Spin dependent ab initio nonlocal No-Core Shell-Model One-Body Densities

TL;DR

This paper derives and analyzes spin-dependent one-body density matrices within the ab initio no-core shell model, highlighting the importance of spin contributions in microscopic optical potential calculations for nucleon-nucleus scattering.

Contribution

It introduces a method to compute and compare spin-orbit contributions of one-body densities with scalar densities in light nuclei using ab initio calculations.

Findings

Spin-orbit contributions are significant in certain nuclei.

Comparison shows differences between spin-dependent and scalar densities.

Results inform more accurate microscopic optical potentials.

Abstract

Constructing microscopic effective interactions (`optical potentials') for nucleon-nucleus (NA) elastic scattering requires in first order off-shell nucleon-nucleon (NN) scattering amplitudes between the projectile and the struck target nucleon and nonlocal one-body density matrices. While the NN amplitudes and the {\it ab intio} no-core shell-model (NCSM) calculations always contain the full spin structure of the NN problem, one-body density matrices used in traditional microscopic folding potential neglect spin contributions inherent in the one-body density matrix. Here we derive and show the expectation values of the spin-orbit contribution of the struck nucleon with respect to the rest of the nucleus for $^{4}$He, $^{6}$He, $^{12}$C, and $^{16}$O and compare them with the scalar one-body density matrix.