Proton-neutron pairing in the deformed BCS approach

Abstract

We examine isovector and isoscalar proton-neutron-pairing correlations for the ground state of even-even Ge isotopes with mass number $A=64–76$ within the deformed BCS approach. For $N=Z$ ${}_{32}{}^{64}\mathrm{Ge}$ the BCS solution with only $T=0$ proton-neutron pairs is found. For other nuclear systems $(N>Z)$ a coexistence of $T=0$ and $T=1$ pairs in the BCS wave function is observed. The problem of fixing of strengths of isoscalar and isovector pairing interactions is addressed. The dependence of number of like and unlike pairs in the BCS ground state on the difference between number of neutrons and protons is discussed. We found that for nuclei with $N$ much bigger than $Z$ the effect of proton-neutron pairing is small but not negligible.