Further evidence for shape coexistence in ${}^{79}$Zn${}^m$ near doubly-magic ${}^{78}$Ni

Isomers close to doubly-magic ${}_{28}^{78}$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 $1\mathrm{/}{2}^{+}$ isomer in ${}_{30}^{79}$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 $1\mathrm{/}{2}^{+}$ isomer at 942(10) keV, slightly below the $5\mathrm{/}{2}^{+}$ state at 983(3) keV. With the use of state-of-the-art shell-model diagonalizations, complemented with Discrete Non Orthogonal shell-model calculations which are used here the first time to interpret shape coexistence, we find low-lying deformed intruder states, similar to other $N=49$ isotones. The $1\mathrm{/}{2}^{+}$ isomer is interpreted as the band-head of a low-lying deformed structure akin to a predicted low-lying deformed band in ${}^{80}$Zn, and points to shape coexistence in ${}^{79,80}$Zn similar to the one observed in ${}^{78}$Ni. The results make a strong case for confirming the claim of shape coexistence in this key region of the nuclear chart.