for $\beta^{+}$/EC decays for neutron-deficient nuclei with atomic numbers Z = 10 - 108 were calculated up to the proton drip line for more than 2000 nuclei using the same model [@Hir93]. These microscopic calculations gave a remarkably good agreement with the then existing experimental data (within a factor of two for more than 73$\%$ of nuclei with experimental half-lives shorter than 1 s for $\beta^{+}$/EC decays). Most nuclei of interest of astrophysical importance are the ones far from stability and one has to rely on theoretical models to estimate their beta decay properties. The accuracy of the pn-QRPA model increases with increasing distance from the $\beta$-stability line (shorter half-lives) [@Hir93; @Sta90]. This is a promising feature with respect to the prediction of experimentally unknown half-lives (specially those present in the stellar interior), implying that the predictions are made on the basis of a realistic physical model.

Nucleosynthesis in proton-rich ejecta occur at low densities. At high densities the composition is neutron-rich. Under terrestrial conditions $^{57}$Zn $\beta^{+}$ decays to $^{57}$Cu. We used the calculated ground and excited state GT strength functions to microscopically calculate the $\beta^{+}$/EC rate of $^{57}$Zn in stellar matter. In proton-rich supernova environments $^{57}$Zn is produced at 