Elastic scattering study of \(\alpha\)- \(^3\)H and \(\alpha\)- \(^3\)He modeled by Malfliet–Tjon potential using phase function method

The interaction potentials for the resonant states of elastic scattering of \(\alpha -^3H\) $\alpha {-}^{3}H$ and \(\alpha -^3He\) $\alpha {-}^{3}He$ systems have been obtained using phase function method. While the interaction for nuclear part has been chosen as the Malfliet–Tjon (MT) form, the infinite-range Coulomb repulsion has been modeled using Hulthén, providing a screening effect to cut off the potential. The scattering phase shifts have been obtained by solving the phase equation for \(\ell =3\) $\ell =3$ using RK-5 method. The interaction parameters are optimized iteratively to minimize the mean absolute percentage error between the obtained and expected scattering phase shifts. Finally, the resonance energies for the [ \(5/2^-\) $5/2^{-}$ , \(7/2^-\) $7/2^{-}$ ] states of \(\alpha -^3H\) $\alpha {-}^{3}H$ and \(\alpha -^3He\) $\alpha {-}^{3}He$ systems have been obtained(experimental) in MeV, from the plots of their partial cross-sections, yielding [2.20 (2.18), 4.18 (4.14)] and [2.98 (2.98), 5.02 (5.14)] respectively. It can be concluded that the interaction potentials obtained using a combination of MT and Hulthén satisfactorily explain the observed scattering data.