Collectivity in the light xenon isotopes: A shell model study

Abstract

The lightest xenon isotopes are studied in the shell model framework, within a valence space that comprises all the orbits lying between the magic closures $N=Z=50$ and $N=Z=82$. The calculations produce collective deformed structures of triaxial nature that encompass nicely the known experimental data. Predictions are made for the (still unknown) $N=Z$ nucleus $^{108}\mathrm{Xe}$. The results are interpreted in terms of the competition between the quadrupole correlations enhanced by the pseudo-SU(3) structure of the positive parity orbits and the pairing correlations brought in by the $0{h}_{11/2}$ orbit. We also have studied the effect of the excitations from the $^{100}\mathrm{Sn}$ core on our predictions. We show that the backbending in this region is due to the alignment of two particles in the $0{h}_{11/2}$ orbit. In the $N=Z$ case, one neutron and one proton align to $J=11$ and $T=0$. In $^{110,112}\mathrm{Xe}$ the alignment begins in the $J=10$, $T=1$ channel and it is dominantly of neutron-neutron type. Approaching the band termination the alignment of a neutron-proton pair to $J=11$ and $T=0$ takes over. In a more academic mood, we have studied the role of the isovector and isoscalar pairing correlations on the structure on the yrast bands of $^{108,110}\mathrm{Xe}$ and examined the possible existence of isovector and isoscalar pairing condensates in these $N~Z$ nuclei.