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Isomers close to doubly-magic $^{78}_{28}$Ni$_{50}$ provide essentialinformation on the shell evolution and shape coexistence near the ${Z=28}$ and${N=50}$ double shell closure. We report the excitation energy measurement ofthe $1/2^{+}$ isomer in $^{79}_{30}$Zn$_{49}$ through independenthigh-precision mass measurements with the JYFLTRAP double Penning trap and withthe ISOLTRAP Multi-Reflection Time-of-Flight Mass Spectrometer. Weunambiguously 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-modeldiagonalizations, complemented with Discrete Non Orthogonal shell-modelcalculations 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 $1/2^{+}$ isomer is interpreted as the band-head of a low-lying deformedstructure akin to a predicted low-lying deformed band in $^{80}$Zn, and pointsto 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 inthis key region of the nuclear chart.

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