We study results from the recent measurement of the 0\ifmmode^\circ\else\textdegree\fi{} $^{59}\mathrm{Co}$(n,p${)}^{59}$Fe cross section in order to compute the stellar electron capture rate of $^{59}\mathrm{Co}$. This nucleus is the second most important electron capture nucleus in the core of a type II supernova progenitor just before core collapse. It is also the first nucleus which has a large effect on the stellar neutronization rate for which Gamow-Teller strength has been measured. The Gamow-Teller resonance has been observed experimentally at a higher energy above the daughter ground state than one would expect from independent particle shell model arguments, but large-basis shell model calculations employing configuration mixing are more successful in predicting the location of the strength. Because of the high energy of the Gamow-Teller resonance, the stellar electron capture rate and associated neutronization is much less than previous estimates had indicated. Similar trends are seen for $^{60}\mathrm{Co}$, the most important electron capture nucleus for supernova progenitors just before core collapse.
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