Gamow-Teller (GT) strength transitions are an ideal probe for testing nuclear structure models. In addition to nuclear structure, GT transitions in nuclei directly affect the early phases of Type Ia and Type-II supernovae core collapse since the electron capture rates are partly determined by these GT transitions. In astrophysics, GT transitions provide an important input for model calculations and element formation during the explosive phase of a massive star at the end of its life-time. Recent nucleosynthesis calculations show that odd-odd and odd-$A$ nuclei cause the largest contribution in the rate of change of lepton-to-baryon ratio. In the present manuscript, we have calculated the GT strength distributions and electron capture rates for odd-odd nucleus ${}^{50}\mathrm{V}$ by using the pn-QRPA theory. At present ${}^{50}\mathrm{V}$ is the first experimentally available odd-odd nucleus in fp-shell nuclei. We also compare our GT strength distribution with the recently measured results of a ${}^{50}\mathrm{V}$($d$, ${}^2\mathrm{He}$)${}^{50}\mathrm{Ti}$ experiment, with the earlier work of Fuller, Fowler, and Newman (referred to as FFN) and subsequently with the large-scale shell model calculations. One curious finding of the paper is that the Brink's hypothesis, usually employed in large-scale shell model calculations, is not a good approximation to use at least in the case of ${}^{50}\mathrm{V}$. SNe Ia model calculations performed using FFN rates result in overproduction of ${}^{50}\mathrm{Ti}$, and were brought to a much acceptable value by employing shell model results. It might be interesting to study how the composition of the ejecta using presently reported QRPA rates compare with the observed abundances.

• Received 9 September 2007

DOI:https://doi.org/10.1103/PhysRevC.76.055803