Odd-particle number random phase approximation and extensions: Applications to particle and hole states around $^{16}$O

TL;DR

This paper discusses extensions of the hole and particle random phase approximation methods for odd-A nuclei, incorporating ground-state correlations and analyzing their effects on single-particle states around oxygen-16.

Contribution

It introduces an extension of hRPA and pRPA based on correlated ground states using time-dependent density-matrix theory, improving modeling of odd-A nuclei.

Findings

Ground-state correlations significantly influence hRPA and pRPA results.

Extensions improve the description of single-particle states around $^{16}$O.

Discussion on coupling of core's center of mass motion to particles/holes.

Abstract

The hole-state random phase approximation (hRPA) and the particle-state random phase approximation (pRPA) for systems like odd $A$ nuclei are discussed. These hRPA and pRPA are formulated based on the Hartree-Fock ground state. An extension of hRPA and pRPA based on a correlated ground state is given using time-dependent density-matrix theory. Applications to the single-particle states around $^{16}$O are presented. It is shown that inclusion of ground-state correlation affects appreciably the results of hRPA and pRPA. The question of the coupling of the center of mass motion of the core to the particle (hole) is also discussed.