Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory

TL;DR

This paper develops a method to extract translationally invariant nonlocal one-body densities from ab initio no-core shell-model calculations, enabling more accurate reaction modeling with nonlocal nuclear interactions.

Contribution

It introduces a new procedure for removing center-of-mass effects from nonlocal densities derived from NCSM and SA-NCSM, which was not previously available.

Findings

Nonlocality increases with angular momentum in ground state densities.

The magnitude of nonlocal contributions decreases with higher angular momentum.

Nonlocal density structures are linked to nuclear shell structure and are complex to model.

Abstract

[Background:] It is well known that effective nuclear interactions are in general nonlocal. Thus if nuclear densities obtained from {\it ab initio} no-core-shell-model (NCSM) calculations are to be used in reaction calculations, translationally invariant nonlocal densities must be available. [Purpose:] Though it is standard to extract translationally invariant one-body local densities from NCSM calculations to calculate local nuclear observables like radii and transition amplitudes, the corresponding nonlocal one-body densities have not been considered so far. A major reason for this is that the procedure for removing the center-of-mass component from NCSM wavefunctions up to now has only been developed for local densities. [Results:] A formulation for removing center-of-mass contributions from nonlocal one-body densities obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived, and applied to the ground state densities of $^4$He, $^6$Li, $^{12}$C, and $^{16}$O. The nonlocality is studied as a function of angular momentum components in momentum as well as coordinate space [Conclusions:] We find that the nonlocality for the ground state densities of the nuclei under consideration increases as a function of the angular momentum. The relative magnitude of those contributions decreases with increasing angular momentum. In general, the nonlocal structure of the one-body density matrices we studied is given by the shell structure of the nucleus, and can not be described with simple functional forms.