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Composite particle, ${(}^{3}He,t)$, charge exchange reactions on targets ${}^{12}C$, ${}^{13}C$, ${}^{18}O$, ${}^{26}Mg$, ${}^{58}Ni$ and ${}^{118,120}Sn$ at 140 MeV/u beam energy have been analyzed by employing distorted wave impulse approximation (DWIA). Specifically, unit cross-section and angular distribution have been calculated using normal optical model potential (NOMP) and single folding optical model potential (SFOMP) for both relativistic and non-relativistic cases. The sensitivity of present results on exchange terms has also been examined and it is pertinent to report here that the inclusion of these effects reduces the cross-section in magnitude up to 60%, which in turn brings it closer to the data except for ${}^{12}C$.

In a recent study by Cole et al. [A. L. Cole et al., Phys. Rev. C86 (2012) 015809], it was concluded that quasi-particle random phase approximation (QRPA) calculations show larger deviations and overestimate the total experimental Gamow–Teller (GT) strength. It was also concluded that QRPA calculated electron capture rates exhibit larger deviation than those derived from the measured GT strength distributions. The main purpose of this study is to probe the findings of the Cole et al. paper. This study gives useful information on the performance of QRPA-based nuclear models. As per simulation results, the capturing of electrons that occur on medium heavy isotopes have a significant role in decreasing the ratio of electron-to-baryon content of the stellar interior during the late stages of core evolution. We report the calculation of allowed charge-changing transitions strength for odd-$A$$fp$-shell nuclei (${}^{45}$Sc and ${}^{55}$Mn) by employing the deformed pn-QRPA approach. The computed GT transition strength is compared with previous theoretical calculations and measured data. For stellar applications, the corresponding electron capture rates are computed and compared with rates using previously calculated and measured GT values. Our finding shows that our calculated results are in decent accordance with measured data. At higher stellar temperature, our calculated electron capture rates are larger than those calculated by independent particle model (IPM) and shell model. It was further concluded that at low temperature and high density regions, the positron emission weak-rates from ${}^{45}$Sc and ${}^{55}$Mn may be neglected in simulation codes.