Super- and hyper-deformation in ${}^{60}$Zn, ${}^{62}$Zn, and ${}^{64}$Ge at high spins

Abstract

Background: The observation of the superdeformed (SD) bands in ${}^{60,62}$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 $1g_{9/2}$ shell. However, the SD-yrast band in ${}^{62}$Zn is assigned negative parity. Purpose: I investigate various SD configurations in the rapidly rotating ${}^{60,62}$Zn and ${}^{64}$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 (EDF) 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 ${}^{60}$Zn by about 4 MeV, which is indicative of the SD doubly-magic nucleus. However, the energy gap in ${}^{64}$Ge is smaller $\sim 2\text{-}3$ MeV, though the quadrupole deformation of the SD states in ${}^{64}$Ge is greater than that of ${}^{60}$Zn. The present calculation predicts the occurrence of the hyperdeformed state in ${}^{60}$Zn and ${}^{64}$Ge at a high rotational frequency $\sim 2.0$ MeV$/\hslash$ 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 ${}^{62}$Zn unique, where the negative-parity SD states appear lower in energy than the positive-parity one.

arXiv comment12 pages, 11 figures; accepted version

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Cited by in corpus (2)

• Multiphonon structure of high-spin states in ${}^{40}$Ca, ${}^{90}$Zr, and ${}^{208}$Pb
• Fast rotation of nuclei with extreme isospin in the vicinity of neutron and proton drip lines