Microscopic model analyses of the elastic scattering of 65 MeV protons from targets of diverse mass

Abstract

Nonlocal coordinate space optical potentials for the scattering of 65 MeV protons from nuclei ranging in mass from 6 Li to 238 U have been defined by folding a complex, medium dependent effective interaction with the density matrix elements of each target. The effective interaction is based upon solutions of the Lippmann-Schwinger and Brueckner-Bethe-Goldstone equations having the Paris potential as input. The nuclear structure information required in our folding model are the one body density matrix elements for the target and the single nucleon bound state wave functions that they weight. For light mass nuclei, very large basis shell model calculations have been made to obtain the one body density matrix elements. For medium and heavy mass nuclei, a very simple shell model prescription has been used. The bound state single particle wave functions that complete the nuclear density matrices are either Woods-Saxon or harmonic oscillator functions. The former are employed in most cases when large basis structure is available. For light nuclei (A ≤ 16) Woods-Saxon potential parameters and harmonic oscillator lengths are determined from fits to electron scattering form factors. For all other nuclei, we use harmonic oscillator functions with the oscillator lengths set from an A 1/6 mass law. Using this microscopic model, optical potentials result from which differential cross sections, analyzing powers and spin rotations are found. In general the calculated results compare very well with data when the effective interactions are determined from a mapping of nucleon-nucleon g matrices. This is not the case when effective interactions built from a mapping of (free) t matrices are used.

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

“…In this connection, it should be noted that there exists a more sophisticated version of the single-folding model [5] where the nonlocal exchange potential is treated exactly in the Schrödinger equation for the scattering wave function. In this approach one calculates the nonlocal nucleon-nucleus potential using the explicit expression for each single-particle wave function |j > taken, e.g., from the shell model.…”

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

“…[20,21] and also with the densities of the cluster-orbital shell-model approximation (COSMA) [9,10,18,19]. In [21] a comparison of the obtained results has been performed to those from the alpha-core approach with the complex and fully non-local effective interaction [22] and also with the non-core model based on the large-scale shell-model (LSSM) calculations (refs. [7,36,37] and references therein).…”

“…A number of works has been devoted to calculations of OP's using the folding approach (see, e.g. [20,21,22,23], [34,35,36,37,38]). For instance, the real parts of OP's for calculating the 6 He+p, 6 He+ 4 He (E lab =151 MeV) [20] and 6 He+p, 8 He+p (E inc < 100 MeV) [21] elastic differential cross sections have been obtained microscopically using realistic M3Y-Paris effective NN interaction [35,38,39] together with the Tanihata et al proton and neutron densities of the helium isotopes [40] in refs.…”

“…We note also the microscopic analysis (refs. [22,23,24,25,26,27]) based on the "coordinate-space g-matrix folding method" [28] (and some modifications [29]), where non-local OP is obtained using a folding of a local medium-dependent NN effective interaction with the target ground-state mixed density. In some of the calculations (e.g.…”

Charge and matter distributions and form factors of light, medium, and heavy neutron-rich nuclei

“…The charge and matter distributions of these nuclei were tested in analyses of differential and total reaction cross sections of the proton scattering on exotic nuclei using different phenomenological and theoretical methods (see, Refs. [16,17,19,[21][22][23][24][25][26][27][28][29][30][31][32]). It was shown (e.g., Ref.…”