Identification of the ${\mathrm{g}}_{\frac{9}{2}}$ proton and neutron band crossing in the $N=Z$ nucleus ${}^{76}\mathrm{Sr}$

High-spin states in ${}^{76}\mathrm{Sr}$ have been studied using Gammasphere plus Microball detector arrays. The known yrast band has been extended beyond the first band crossing, which involves the simultaneous alignment of pairs of ${\mathrm{g}}_{\frac{9}{2}}$ protons and neutrons, to a tentative spin of $24\hslash$. The data are compared with the results of cranked relativistic mean-field (CRMF) and cranked relativistic Hartree-Bogoliubov (CRHB) calculations. The properties of the band, including the ${\mathrm{g}}_{\frac{9}{2}}$ proton/neutron band crossing frequency and moments of inertia, are found to be well reproduced by the CRHB calculations. Furthermore, the unpaired CRMF calculations show quite good agreement with the data beyond the band crossing region, indicating that pairing is weak at these frequencies. The high spin results suggest that there is little evidence for an isoscalar $(t=0)$ $\mathit{np}$ pair field. Moreover, a systematic study of the band crossings in even-even $N=Z$ nuclei for the first time reveals that there is no evidence to support the existence of the Coulomb antipairing effect caused by the Coulomb exchange term.

Figure 1

Partial $\gamma$-ray spectrum showing the yrast band in ${}^{76}\mathrm{Sr}$. The spectrum was produced from a $E_{\gamma }\text{−}{E}_{\gamma }\text{−}{E}_{\gamma }$ cube by adding together five spectra created using (a) 262 keV in coincidence with all higher transitions, with the exception of 894 and 1349 keV (b) 484 and 700 keV transitions in coincidence with all higher transitions with the exception of 894 and 1349 keV (c) 894 and 1069 keV in coincidence with all higher transitions (d) 1517 keV in coincidence with all higher transitions and (e) 1593 keV in coincidence with all higher transitions. The weak γ ray marked with an asterisk at 1915 keV is a contaminant from ${}^{73}\mathrm{Br}$.

Figure 2

The upper (lower) panels show the dynamic $J^{(2)}$ (kinematic $J^{(1)}$) moments of inertia, respectively. Circles are used for the ${}^{76}\mathrm{Sr}$ data (solid for firmly established transitions and open circle for the point incorporating the tentative 1953 keV transition). The solid and dashed lines show theoretical values obtained in the CRHB+LN and CRMF calculations, respectively, which are taken from Ref. [9].

Figure 3

Kinematic (solid lines) moments of inertia [and dynamic (dashed lines) moments of inertia for ${}^{60}\mathrm{Zn}$, ${}^{76}\mathrm{Sr}$] as a function of rotational frequency for a superdeformed band in ${}^{60}\mathrm{Zn}$ and the yrast bands in ${}^{68}\mathrm{Se}$, ${}^{72}\mathrm{Kr}$, and ${}^{76}\mathrm{Sr}$.