 232 Th nuclei is studied. The derived DCCOMP couples almost all excited levels below 1 MeV of exci- tation energy of the corresponding even-even actinides. The ground state, octupole, beta, gamma, and non-axial bands are coupled. The first two isobar analogue states (IAS) popu- lated in the quasi-elastic (p,n) reaction are also coupled in the proton induced calculation, making the potential approximately Lane consistent. The coupled-channel potential is based on a soft-rotor description of the target nucleus structure, where dynamic vibrations are considered as perturbations of the rigid rotor underlying structure. Matrix elements required to use the proposed structure model in Tamura coupled-channel scheme are de- rived. Calculated ratio R(U238=T h232) of the total cross-section di erence to the aver- aged T for 238 U and 232 Th nuclei is shown to be in excellent agreement with measured data.

Neutron shell structure of 58,60,62,64Ni nuclei and its study within a mean-field model with dispersive optical-model potential

Experimental single-particle energies and occupation probabilities for neutron states near the Fermi energy in 58,60,62,64Ni nuclei were obtained from joint evaluation of the data on nucleon stripping and pickup reactions on the same nucleus. Degeneracy of the 2p 3/2,1/2 and 1f 5/2 subshells was demonstrated. The resulting data were analyzed within a mean-field model with dispersive optical-model potential. Good agreement was obtained between the calculated and experimental single-particle energies of the subshells.

Energies of the single-particle proton 1f and 2p states in the 58,60,62,64Ni isotopes

Single-particle energies corresponding to the maximum value of the spectroscopic factor were obtained for the proton states near the Fermi energy in the 58,60,62,64Ni nuclei by the joint evaluation of the data on the stripping and pickup reactions on the same nucleus. These results are compared with the center-of-gravity energies of the single-particle state fragment distributions obtained by the same method and with the single-particle energies calculated with the potential of X. Koura and M. Yamada and with the dispersive optical model potential. The single-particle state fragmentation effect is discussed.

Global dispersive optical model potential for proton as projectile in the energy region up to 200 MeV

Based on the existing experimental data of elastic scattering angular distributions and nonelastic cross sections, we present a set of global dispersive optical model potential (OMP) parameters for proton as projectile, which can basically reproduce the experimental data for target nuclei from 24Mg to 238U with the incident energy up to 200 MeV.

Calculation of single-particle energies of bound nucleon states in nuclei with 40 ≤ A ≤ 208 using global parameters of dispersive optical model potential

Single-particle energies of bound neutron and proton states in nuclei with mass numbers 40 ≤ A ≤ 208 are calculated within the dispersive optical model with different sets of global parameters. The results of the calculation are compared with the experimental data and the predictions of the relativistic mean-field model.

Is a global coupled-channel dispersive optical model potential for actinides feasible?

An isospin-dependent coupled-channel optical model potential containing a dispersive term with a nonlocal contribution is used to simultaneously fit the available experimental database (including strength functions and scattering radius) for neutron and proton scattering on strongly deformed $^{238}\mathrm{U}$ and $^{232}\mathrm{Th}$ nuclei. The energy range 0.001--200 MeV is covered. A dispersive coupled-channel optical model (DCCOM) potential with parameters that show a smooth energy dependence and energy-independent geometry are determined from fits to the entire data set. Calculations using the obtained DCCOM potential reproduce measured total cross-section differences between $^{232}\mathrm{Th}$ and $^{238}\mathrm{U}$ within experimental uncertainty. The isovector terms and the observed very weak dependence of the geometrical parameters on mass number A allow us to extend the derived potential parameters to neighboring actinide nuclei with great confidence.

Nucleon–nucleus real potential of Woods–Saxon shape between −60 and +60 MeV for the 40 ⩽ A ⩽ 208 nuclei

Nucleon differential elastic scattering cross sections, total proton reaction cross sections and single-particle energies of nucleon bound states for 40Ca, 90Zr and 208Pb nuclei are reanalysed in terms of the dispersive optical model at energy from −75 MeV to 60 MeV. The real effective Woods–Saxon potential, which corresponds to the real part of the dispersive optical model potential, is studied with respect to its dependence on A, Z, E and on projectile nature (proton or neutron). For the first time, a parametrization of the Woods–Saxon real part of the nucleon–nucleus optical potential is proposed for the 40 ⩽ A ⩽ 208 nuclei in an energy range from −60 MeV to +60 MeV, which obviously includes the Fermi energy range. The parametrization reflects the dispersion relation between the real and imaginary parts of the optical model potential through the energy dependence of the radius parameter of the real part of the potential. The method of determining the imaginary part of the optical model potential, which is symmetrical relative to the Fermi energy, is also proposed for the nuclei with 40 ⩽ A ⩽ 208. Differential elastic scattering cross sections, total neutron interaction cross sections, total proton reaction cross sections and single-particle energies of the nucleon bound states are calculated in terms of the proposed nucleon–nucleus potential parametrization for some of the (n + A) and (p + A) (40 ⩽ A ⩽ 208) systems and compared with the available experimental data, yielding a fairly good agreement.

Dispersion relations in the nuclear optical model

We have developed a code to calculate integrals arising from the dispersion relation between the real and the imaginary parts of the nuclear optical model potential (OMP). Both, analytical solution for the most common dispersive OMP, and the general numerical solution, are included. In the numerical integration, fast convergence is achieved by means of the Gauss–Legendre integration method, which offers accuracy, easiness of implementation and generality for dispersive optical model calculations. The numerical method is validated versus analytical solution. The use of this package in the OMP parameter search codes allows for an efficient and accurate dispersive analysis.

Dispersive spherical optical model of neutron scattering from27Alup to 250 MeV

A spherical optical model potential (OMP) containing a dispersive term is used to fit the available experimental database of angular distribution and total cross section data for n + Al27 covering the energy range 0.1- 250 MeV using relativistic kinematics and a relativistic extension of the Schroedinger equation. A dispersive OMP with parameters that show a smooth energy dependence and energy independent geometry are determined from fits to the entire data set. A very good overall agreement between experimental data and predictions is achieved up to 150 MeV. Inclusion of nonlocality effects in the absorptive volume potential allows to achieve an excellent agreement up to 250 MeV.

Proton-90Zr mean field between -60 and +185 MeV from a dispersive optical model analysis.

Elastic scattering of protons from $^{90}\mathrm{Zr}$ in the energy range ${\mathit{E}}_{\mathit{p}}$=9.8 to 135 MeV is analyzed using a dispersive optical model potential (OMP). In this analysis, a dispersion relation connects the volume integrals of the imaginary and the real parts of the OMP. Best-fit dispersive OMP parameters are obtained from fits to experimental cross section and analyzing power data at each energy, while the volume integrals of the imaginary potential and dispersive correction terms are fixed at the empirical values obtained in the individual proton elastic scattering analyses from 9.8 to 135 MeV. Predictions of the cross section and analyzing power angular distributions from the best-fit dispersive OMP and conventional OMP are obtained, and give similar quality fits to data. A dispersive OMP with parameters that show a smooth energy dependence are determined from fits to the entire data set. Comparison of cross sections and analyzing powers calculated by the dispersive OMP with experimental data at 160 and 185 MeV is also presented. The dispersive OMP with a smooth energy dependence is extended to the negative energy region with the guidance of the known first single-particle and single-hole state energies near the Fermi energy, ${\mathit{E}}_{\mathit{F}}$=-6.8 MeV, to provide parameters for the shell model potential. This analysis also provides estimates for single-particle and hole energies ${\mathit{E}}_{\mathit{n}\mathit{l}\mathit{j}}$, root-mean-square radii ${\mathit{R}}_{\mathit{n}\mathit{l}\mathit{j}}$, expectat ion values of the effective mass 〈${\mathit{m}}^{\mathrm{*}}$/m${\mathrm{〉}}_{\mathit{n}\mathit{l}\mathit{j}}$, occupation probabilities ${\mathit{N}}_{\mathit{n}\mathit{l}\mathit{j}}$, absolute spectroscopic factors ${\mathit{S}}_{\mathit{n}\mathit{l}\mathit{j}}$, and spectral functions ${\mathrm{\ensuremath{\zeta}}}_{\mathit{n}\mathit{l}\mathit{j}}$(${\mathit{E}}_{\mathit{x}}$) for proton single-particle and single-hole orbits in $^{90}\mathrm{Zr}$. These estimates are compared with available experimental information.

Dispersion relation analysis of d+208Pb elastic scattering.

Elastic scattering of deuterons from $^{208}\mathrm{Pb}$ in the energy range ${\mathit{E}}_{\mathit{d}}$=9 to 79.2 MeV is analyzed using a dispersive optical model potential (OMP). In this analysis, a dispersion relation connects the volume integrals of the imaginary and the real parts of the OMP. Best-fit dispersive OMP parameters are obtained from fits to experimental cross-section and analyzing power data at one energy, and dispersive OMP parameters with a smooth energy dependence are determined from fits to the entire data set. Comparisons, showing fits of similar quality, of the predictions of the cross sections and analyzing powers given by the best-fit dispersive OMP and standard OMP are presented. Dispersive OMP parameters with a smooth energy dependence also give a good description of the experimental data.

Evidence for parity dependence in the neutron-40Ar optical model potential.

The neutron dispersive optical model potential that was developed previously from an analysis of extensive data on the neutron${\mathrm{\ensuremath{-}}}^{40}$Ca system is adapted to the neutron${\mathrm{\ensuremath{-}}}^{40}$Ar system by adjusting the central depth of the local equivalent of the Hartree-Fock-type potential. The n${\mathrm{\ensuremath{-}}}^{40}$Ar data for this adjustment are the total cross section for 11E40 MeV and the centroid energy for the observed single-particle and single-hole states of the valence shells. The resulting potential for n${\mathrm{\ensuremath{-}}}^{40}$Ar yields good predictions for the particle-hole gap for the valence shells and for the energy-averaged s-wave and p-wave scattering functions in the resonance region. However, it gives a poor prediction for the total cross section from 2 to 11 MeV. A similar discrepancy was observed earlier for $^{40}\mathrm{Ca}$. A parity dependence in the surface imaginary potential is suggested from a more careful examination of the s-wave and p-wave scattering functions for $^{40}\mathrm{Ar}$; that parity dependence gives a good prediction of the total cross section for 2 to 11 MeV.

Extrapolation of the dispersive optical model to the resonance region for neutrons on 86Kr.

The neutron-/sup 86/Kr mean field is formulated in terms of a dispersive optical model potential in which the real part contains dispersive contributions derived from the imaginary part by the dispersion relation. The dispersive contribution is added to the Hartree-Fock potential, which is assumed to have a Woods-Saxon shape and a depth that decreases linearly with increasing energy. The shape parameters for all components of the potential are assumed to be independent of energy. The model is formulated in terms of the energy relative to the Fermi energy, and the imaginary potential is assumed to be symmetric about the Fermi energy, which is set equal to -7.7 MeV on the basis of the empirical level structure for n-/sup 86/Kr. All other parameters are taken from earlier analyses of other nuclei, particularly of /sup 89/Y. The model is shown to give good overall predictions for the n-/sup 86/Kr mean field by comparison to the following three sets of empirical data: (i) the observed energies of the occupied and unoccupied valence levels, (ii) the energy-averaged total cross section for neutron energies up to 25 MeV, and (iii) the averaged scattering functions for s-, p-, and d-wave neutrons in the resolved resonance regionmore » from 0.015 to 0.96 MeV. The latter comparison is the unique feature of this work; the partial-wave-scattering functions that are available for s, p, and d waves in the resonance region for /sup 86/Kr make possible detailed comparisons to the scattering functions from the model.« less