Isoscalar and isovector pair correlations in an isospin-invariant pairing plus quadrupole model

Abstract

Isovector and isoscalar correlations are investigated using an isospin-invariant pairing plus quadrupole model with inclusion of an isoscalar pairing force. An exact shell model calculation is carried out on the ${(g}_{9/2}{)}_{p}{(g}_{9/2}{)}_{n}$ shell, as a schematic example. We study isoscalar $(\ensuremath{\tau}=0)$ and isovector $(\ensuremath{\tau}=1)$ pair correlations in the ground state and excited states, and examine the interplay between isoscalar and isovector correlations. Under the single ${g}_{9/2}$ shell approximation, it is found that, for the $N=Z$ even-even system, the number of $\ensuremath{\tau}=1, J=8$ pairs increases drastically in a state with total spin $I=8$ along the yrast line. For $N=Z$ odd-odd systems, there is a crossing of an even-spin ground band by an odd-spin band at $I=1$ along the yrast line. The $\ensuremath{\tau}=0, J=9$ proton-neutron correlations increase suddenly at $I=7.$ This can be interpreted as the alignment of a proton-neutron pair. Finally, we examine the $J=0$ pair correlations in ground states of even-even and odd-odd systems.