Abstract. Considering the Hulthén potential as the nuclear part of interaction regular solution is derived by exploiting the Frobenius method. The Jost function is constructed by utilizing its integral representation in terms of regular solution. The scattering phase shifts and cross-sections are calculated for the $n−^3$He system from the on-shell Jost function. The results obtained are in close conformity with the previous works that exist in the literature.

Key words: Hulthén potential, Frobenius method, Jost Function, phase shifts, scattering cross-sections.