Super- and hyperdeformation in ${}^{60}\mathrm{Zn}, {}^{62}\mathrm{Zn}$, and ${}^{64}\mathrm{Ge}$ at high spins

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 $1g_{9/2}$ 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 $\approx 2–3$ 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 $\approx 2.0\mathrm{MeV}/\hslash$ 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 ${}^{62}\mathrm{Zn}$ unique, where the negative-parity SD states appear lower in energy than the positive-parity one.

Figure 1

Excitation energies of the rotational bands in ${}^{60}\mathrm{Zn}$. Solid (dotted) lines represent positive (negative) parity, and closed (open) symbols denote signature $\alpha =0(\alpha =+1)$. A smooth part $AI(I+1)$ is subtracted with an inertia parameter $A=0.025$ MeV in plotting the excitation energies. The subscript $\pi$ or $\nu$ to specify the configuration is omitted.

Figure 2

(a) Kinematic and (b) dynamic moments of inertia of the SD band in ${}^{60}\mathrm{Zn}$. Numerical results obtained by varying $f_0$ are also shown, where $C_0^s$ is multiplied by $f_0$.

Figure 3

As Fig. 1 but for ${}^{62}\mathrm{Zn}$. (a) Experimental data for the WD1, SD1, SD2, SD3, and SD4 bands [25, 49]. The parity of SD4 is not defined. (b) Numerical results obtained by employing the SkM* functional.

Figure 4

Dynamic moments of inertia plotted as functions of rotational frequency. The experimental data [49] are compared with the numerical results.

Figure 5

Evolution of quadrupole deformation of protons, as a function of the rotational frequency, for the selected configurations.

Figure 6

Calculated relative energies of the ${\left[8877\right]}_{\pi }{\left[9878\right]}_{\nu }$ and ${\left[8877\right]}_{\pi }{\left[9887\right]}_{\nu }$ configurations employing several Skyrme-type functionals.

Figure 7

As Fig. 3 but for ${}^{64}\mathrm{Ge}$, calculated by employing the SkM* and SLy4 functionals.

Figure 8

Single-neutron Routhians as functions of the rotational frequency for the ${\left[9977\right]}_{\pi }{\left[9977\right]}_{\nu }$ configuration in ${}^{64}\mathrm{Ge}$. Solid, dash-dotted, dashed, and dash-dot-dotted lines denote the orbitals with $(\mathfrak{p},\alpha )=(+1,+1/2),(+1,-1/2),(-1,+1/2)$, and $(-1,-1/2)$, respectively.

Figure 9

As Fig. 5 but for ${}^{64}\mathrm{Ge}$.

Figure 10

As Fig. 8 but for the HD ${\left[8888\right]}_{\pi }{\left[8888\right]}_{\nu }$ configuration.

Figure 11

Particle density distributions for protons (left) and neutrons (right) of the HD state in ${}^{64}\mathrm{Ge}$ (upper) and ${}^{62}\mathrm{Zn}$ (lower) at ${\omega }_{\mathrm{rot}}=2.0$ MeV.