The Nuclear Structure and Associated Electron Capture Rates on Odd-Z Nucleus $^{51}$V in Stellar Matter

The Gamow-Teller strength distribution function, B(GT), for the odd Z parent $^{51}$V, $N-Z$ =5, up to 30 MeV of excitation energy in the daughter $^{51}$Ti is calculated in the domain of proton-neutron Quasiparticle Random Phase Approximation (pn-QRPA) theory. The pn-QRPA results are compared against other theoretical calculations, (n, p) and high resolution (d, $^{2}$He) reaction experiments. For the case of (d, $^{2}$He) reaction the calibration was performed for $0\leq E_{j} \leq 5.0$ MeV, where the authors stressed that within this excitation energy range the $\Delta L = 0$ transition strength can be extracted with high accuracy for $^{51}$V. Within this energy range the current pn-QRPA total B(GT) strength 0.75 is in good agreement with the (d, $^{2}$He) experiment's total strength of 0.9 $\pm$ 0.1. The pn-QRPA calculated Gamow-Teller centroid at 4.20 MeV in daughter $^{51}$Ti is also in good agreement with high resolution (d, $^{2}$He) experiment which placed the Gamow-Teller centroid at 4.1 $\pm$ 0.4 MeV in daughter $^{51}$Ti. The low energy detailed Gamow-Teller structure and Gamow-Teller centroid play a sumptuous role in associated weak decay rates and consequently affect the stellar dynamics. The stellar weak rates are sensitive to the location and structure of these low-lying states in daughter $^{51}$Ti. The calculated electron capture rates on $^{51}$V in stellar matter are also in good agreement with the large scale shell model rates.