Number conservation in odd-particle number random phase approximation and extensions

TL;DR

This paper investigates how well the odd-particle number random-phase approximation (oRPA) and its extension (EoRPA) conserve particle number, showing that EoRPA significantly improves number conservation by including ground-state correlations.

Contribution

The study demonstrates the impact of ground-state correlations on number conservation in oRPA and introduces EoRPA as an improved method for this purpose.

Findings

Number conservation is not maintained in oRPA and EoRPA for $^{16}$O.

EoRPA significantly improves number conservation over oRPA.

Ground-state correlations are crucial for accurate number conservation.

Abstract

The number conservation law in the odd-particle number random-phase approximation (oRPA) and its extension (EoRPA) is studied by applying them to a pairing model and $^{16}$O. It is found in the application to $^{16}$O that the number conservation law is not fulfilled in oRPA and EoRPA and that it is drastically improved in EoRPA due to the inclusion of ground-state correlation effects.