Measurement of astrophysically important excitation energies of $^{58}$Zn with GRETINA

The level structure of proton-rich $^{58}$Zn has been measured with the next-generation $\gamma$-ray tracking array GRETINA in conjunction with the large-acceptance spectrometer S800 at the National Superconducting Cyclotron Laboratory at MSU. $^{58}$Zn is expected to play an important role in the rapid proton capture process (rp process) during Type I X-ray bursts. $^{58}$Zn is located in the vicinity of doubly-magic $^{56}$Ni, which is a waiting point for further processing in the rp process. The reaction $^{57}$Cu(p,$\gamma$)$^{58}$Zn determines the effective lifetime of $^{56}$Ni since the electron-capture lifetime of $^{56}$Ni is larger than 1000~s and $^{56}$Ni is in (p,$\gamma$)~-~($\gamma$,p) equilibrium with $^{57}$Cu at typical rp-process temperatures. Proton capture on $^{57}$Cu is the only open break-out reaction channel within typical burst timescales. So far, the $^{57}$Cu(p,$\gamma$) rate has large uncertainties due to the unknown level structure of $^{58}$Zn. This presentation will focus on the details of the study and present the extracted level scheme of $^{58}$Zn. Moreover, the astrophysical implications will be discussed.