Microscopic potentials for polarized triton elastic scattering

The double folding model is used to calculate real central and spin-orbit potentials for triton elastic scattering. These potentials are used to fit cross sections and analysing powers at 17 MeV for targets ranging from ²⁶Mg to ²⁰⁸Pb. For most targets the data are described as well as with phenomenological potentials. The real central potential can be used without any substantial renormalisation, but the spin-orbit potential needs to be increased in strength by a factor between 2 and 6. Comparisons are made with phenomenological studies of triton and ³He elastic scattering and with similar microscopic studies of ³He scattering.     

Optical model analysis of p+6He scattering over a wide range of energy

Optical-model analysis of proton elastic scattering from ⁶He has been carried out for eight sets of elastic scattering data at energies, 24.5, 25.0, 36.2, 38.3, 40.9, 41.6, 71.0 and 82.3 MeV/n respectively. The vector analyzing power and differential cross section for the elastic scattering of ⁶He nucleus from polarized protons at 71 MeV have been analyzed in the framework of the optical model potentials. The data are, first, analyzed in term of phenomenological potentials using the Woods-Saxon form for the real and imaginary parts supplemented by a spin-orbit potential of Thomas form. The analysis has been also performed using microscopic complex potentials.     

Microscopic study on proton elastic scattering of light exotic nuclei at energies below than 100 MeV/nucleon

The proton elastic scattering data on some light exotic nuclei, namely, ^{6, 8}He, ^{9, 11}Li, and ^{10, 11, 12}Be, at energies below than 100MeV/nucleon are analyzed using the single folding optical model. The real, imaginary, and spin-orbit parts of the optical potential (OP) are constructed only from the folded potentials and their derivatives using M3Y effective nucleon-nucleon interaction. These OP parts, their renormalization factors and their volume integrals are studied. The surface and spin-orbit potentials are important to fit the experimental data. Three model densities for halo nuclei are used and the sensitivity of the cross-sections to these densities is tested. The imaginary OP within high-energy approximation is used and compared with the single folding OP. This OP with few and limited fitting parameters, which have systematic behavior with incident energy, successfully describes the proton elastic scattering data with exotic nuclei.     

Analyzing Power in Elastic Scattering of Polarized Protons from Neutron-rich Helium Isotopes

The vector analyzing power has been measured for the elastic scattering of neutron-rich ⁶He from polarized protons at 71 MeV/nucleon. Two approaches based on local one-body potentials were applied to investigate the spin-orbit interaction between a proton and a ⁶He nucleus. An optical model analysis revealed that the spin-orbit potential for ⁶He is characterized by a shallow and long-ranged shape compared with the global systematics of stable nuclei. A semi-microscopic analysis with a α + n + n cluster folding model suggests that the inclusion of realistic interaction between a proton and the α core is important in describing the p-⁶He elastic scattering.     

Elastic 3He scattering from even Ar isotopes and backward-angle anomalies in the systematics of elastic 3He scattering

Angular distributions have been measured for ³He elastic scattering from ^{36, 38, 40}Ar at 26.5 MeV and from ³⁶Ar and ⁴⁰Ca at energies between 24.5 and 28 MeV. This scattering clearly shows features of “anomalous” backward-angle scattering, which is discussed in the systematics of ³He scattering from heavier target nuclei. The data for “anomalous” scattering can be described by optical potentials which show features significantly different from those of “normal” scattering. These features are smaller radius parameters for the real optical potential and a strongly reduced volume integral for the imaginary potential.     

Energy dependence of the elastic scattering 40Ca(3He, 3He) in the energy range 10.0 to 18.0 MeV

Differential cross sections for the elastic scattering of 18, 16, 14, 12 and 10 MeV ³He particles by ⁴⁰Ca were measured and analyzed in terms of the optical model with volume imaginary and real spin-orbit potentials. Angular distributions have been measured in 5° steps between 25° and 175°. Four sets of optical model parameters were established and in two of these, sets A and B, systematic variations with energy of the real, volume imaginary and spin-orbit potentials were obtained. The geometrical parameters were not varied as a function of energy. The effect of the matching radius R_M on the optical model calculations, was investigated. It was found that the matching radius should be calculated using the geometrical parameters of the potential that yields the largest value for R_M according to the receipe R_M = R + 7a where R is the nuclear radius and a is the diffuseness.     

The elastic scattering of 33 MeV He particles from Ni,Cu and Zn

Differential cross sections have been measured for the elastic scattering of 33 MeV ³He particles from targets of ^58,60,62,64Ni,^63,65Cu and ^64,66,68Zn over the angular range 5° to 175°. The data have been analysed with the optical model, with particular emphasis on the investigation of the ambiguities in the real potential, the form of the imaginary potential and the use of a spin-orbit term.     

Elastic scattering of polarised helions from 40,44,48Ca

A phenomenological analysis of the polarised helion elastic scattering data from the ^44,48Ca targets, as well as a re-analysis of the ${}^3\text{He}\text{+}{}^{40}\text{Ca}$ data, has been carried out. It is demonstrated that the spin-orbit potential required to reproduce the polarisation distribution is not unique. Although spin-orbit potentials with the anomalously small diffuseness parameters (a_s ～ 0.2 fm) are found, there are others with larger values (up to 1.05 fm) which can also account for the data in this target mass range. The average strength of the “anomalous” spin-orbit potentials for the three targets is found to be consistent with the values deduced for the proton and deuteron scattering, provided the potential family with the real volume integral per particle pair in the region of 330 MeV · fm³ is considered physically meaningful.     

Antisymmetry and channel coupling contributions to the absorption for p+αd+3He

To understand recently established empirical p+α potentials, RGM calculations followed by inversion are made to study contributions of the d+³He reaction channels and deuteron distortion effects to the p+α potential. An equivalent study of the d+³He potential is also presented. The contributions of exchange non-locality to the absorption are simulated by including an phenomenological imaginary potential in the RGM. These effects alone strongly influence the shape of the imaginary potentials for both p+α and d+³He. The potentials local-equivalent to the fully antisymmetrised-coupled channels calculations have a significant parity-dependence in both real and imaginary components, which for p+α is qualitatively similar to that found empirically. The effects on the potentials of the further inclusion of deuteron distortion are also presented. The inclusion of a spin-orbit term in the RGM, adds additional terms to the phase-equivalent potential, most notably the comparatively large imaginary spin-orbit term found empirically.     

Energy dependence of the optical model parameters for 3He ions scattered from 40Ca and 58Ni

The differential cross sections for the elastic scattering of ³He ions on targets of ⁴⁰Ca and ⁵⁸Ni have been measured at incident energies of 27.7, 51.4, 73.2 and 83.5 MeV. The results of optical model analyses showed that only one unique potential (J_R ≈ 330 MeV · fm³) with a surface absorptive term can provide acceptable fits to the large angle elastic scattering cross sections at 83.5 MeV. The particular geometrical set found at 83.5 MeV could not, however, give an adequate fit to the data with energy less than 40 MeV. Subsequent analyses indicated that a break in the energy dependence of the real potential is observed for the low energy data. Explicit energy dependent terms were obtained by fitting all the data simultaneously. These phenomenological potentials were also compared with the folded nucleon-nucleus potential. The influence of the α-particle channels on the elastic scattering of ³He ions at 83.5 MeV was also examined.     

On high-energy elastic scattering of protons by nuclei

The two coupled channel formalism for high energy elastic scattering [1] is extended to include spin and isospin effects. For a spin and isospin zero nucleus these manifest themselves by additional spin-orbit terms in the potentials. Explicit formulas for these potentials are obtained in terms of the fully spin and isospin dependent nucleon-nucleon scattering amplitude, the ground state nuclear form factor and the state dependent correlation functions. The coupling potential except for a small term arising from double spin and isospin flip process involving nuclear excitation depends only upon the pair correlations.Numerical calculations are performed for the elastic scattering of 1 GeV protons incident on ⁴He. Various phenomenological dynamical two-body correlations as well as correlations generated from the Reid soft-core and Tabakin potentials in an approximate Brueckner-Hartree-Fock calculation are considered. The angular distribution beyond its first diffraction minimum as well as the polarization in the same angular range are shown to be sensitive to these correlations. However, the present accuracy of the experimental data and the lack of knowledge of the nucleon-nucleon scattering amplitude prevent any definitive conclusion about their nature.     

Real part of the optical potential for composite particles

The optical potential for a composite particle is most simply approximated by the sum of the optical potentials of the constituent nucleons. Restricting ourselves to the real parts of the potentials we use this model as a first approximation in a calculation of the potentials for d, ³He, α and ¹²C. We add corrections for (i) the energy dependence of the nucleon potentials, (ii) three-body terms, (iii) the Pauli principle. All corrections can be important and that for the Pauli principle can be very large. We obtain a good explanation of the following phenomena: (a) the deuteron potential is nearly the sum of the neutron and proton potentials, (b) the potential for ³He is about 20 % less than the sum of the potentials of the nucleons in the ³He projectile, (c) the volume integral of the potential for ³He falls at both high and low energies in the energy range 20–100 MeV, (d) shallow potentials with large radii are found for low energy (30 MeV) scattering of α-particles, (e) deeper potentials are found for higher energy α-particle scattering. We predict shallow potentials for ¹²C scattering from light targets but deeper potentials for heavier targets.     

Calculation of the 6He + p elastic scattering cross sections within the folding approach and the high-energy approximation for the optical potential

Data on cross sections for the ⁶He + p elastic scattering at energies of tens of MeV/nucleon are analyzed by calculating the microscopic optical potential (OP) (its real and imaginary parts). The effect produced on the cross section by the dependence of the nucleon-nucleon potential on the nuclear matter density, the role of the spin-orbit interaction, and the role of nonlinearity and renormalization of the microscopic OP are studied. A comparison with the experimental data allows sensitivity of cross sections to these effects to be tested.     

The energy dependence of 6Li optical potentials

The energy dependence of ⁶Li optical potentials for elastic scattering from ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, ⁹⁰Zr and ²⁰⁸Pb targets has been investigated by simultaneously fitting several data sets over a wide energy range. Both Saxon-Woods and double-folded real potentials have been used. In general, there is no requirement for energy dependence in either the real or imaginary potential for any of these targets, whether Saxon-Woods or folded real potentials are used. The main exception is ²⁸Si when energy dependence is required to simultaneously fit low-energy data and high-energy rainbow scattering with folded potentials. The degree to which the potentials are determined is discussed.     

Vector analyzing power in the elastic scattering of 6Li by 4He

The elastic scattering of vector polarized ⁶Li by ⁴He has been investigated in the energy range of 15.1 to 22.7 MeV. The observed large analyzing powers indicate a strong spin-orbit potential for the ⁶Li⁴He interaction. Optical model calculations using a simple L · S-potential without exchange do not reproduce the data.     

6Li elastic scattering ON 12C, 16O, 40Ca, 58Ni, 74Ge, 124Sn, 166Er and 208Pb at E(6Li) = 50.6 MeV

The elastic scattering of ⁶Li ions from a variety of targets, A = 12 to 208, has been measured at a bombarding energy of 50.6 MeV. The angular distributions are characteristic of strongly absorbed particles, such as ³He and heavy ions, and less diffractive than for ⁴He. A simple optical model with Woods-Saxon real and imaginary volume potentials is adequate to fit the data. Spin-orbit effects are not apparent in the data.     

Effective nucleon-nucleon forces and interaction of light exotic nuclei with stable nuclei at low energies

The effect of the density dependence of effective nucleon-nucleon forces on the folded potential of the interactions of the light exotic nuclei ⁶He, ¹¹Li, ¹¹Be, and ⁸B with the stable nucleus ¹²C is studied, and the corresponding experimental data on the total reaction cross sections and on elastic scattering are analyzed. A semimicroscopic double-folding model featuring various density-dependent forces based on the M3Y interaction is used together with the nucleon densities as calculated within the density-functional method by using a unified set of parameters for all the above nuclei. It is shown that the angular distributions recently measured for elastic ⁶He scattering on ¹²C at an energy of 41.6 MeV per projectile nucleon and for elastic ¹¹Be scattering on ¹²C at an energy of 49.3 MeV per projectile nucleon can be described satisfactorily if the real part of the optical folded potential is supplemented with a surface term mimicking the contribution of the dynamical polarization potential.