where $\rho $ is the baryon density, $Y_{e}
$ is the ratio of electron number to the baryon number, and $N_{A} $ is the Avogadro’s number.

$$\label{GrindEQ__14_}
\rho Y_{e} \, =\, \frac{1}{\pi ^{2} N_{A} } (\frac{m_{e} c}{\hbar }
)^{3} \int _{0}^{\infty }(G_{-}  -G_{+} )p^{2} dp,$$

where $p\, =\, (w^{2} -1)^{1/2} $ is the electron or positron momentum.

The total capture/decay rate per unit time for a nucleus in thermal equilibrium at temperature $T$ for any weak process is then given by

$$\label{GrindEQ__15_}
\lambda  \, =\, \sum _{ij}P_{i} \lambda _{ij}.$$

Here $P_{i} $ is the probability of occupation of parent excited states and follows the normal Boltzmann distribution. The summation over all initial and final states is carried out until satisfactory convergence in the rate calculations is achieved.

Gamow-Teller Strength Distributions
===================================

The charge exchange reactions with high resolution are important probe for the study of nuclear structure in astrophysics. The GT strengths play an important role in electron capture and beta decay processes in the dynamics of stellar collapse [@Nabi07; @Fujita05]. Experimentally the (p, n), (n, p), (d, 2He), and (2He, t) reactions can be used to probe the GT transitions (in both directions) at higher excitation energies. Turning to 