Further Evidence for Shape Coexistence in ${{}^{79}\mathrm{Zn}}^m$ near Doubly Magic ${}^{78}\mathrm{Ni}$

Isomers close to doubly magic ${}_{28}{}^{78}{\mathrm{Ni}}_{50}$ provide essential information on the shell evolution and shape coexistence near the $Z=28$ and $N=50$ double shell closure. We report the excitation energy measurement of the $1/2^{+}$ isomer in ${}_{30}{}^{79}{\mathrm{Zn}}_{49}$ through independent high-precision mass measurements with the JYFLTRAP double Penning trap and with the ISOLTRAP multi-reflection time-of-flight mass spectrometer. We unambiguously place the $1/2^{+}$ isomer at 942(10) keV, slightly below the $5/2^{+}$ state at 983(3) keV. With the use of state-of-the-art shell-model diagonalizations, complemented with discrete nonorthogonal shell-model calculations which are used here for the first time to interpret shape coexistence, we find low-lying deformed intruder states, similar to other $N=49$ isotones. The $1/2^{+}$ isomer is interpreted as the bandhead of a low-lying deformed structure akin to a predicted low-lying deformed band in ${}^{80}\mathrm{Zn}$, and points to shape coexistence in ${}^{79,80}\mathrm{Zn}$ similar to the one observed in ${}^{78}\mathrm{Ni}$. The results make a strong case for confirming the claim of shape coexistence in this key region of the nuclear chart.

Figure 1

(a) A typical TOF-ICR spectrum for the $1/2^{+}$ state in ${}^{79}{\mathrm{Zn}}^{+}$. Colored bins indicate the number of detected ions. Darker shades correspond to more ions and lighter shades to fewer ions. The solid red line represents the fit to the data points (black) using the model from Ref. [38]. The cyclotron frequencies are indicated with a vertical black dashed line for the ground state (not present in this spectrum) and a vertical blue dash-dotted line for the isomer. (b) Time-of-flight spectrum for the MR-TOF MS data. The TOF of the ground state is indicated by a vertical black dashed line, and the TOF of the isomer by a vertical blue dash-dotted line. The solid red line represents the fit to the data using the model from Ref. [39].

Figure 2

Occupancy differences between excited states in ${}^{79,80}\mathrm{Zn}$, and ${}^{78}\mathrm{Ni}$ with their respective ground states. The data for ${}^{78}\mathrm{Ni}$ is taken from [19].

Figure 3

DNO-SM expansions in the $(\beta ,\gamma )$ plane (using the same energy scale) for low-lying states in ${}^{79}\mathrm{Zn}$ ($9/2_1^{+}$, $1/2_1^{+}$ and $5/2_1^{+}$ in upper panel) and ${}^{80}\mathrm{Zn}$ ($0_1^{+}$ and $0_2^{+}$ in lower panel). The radius of circles represents the normalized probability of finding a deformation point $(\beta ,\gamma )$ in the corresponding state.