We have applied the effective field theory (EFT) approach to achieve the astrophysical s-factor for the transition to the first $2P_{1/2^{-}}$ excited state of $^{7}Li$ nucleus in the $^{3}H(\alpha ,\gamma )^{7}Li$ radiative capture reaction. The $E_{1}$ electrical transition from the $2S_{1/2}, 2P_{1/2}$ and $3S_{1}$ incoming states have studied in the range of $E\leq 1.5$ MeV up to leading order (LO) in the presence of Coulomb effects. This work has been performed in continuation of our studies on the $^{3}H-\alpha $ reaction for the transition to the ground $2P_{3/2^{-}}$ state of $^{7}Li$ . Both the results have been summed up to obtain the $S_{34}(E)$ and compared with the available theoretical and experimental data.
