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Angle-integrated cross-section measurements of the $^{56}$Ni(d,n) and (d,p)stripping reactions have been performed to determine the single-particlestrengths of low-lying excited states in the mirror nuclei pair$^{57}$Cu-$^{57}$Ni situated adjacent to the doubly magic nucleus $^{56}$Ni.The reactions were studied in inverse kinematics utilizing a beam ofradioactive $^{56}$Ni ions in conjunction with the GRETINA $\gamma$-array.Spectroscopic factors are compared with new shell-model calculations using afull $pf$ model space with the GPFX1A Hamiltonian for the isospin-conservingstrong interaction plus Coulomb and charge-dependent Hamiltonians. Theseresults were used to set new constraints on the $^{56}$Ni(p,$\gamma$)$^{57}$Cureaction rate for explosive burning conditions in x-ray bursts, where $^{56}$Nirepresents a key waiting point in the astrophysical rp-process.

physics letters b

Single-particle shell strengths near the doubly magic nucleus $^{56}$Ni  and the $^{56}$Ni(p,$\gamma$)$^{57}$Cu reaction rate in explosive  astrophysical burning