Investigating nuclear shell structure in the vicinity of Ni 78: Low-lying excited states in the neutron-rich isotopes Zn 80,82

The low-lying level structures of nuclei in the vicinity of $^{78}\mathrm{Ni}$ were investigated using in-beam $\ensuremath{\gamma}$-ray spectroscopy to clarify the nature of the nuclear magic numbers $Z=28$ and $N=50$ in systems close to the neutron drip line. Nucleon knockout reactions were employed to populate excited states in $^{80}\mathrm{Zn}$ and $^{82}\mathrm{Zn}$. A candidate for the ${4}_{1}^{+}$ level in $^{80}\mathrm{Zn}$ was identified at 1979(30) keV, and the lifetime of this state was estimated to be ${136}_{\ensuremath{-}67}^{+92}$ ps from a line-shape analysis. Moreover, the energy of the ${2}_{1}^{+}$ state in $^{82}\mathrm{Zn}$ is reported to lie at 621(11) keV. The large drop in the ${2}_{1}^{+}$ energy at $^{82}\mathrm{Zn}$ indicates the presence of a significant peak in the $E({2}_{1}^{+})$ systematics at $N=50$. Furthermore, the $E({4}_{1}^{+})/E({2}_{1}^{+})$ and $B(E2;{4}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})/B(E2;{2}_{1}^{+}\ensuremath{\rightarrow}{0}_{\mathrm{g}.\mathrm{s}.}^{+})$ ratios in $^{80}\mathrm{Zn}$ were deduced to be $1.32(3)$ and $1.{12}_{\ensuremath{-}60}^{+80}$, respectively. These results imply that $^{80}\mathrm{Zn}$ can be described in terms of two-proton configurations with a $^{78}\mathrm{Ni}$ core and are consistent with a robust $N=50$ magic number along the Zn isotopic chain. These observations, therefore, indicate a persistent $N=50$ shell closure in nuclei far from the line of $\ensuremath{\beta}$ stability, which in turn suggests a doubly magic structure for $^{78}\mathrm{Ni}$.