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Background: The evolution of shell structure around doubly magic exoticnuclei is of great interest in nuclear physics and astrophysics. In the`southwest' region of $^{78}$Ni, the development of deformation might trigger amajor shift in our understanding of explosive nucleosynthesis. To this end, newspectroscopic information on key close-lying nuclei is very valuable.  Purpose: We intend to measure the isomeric and $\beta$ decay of $^{75}$Co,with one-proton and two-neutron holes relative to $^{78}$Ni, to access newnuclear structure information in $^{75}$Co and its $\beta$-decay daughters$^{75}$Ni and $^{74}$Ni.  Methods: The nucleus $^{75}$Co is produced in relativistic in-flight fissionreactions of $^{238}$U at the Radioactive Ion Beam Factory in the RIKEN NishinaCenter. Its isomeric and $\beta$ decay are studied exploiting the BigRIPS andEURICA setups.  Results: We obtain partial $\beta$-decay spectra for $^{75}$Ni and $^{74}$Ni,and report a new isomeric transition in $^{75}$Co. The energy[$E_{\gamma}=1914(2)$ keV] and half-life [$t_{1/2}=13(6)$ $\mu$s] of thedelayed $\gamma$ ray lend support for the existence of a $J^{\pi}=(1/2^-)$isomeric state at 1914(2) keV. A comparison with PFSDG-U shell-modelcalculations provides a good account for the observed states in $^{75}$Ni, butthe first calculated $1/2^-$ level in $^{75}$Co, a prolate $K=1/2$ state, ispredicted about 1 MeV below the observed $(1/2^-)$ level.  Conclusions: The spherical-like structure of the lowest-lying excited statesin $^{75}$Ni is proved. In the case of $^{75}$Co, the results suggest that thedominance of the spherical configurations over the deformed ones might bestronger than expected below $^{78}$Ni. Further experimental efforts to discernthe nature of the $J^{\pi}=(1/2^-)$ isomer are necessary.

physical review. c

Persistence of the ${Z=28}$ shell gap in ${A=75}$ isobars:  Identification of a possible ${(1/2^-)}$ ${\mu}$s isomer in ${^{75}}$Co and  ${\beta}$ decay to ${^{75}}$Ni