Nucleus Optical Potential Research Articles

η nucleus optical potential in a chiral unitary approach

The self-energy of an η in a nuclear medium is calculated in a chiral unitary model, and applied to η states in nuclei. Our calculation predicts an attractive η nucleus optical potential which can accommodate many η bound states in different nuclei.

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.

Strong Interactions in Strange Exotic Atoms

Strong interaction level shifts and widths in Σ- and K- atoms have been analyzed. The phenomenological density dependent approach as well as the relativistic mean field (RMF) model yield Σ nucleus optical potentials with a repulsive real part in the nuclear interior. This has important consequences for the spectroscopy of Σ hypernuclei. The study of K- atoms cannot resolve the depth of the K- nucleus potential. The fits to the kaonic atom data are satisfactory for both the relatively shallow potentials derived from chiral models and for the deep potentials based on the phenomenological and RMF analyses.

Pion-nucleus optical potential valid up to the Δ-resonance region

We present in this article an optical potential for the $\pi$-nucleus interaction that can be used in various studies involving $\pi$-nucleus channels. Based on earlier treatments of the low energy $\pi$-nucleus optical potential, we have derived a potential expression applicable from threshold up to the $\Delta$-resonance region. We extracted the impulse approximation form for this potential from the $\pi-N$ scattering amplitude and then added to it kinematical and physical corrections. The kinematic corrections arise from transforming the impulse approximation expression from the $\pi-N$ center of mass frame to the $\pi$-nucleus center of mass frame, while the physical corrections arise mostly from the many-body nature of the $\pi$-nucleus interaction. By taking advantage of the experimental progress in our knowledge of the $\pi-N$ process, we have updated earlier treatments with parameters calculated from state-of-the-art experimental measurements.

Kaonic Nuclei and Kaon-Nucleus Interactions

Although kaonic atoms provide valuable information concerning the K � -nucleus interaction at low energies, they cannot fully determine the K � -nucleus optical potential. We

Medium effects to theN(1535)resonance andηmesic nuclei

The structure of $\ensuremath{\eta}$-nucleus bound systems $(\ensuremath{\eta}$ mesic nuclei) is investigated as one of the tools to study in-medium properties of the ${N(1535)(N}^{*})$ resonance by using the chiral doublet model to incorporate the medium effects of the ${N}^{*}$ resonance in a chiral symmetric way. We find that the shape and depth of the $\ensuremath{\eta}$-nucleus optical potential are strongly affected by the in-medium properties of the ${N}^{*}$ and nucleon. Especially, as a general feature of the potential, the existence of a repulsive core of the $\ensuremath{\eta}$-nucleus potential at the nuclear center with an attractive part at the nuclear surface is concluded. We calculate the level structure of bound states in this ``central-repulsive and surface-attractive'' optical potential and find that the level structure is sensitive to the in-medium properties of the ${N}^{*}.$ The ${(d,}^{3}\mathrm{He})$ spectra are also evaluated for the formation of these bound states to investigate the experimental feasibility. We also make comments on the possible existence of halo-like $\ensuremath{\eta}$ states in $\ensuremath{\beta}$-unstable halo nuclei.

Improved global α-optical model potentials at low energies

Many nuclear astrophysics applications involve radiative α-particle captures, α decays and α-particle transfer reactions. Theoretical estimates of the corresponding reaction rates within the framework of the statistical model of Hauser–Feshbach remain highly uncertain due to the poor knowledge of the α–nucleus optical model potential, especially at low energies far below the Coulomb barrier. In the present paper we propose a new global α-optical potential that takes into account the strong energy dependence and nuclear structure effects that characterize the α–nucleus interaction. The real part of the potential is calculated using a double-folding procedure over the M3Y effective nucleon–nucleon interaction. A Woods–Saxon potential is used for the imaginary potential where now a new parameterization is introduced to describe its energy dependence. The influence of purely volume absorption or volume plus surface absorption on the description of the experimental data is investigated. Finally, the dispersive relation is applied to relate the real and imaginary parts of the optical model potential and reduce the ambiguities in deriving the potential from experimental data. The three potentials considered are able to reproduce well the bulk of experimental data on ( α, γ), ( α, n), ( α, p) and (n, α ) reactions as well as the existing elastic scattering data at energies of relevance to astrophysical applications. However, when considering reaction rates on experimentally unexplored targets, deviations within a factor of 10 are found. These uncertainties are principally due to the difficulty in constraining the diffuseness of the imaginary potential from analyses of existing experimental data.

Folding model analysis of elastic and inelastic proton scattering on sulfur isotopes

The folding formalism for the nucleon–nucleus optical potential and inelastic form factor is applied to study elastic and inelastic proton scattering on 30–40S isotopes. A recently developed realistic density dependent M3Y interaction, well tested in the folding analysis of nucleus–nucleus elastic and inelastic scattering, is used as effective NN interaction. The nuclear ground state and transition densities (for the 2 + excitations in sulfur isotopes) are obtained in the Hartree–Fock-BCS and QRPA approaches, respectively. The best fit ratios of transition moments M n 2 + / M p 2 + for the lowest 2 + states in sulfur isotopes are compared to those obtained earlier in the DWBA analysis of the same data using the same structure model and inelastic form factors obtained with the JLM effective interaction. Our folding + DWBA analysis has shown quite a strong isovector mixing in the elastic and inelastic scattering channels for the neutron rich 38,40S nuclei. In particular, the relative strength of the isovector part of the transition potential required by the inelastic p+ 38 S data is significantly stronger than that obtained with the corresponding QRPA transition density.

Density dependence of microscopic nucleon optical potential in first order Brueckner theory

In the present work we apply the lowest order Brueckner theory of infinite nuclear matter to obtain nucleon–nucleus optical potential for p-40Ca elastic scattering at 200 MeV using Urbana V14 soft core internucleon potential. We have investigated the effect of target density on the calculated nucleon–nucleus optical potential. We find that the calculated optical potentials depend quite sensitively on the density distribution of the target nucleus. The important feature is that the real part of calculated central optical potential for all densities shows a wine-bottle-bottom type behaviour at this energy. We also discuss the effect of our new radial dependent effective mass correction. Finally, we compare the prediction of our calculated nucleon optical potential using V14 with the prediction using older hard core Hamada–Johnston internucleon potential for p-40Ca elastic scattering at 200 MeV.

Calculation of nucleus–nucleus cross sections at intermediate energies using Glauber theory

Nucleus–nucleus cross sections are calculated using nucleon–nucleus optical potentials in the framework of Glauber theory. The resulting cross sections are compared with experimental data. The reaction cross sections for various light nuclei including loosely bound nuclei are calculated from the nucleus–nucleus phase shift functions which need the nuclear density and the optical potential as an input. The calculated reaction cross sections in the energy range of 30 to 800 MeV/nucleon are in agreement with experimental data within error bars. The elastic differential cross sections of 4,6He+ 12C and 12C+ 12C are calculated at 41 MeV/nucleon and 30, 200 MeV/nucleon, respectively. At lower energy, a correction beyond the eikonal approximation improves the agreement between measured and calculated angular distributions significantly.

The Landau parameters of nuclear matter in relativistic Hartree approximation

The Landau parameters of nuclear matter have been calculated in relativistic Hartree approximation as a function of a renormalization scale. The results have then been compared to the empirical values deduced from constraints on isoscalar compression modes, spin-orbit splitting in nuclei and energy dependence of the nucleon–nucleus optical potential. For comparison, the results obtained for relativistic non-linear models and Dirac–Brueckner–Hartree–Fock calculations are also shown.

Nonlocalities and Fermi motion corrections in K − atoms

We evaluate the p-wave K −N amplitudes from the chiral Lagrangians and from there construct the p-wave part of the K − nucleus optical potential plus a small s-wave part induced from the elementary p-wave amplitude and the nuclear Fermi motion. Simultaneously, the momentum and energy dependence of the s-wave optical potential, previously developed, are taken into account and shown to generate a small p-wave correction to the optical potential. All the corrections considered are small compared to the leading s-wave potential, and lead to changes in the shifts and widths which are smaller than the experimental errors. A thorough study of the threshold region and low densities is conducted, revealing mathematical problems for which a physical solution is given.

α-nucleus optical potential in the double-folding model

The double-folding formalism for the $\ensuremath{\alpha}$-nucleus optical potential is revised to study the exchange effects and density dependence of the effective nucleon-nucleon $(\mathrm{NN})$ interaction in detail. A realistic density dependent M3Y interaction, based on the G-matrix elements of the Paris NN potential, has been used in the folding calculation. The local approximation for the nonlocal one-body density matrix in the calculation of the exchange potential was tested by using the harmonic oscillator representation of the nonlocal density matrices of the $\ensuremath{\alpha}$-particle and target nucleus. The inclusion of a realistic density dependence into the effective NN interaction was shown to be vital for a correct description of the refractive $\ensuremath{\alpha}$-nucleus scattering data. A high sensitivity of the density distributions of the $\ensuremath{\alpha}$-particle and target nucleus to the shape of the $\ensuremath{\alpha}$-nucleus potential was found, which can be used in the folding analysis to test various density models for the $\ensuremath{\alpha}$-particle and target as well as to choose the most realistic approximation for the overlap density in the dinuclear system. Our results also stress the importance of $\ensuremath{\alpha}$-nucleus scattering experiment in the nuclear structure study.

Saturation of low-energy antiproton annihilation on nuclei

Recent measurements of very low-energy ( p L <100 MeV/ c) p̄ annihilation on light nuclei reveal apparent suppression of annihilation upon increasing the atomic charge Z and mass number A. Using p̄-nucleus optical potentials V opt, fitted to p̄-atom energy-shifts and -widths, we resolve this suppression as due to the strong effective repulsion produced by the very absorptive V opt. The low-energy p̄-nucleus wavefunction is kept substantially outside the nuclear surface and the resulting reaction cross section saturates as function of the strength of Im V opt . This feature, for E>0, parallels the recent prediction, for E<0, that the level widths of p̄ atoms saturate and, hence, that p̄ deeply bound atomic states are relatively narrow. Antiproton annihilation cross sections are calculated at p L =57 MeV/ c across the periodic table, and their dependence on Z and A is classified and discussed with respect to the Coulomb focussing effect at very low energies.

Pion elastic scattering and double charge exchange on heavy nuclei in the generalized seniority model

The $\ensuremath{\pi}$-nucleus optical potential is extended to open shell nuclei by employing the generalized seniority model and partial Pauli blocking. The calculated optical potentials are fit to $\ensuremath{\pi}$-nucleus elastic scattering data on ${}^{90}\mathrm{Zr}$ and ${}^{208}\mathrm{Pb}$ at resonance as well as low energies. The ranges of the $\ensuremath{\pi}N$ interaction are determined by a best fit to experimental data. The angular distribution at 48 MeV pion lab energy and energy dependence of the double charge exchange cross section on Te isotopes are calculated. The existing experimental data are reproduced by using the ranges in the vicinity of the averaged ranges of ${}^{90}\mathrm{Zr}$ and ${}^{208}\mathrm{Pb}$ determined in fitting elastic-scattering data.

Microscopic Model Analyses of the Elastic Scattering of 25, 30 and 40 MeV Protons from Targets of Diverse Mass

An extensive survey and analysis of cross-section and analysing power data from proton elastic scattering at energies 25 to 40 MeV is presented. The data are compared with predictions obtained from a full folding specification of the proton–nucleus optical potentials. Isotope and energy variation of the data is explained.

Phenomenology ofK+-nucleus scattering

A density expansion of the ${K}^{+}$-nucleus optical potential is used within a momentum-space approach to analyze the experimental total and elastic differential cross section data. We add to the microscopic first-order optical potential a phenomenological higher-order term proportional to the nucleon density raised to a power $\ensuremath{\alpha}.$ A fit to the total cross section data yields a value for $\ensuremath{\alpha}$ of $2.85\ifmmode\pm\else\textpm\fi{}0.25$ and a strength for the potential that decreases slightly faster than the inverse of the kaon laboratory momentum. To obtain a higher-order potential compatible with all the data and with parameters that are target independent, a renormalization of the differential cross section data by 30%, consistent with our estimate of systematic errors, is made. The need for such a large renormalization is explained.

Pion-nucleus scattering at medium energies with densities from chiral effective field theories

Abstract Recently developed chiral effective field theory models provide excellent descriptions of the bulk characteristics of finite nuclei, but have not been tested with other observables. In this work, densities from both relativistic point-coupling models and mean-field meson models are used in the analysis of meson-nucleus scattering at medium energies. Elastic scattering observables for 790 MeV/ c π ± on 208 Pb are calculated in a relativistic impulse approximation, using the Kemmer-Duffin-Petiau formalism to calculate the π ± nucleus optical potential.

Nuclear dependence of the coherentηphotoproduction reaction in a relativistic approach

We study the nuclear (or $A)$ dependence of the coherent $\ensuremath{\eta}$ photoproduction reaction in a relativistic impulse approximation approach. We use a standard relativistic parametrization of the elementary amplitude, based on a set of four Lorentz- and gauge-invariant amplitudes, to calculate the coherent production cross section from ${}^{4}\mathrm{He}$, ${}^{12}\mathrm{C}$, and ${}^{40}\mathrm{Ca}$. In contrast to nonrelativistic treatments, our approach maintains the full relativistic structure of the process. The nuclear structure affects the process through the ground-state tensor density. This density is sensitive to relativistic effects and depends on $A$ in a different manner than the vector density used in nonrelativistic approaches. This peculiar dependence results in ${}^{4}\mathrm{He}$ having a cross section significantly smaller than that of ${}^{12}\mathrm{C}$---in contrast to existent nonrelativistic calculations. Distortion effects are incorporated through an $\ensuremath{\eta}$-nucleus optical potential that is computed in a simple ``$t\ensuremath{\rho}$'' approximation.

Nuclear incompressibility and density dependentNNinteractions in the folding model for nucleus-nucleus potentials

A generalized version of density dependence has been introduced into the M3Y effective nucleon-nucleon $(\mathrm{NN})$ interaction that was based on the $G$-matrix elements of the Paris $\mathrm{NN}$ potential. The density dependent parameters have been chosen to reproduce the saturation binding energy and density of normal nuclear matter within a Hartree-Fock scheme, but with various values for the corresponding nuclear incompressibility $K$ ranging from 176 to 270 MeV. We use these new density dependent interactions in the folding model to calculate the real parts of $\ensuremath{\alpha}$-nucleus and nucleus-nucleus optical potentials for those systems where strongly refractive scattering patterns have been observed. These provide some information on the potentials at short distances, where there is a strong overlap of the projectile and target density distributions, and hence where the density dependence of the interaction plays an important role. We try to infer, from careful optical model (OM) analyses, the sensitivity of the scattering data to different $K$ values. Results obtained for elastic $\ensuremath{\alpha}$ scattering on targets ranging from ${}^{12}$C to ${}^{208}$Pb allow us to determine unambiguously that the $K$ value favored in this approach is within the range of 240 to 270 MeV. Similar OM analyses have also been done on measurements of the elastic scattering of ${}^{12}$C+${}^{12}$C, ${}^{16}$O+${}^{12}$C, and ${}^{16}$O+${}^{16}$O at incident energies up to 94 MeV/nucleon. These data were found to be much less sensitive over such a narrow range of $K$ values. This lack of sensitivity is due mainly to the smaller maximum overlap density which occurs for these systems, compared to that which is formed in an $\ensuremath{\alpha}$-nucleus collision. This makes the effects of density dependence less substantial. Another reason is that a small difference between two folded heavy ion potentials can often be compensated for, in part, by a small overall renormalization of one of them. This renormalization is often allowed in optical model analyses, and interpreted, for example, as accounting for a contribution from a higher-order dynamic polarization potential. In an attempt to avoid this ambiguity, some OM analyses of the extensive and accurate data for ${}^{16}$O+${}^{16}$O scattering were done using the unrenormalized folded potentials, together with the explicit addition of a correction term, expressed in terms of cubic splines. This correction term can be interpreted as representing a contribution to the real potential from the dynamic polarization potential. The results of such a ``folding+spline'' analysis suggest a tendency to favor the same $K$ value range that was found in the OM analyses of $\ensuremath{\alpha}$-nucleus scattering.