Abstract
Electron capture and \ensuremath{\beta} decay play important roles in the evolution of presupernovae stars and their eventual core collapse. These rates are normally predicted through shell-model calculations. Experimentally determined strength distributions from charge-exchange reactions are needed to test modern shell-model calculations. We report on the measurement of the Gamow-Teller strength distribution in $^{58}\mathrm{Co}$ from the $^{58}\mathrm{Ni}$($t$,$^{3}\mathrm{He}$) reaction with a secondary triton beam of an intensity of $~{10}^{6}$ pps at 115 MeV/nucleon and a resolution of $~250$ keV. Previous measurements with the $^{58}\mathrm{Ni}$$(n,p)$ and the $^{58}\mathrm{Ni}$($d$,$^{2}\mathrm{He}$) reactions were inconsistent with each other. Our results support the latter. We also compare the results to predictions of large-scale shell-model calculations using the KB3G and GXPF1 interactions and investigate the impact of differences between the various experiments and theories in terms of the weak rates in the stellar environment. Finally, the systematic uncertainties in the normalization of the strength distribution extracted from $^{58}\mathrm{Ni}$($^{3}\mathrm{He}$, $t$) are described and turn out to be nonnegligible due to large interferences between the $\ensuremath{\Delta}L=0,\ensuremath{\Delta}S=1$ Gamow-Teller amplitude and the $\ensuremath{\Delta}L=2,\ensuremath{\Delta}S=1$ amplitude.
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