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