Effect of Pauli principle on the deformed QRPA calculations and its consequence in the $\beta$-decay calculations of deformed even-even nuclei

TL;DR

This paper incorporates the Pauli Exclusion Principle into deformed QRPA calculations by replacing the Quasi-Boson Approximation with a renormalized approach, improving the accuracy of beta-decay predictions for deformed even-even nuclei.

Contribution

It introduces a new formalism that accounts for PEP in QRPA, avoiding solution collapse and enabling predictions in less-explored nuclear regions.

Findings

QRPA solutions no longer collapse with realistic parameters

Predicted beta-decay rates align with existing calculations

Method extends QRPA applicability to nuclei with limited experimental data

Abstract

In this work, we take into consideration of Pauli Exclusion Principle(PEP) in the quasi-particle random phase approximation (QRPA) calculations for the deformed systems by replacing the traditional Quasi-Boson Approximation(QBA) with the renormalized one. With this new formalism, the parametrization of QRPA calculations has been changed and the collapse of QRPA solutions could be avoid for realistic $g_{pp}$ values. We further find that the necessity of renormalization parameter of particle-particle residual interaction $g_{pp}$ in QRPA calculations is due to the exclusion of PEP. So with the inclusion of PEP, we could easily extend the deformed QRPA calculations to the less explored region where lack of experimental data prevent effective parametrization of $g_{pp}$ for QRPA methods. With this theoretical improvement, we give predictions of weak decay rates for even-even isotopes in the rare earth region and the results are then compared with existing calculations.