Random Phase Approximation without Bogoliubov Quasi-particles

TL;DR

This paper introduces a novel version of the random phase approximation for nuclear vibrations that conserves particle number exactly and does not rely on the quasi-particle vacuum, tested in specific limiting cases.

Contribution

It develops a particle-number conserving RPA based on the pair condensate, differing from traditional approaches that use quasi-particle vacua.

Findings

The theory is applicable to low-energy nuclear vibrations.

It successfully reproduces known limits in degenerate and vanishing pairing cases.

Abstract

A new version of random phase approximation is proposed for low-energy harmonic vibrations in nuclei. The theory is not based on the quasi-particle vacuum of the BCS/HFB ground state, but on the pair condensate determined in Ref. [4]. The current treatment conserves the exact particle number all the time. As a first test the theory is considered in two special cases: the degenerate model (large pairing limit) and the vanished-pairing limit.