Proton-neutron quasiparticle random phase approximation (pn-QRPA) theory has recently been used for the calculation of stellar weak interaction rates of the fp-shell nuclide with success. Neutrino losses from protoneutron stars play a pivotal role in deciding if these stars would be crushed into black holes or explode as supernovas. The product of abundance and positron capture rates on ${}^{55}\mathrm{Co}$ is substantial and as such can play a role in the fine tuning of input parameters of simulation codes especially in the presupernova evolution. Recently we introduced our calculation of capture rates on ${}^{55}\mathrm{Co}$, in a luxurious model space of $7\hslash \hspace{1em}\omega$, employing the pn-QRPA theory with a separable interaction. Simulators, however, may require these rates on a fine scale. Here we present for the first time an expanded calculation of the neutrino energy loss rates and positron capture rates on ${}^{55}\mathrm{Co}$ on an extensive temperature-density scale. This type of scale is appropriate for interpolation purposes and of greater utility for simulation codes. The pn-QRPA calculated neutrino energy loss rates are enhanced roughly up to two orders of magnitude compared with the large-scale shell model calculations and favor a lower entropy for the core of massive stars.

This project aims to investigate the most important weak interaction nuclei in the presupernova evolution of massive stars. To achieve this goal, an ensemble containing 728 nuclei in the mass range of A = 1–100 was considered. We computed the mass fractions of these nuclei using Saha’s equation for predetermined values of T, ρ, and Y _e and assuming nuclear statistical equilibrium. The nuclear partition functions were obtained using a newly introduced recipe where excited states, up to 10 MeV, were treated as discrete. The weak interaction rates (electron capture (ec) and β-decay (bd)) were calculated in a totally microscopic fashion using the proton–neutron quasiparticle random phase approximation model and without assuming the Brink–Axel hypothesis. The calculated rates were coupled with the computed mass fractions to investigate the time rate of change of lepton to baryon fraction of the stellar matter. We compare our results with the previous calculations reported in the literature. Noticeable differences up to orders of magnitude are reported with previous calculations. These differences may influence the evolution of the star in the later stages of presupernova. We present a list of the top 50 ec and bd nuclei, which have the largest effect on Y _e for conditions after silicon core burning. The competition between the ec and bd rates in the stellar core was investigated and it was found that Y _e = 0.424–0.455 is the interval where the bd results are bigger than the ec rates.

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.

Electron captures on nuclei play an important role in the collapse of stellar core in the stages leading to a type-II supernova. Recent observations of subluminous Type II-P supernovae (e.g., 2005cs, 2003gd, 1999br) were able to rekindle the interest in 8–10 $M_{\odot }$ which develop O+Ne+Mg cores. We used the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory to calculate the $B$(GT) strength for ${}^{24}\mathrm{Mg}$ $\to$ ${}^{24}\mathrm{Na}$ and its associated electron capture rates for incorporation in simulation calculations. The calculated rates, in this article, have differences with the earlier reported shell model and Fuller, Fowler, and Newman [2] (hereafter F${}^2\mathrm{N}$) rates. We compared Gamow-Teller (GT) strength distribution functions and found fairly good agreement with experiment and shell model. However, the GT centroid and the total GT strength, which are useful in the calculation of electron capture rates in the core of massive presupernova stars, lead to the enhancement of our rate up to a factor of 4 compared to the shell model rates at high temperatures and densities.