Cross Section for  \(^3H(\alpha ,\gamma )^7Li\) Astrophysical Reaction Using Scattering Phase Shifts

The chemical abundance of different elements in Universe depends substantially on the nuclear structure and nuclear reactions. In order to determine the primordial \(^7Li\) abundance in the early Universe, the \(^3H(\alpha ,\gamma )^7Li\) radiative-capture process is of great astronomical relevance. The calculations of primordial nucleosynthesis offer some thorough and comprehensive assessments of main assumptions of the big-bang model. The key information required for these calculations is nuclear reaction rate \(N_A <\sigma v>\) , which further depends on the velocity-averaged cross section ( \(\sigma \) ) of the nuclear reaction. Astrophysical S-factor calculations also require the total cross section of any reaction. The cross section for \(^3He(\alpha ,\gamma )^7Be\) Astrophysical reaction has already been obtained by our group for laboratory energies up-to 9 MeV. In this work, we have calculated cross section for the reaction \(^3H(\alpha ,\gamma )^7Li\) by calculating scattering phase shifts using Phase function method. The phase shifts are calculated for laboratory energies below 15 MeV for \(\frac{5}{2}^-\) and \(\frac{7}{2}^-\) resonant states of \(^7Li\) (partial wave \(\ell =3\) ). The calculated resonance energies ( \(E_r\) ) and width of resonance \(\Gamma \) are: \(E_r=2.19\) MeV ( \(exp = 2.18\) MeV), \(\Gamma = 0.090\) MeV ( \(exp = 0.069\) MeV) for \(\frac{7}{2}^-\) resonant state and \(E_r= 3.60\) MeV ( \(exp=4.14\) MeV), \(\Gamma = 0.704\) MeV ( \(exp=0.918\) MeV) for \(\frac{5}{2}^-\) resonant state.