Super- and hyperdeformation in ⁶⁰Zn, ⁶²Zn, and ⁶⁴Ge at high spins

Abstract

Background: The observation of the superdeformed (SD) bands in ⁶⁰, ⁶²Zn 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 1g₉/₂ shell. However, the SD-yrast band in ⁶²Zn is assigned negative parity. Purpose: I investigate various SD configurations in the rapidly rotating ⁶⁰, ⁶²Zn and ⁶⁴Ge, 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 ⁶⁰Zn by about 4 MeV, which is indicative of the SD doubly magic nucleus. However, the energy gap in ⁶⁴Ge is smaller ≈2–3 MeV, though the quadrupole deformation of the SD states in ⁶⁴Ge is greater than that of ⁶⁰Zn. The present calculation predicts the occurrence of the hyperdeformed state in ⁶⁰Zn and ⁶⁴Ge at a high rotational frequency ≈2.0MeV/ℏ due to the occupation of the h₁₁/₂ 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 ⁶²Zn unique, where the negative-parity SD states appear lower in energy than the positive-parity one.