BruecknerG-matrix approach for neutron-proton pairing correlations in the deformed BCS approach

Abstract

Ground states of even-even Ge isotopes with mass number $A=64\text{--}76$ have been studied in the deformed Bardeen-Cooper-Schrieffer (BCS) theory by taking neutron-proton $(np)$ pairing correlations as well as neutron-neutron $(nn)$ and proton-proton $(pp)$ pairing correlations. The $np$ pairing has two different modes $J=0,\phantom{\rule{4pt}{0ex}}T=1$ (isotriplet) and $J=1,\phantom{\rule{4pt}{0ex}}T=0$ (isosinglet). In this work, the Brueckner $G$ matrix, based on the CD-Bonn potential, has been exploited to reduce the ambiguity regarding nucleon-nucleon interactions inside nuclei compared to the results by a simple schematic phenomenological force. We found that the $G$ matrix plays important roles to obtain reasonable descriptions of even-even nuclei compared to the schematic force. The $np$ pairing strength has been shown to have a clear correlation with quadrupole deformation parameter ${\ensuremath{\beta}}_{2}$ for the isotopes, and affects the smearing of the Fermi surfaces of not only $N=Z$ nuclei but also $N\ensuremath{\ne}Z$ nuclei. In particular, the coexistence of the like particle ($nn$ and $pp$) and the $np$ pairing modes was found to become more salient by the $G$-matrix approach than by the schematic force approach.