The Inglis-Belyaev formula and the hypothesis of the two-quasiparticle excitations (version 2012)

TL;DR

This paper revisits the Inglis-Belyaev formula for vibrational parameters, identifies issues caused by derivatives, and proposes removing these derivatives to eliminate spurious singularities in the model.

Contribution

It demonstrates that the derivatives in the cranking formula are unfounded and proposes a simplified version without derivatives to fix known drawbacks.

Findings

Removing derivatives eliminates singularities in the formula.

The simplified formula resolves spurious resonances.

The approach improves the reliability of vibrational parameter calculations.

Abstract

The goal of the present work is to revisit the cranking formula of the vibrational parameters, especially its well known drawbacks. The latter can be summarized as spurious resonances or singularities in the behavior of the mass parameters in the limit of unpaired systems. It is found that these problems are simply induced by the presence of two derivatives in the formula. In effect, this formula is based on the hypothesis of contributions of excited states due only to two quasiparticles. But it turns out that this is not the case for the derivatives. We deduce therefore that the derivatives are not well founded in the formula. We propose then simply to suppress these terms from the formula. Although this solution seems to be simplistic, it solves definitively all its inherent problems.