Separable character of ab initio No-Core Shell Model one-body densities

TL;DR

This paper investigates the off-shell properties of one-body density matrices in nuclei using the No-Core Shell Model, revealing a separable structure that simplifies their characterization across different nuclei and interactions.

Contribution

It demonstrates that one-body density matrices in NCSM are approximately separable, characterized by few terms, independent of interactions and computational details.

Findings

Density matrices are characterized by few singular values.

Separable structure is consistent across different nuclei and interactions.

Findings are independent of computational specifics.

Abstract

Motivated by recent findings on the separability of optical potentials that are derived from folding off-shell densities with off-shell nucleon-nucleon amplitudes, we study the off-shell character of one-body density matrices created within the No-Core Shell Model (NCSM). Concentrating on nuclei with a 0$^+$ ground state from $^4$He through $^{48}$Ca, we investigate the off-shell character of their one-body density matrices in momentum space when using the momentum transfer and the average momentum as variables. A singular value decomposition of the one-body density matrices reveals that they can be characterized by only very few terms, depending on the mass number of the nucleus. These findings are independent of the nucleon-nucleon interactions employed, as well as from computational specifics as grid spacing and size of the model space.