Super- and hyperdeformation inZn60, Zn62, andGe64at high spins

Abstract

Background: The observation of the superdeformed (SD) bands in $^{60,62}\mathrm{Zn}$ indicates that the particle number 30 is a magic particle number, where two- and four-neutron single particles are considered to be promoted to the intruder $1{g}_{9/2}$ shell. However, the SD-yrast band in $^{62}\mathrm{Zn}$ is assigned negative parity.Purpose: I investigate various SD configurations in the rapidly rotating $^{60,62}\mathrm{Zn}$ and $^{64}\mathrm{Ge}$, and attempt elucidating the different roles of the energy gaps at particle numbers 30 and 32.Method: I employ a nuclear energy-density functional method: the configuration-constrained cranked Skyrme-Kohn-Sham approach is used to describe the rotational bands near the yrast line.Results: The negative-parity SD bands appear higher in energy than the positive-parity SD-yrast band in $^{60}\mathrm{Zn}$ by about 4 MeV, which is indicative of the SD doubly magic nucleus. However, the energy gap in $^{64}\mathrm{Ge}$ is smaller $\ensuremath{\approx}2--3$ MeV, though the quadrupole deformation of the SD states in $^{64}\mathrm{Ge}$ is greater than that of $^{60}\mathrm{Zn}$. The present calculation predicts the occurrence of the hyperdeformed state in $^{60}\mathrm{Zn}$ and $^{64}\mathrm{Ge}$ at a high rotational frequency $\ensuremath{\approx}2.0\phantom{\rule{4pt}{0ex}}\mathrm{MeV}/\ensuremath{\hbar}$ due to the occupation of the ${h}_{11/2}$ shell.Conclusions: An SD-shell gap at particle number 30 and 32 appears at different deformations and the energy gap at particle number 32 is low, which make the SD structures of $^{62}\mathrm{Zn}$ unique, where the negative-parity SD states appear lower in energy than the positive-parity one.