A Comprehensive Analysis of Alpha–Nucleon Phase Shifts Using Modified Hylleraas Potential

The burgeoning interest in theoretical physics, particularly within the microscopic domain and in the context of many-body systems, necessitates the employment of the $${}^{4}$$ He nucleus as an exemplar for the investigation of nuclear forces via an array of theoretical modelling methodologies. Rigorous importance of the study of alpha–nucleon system developed the curiosity among the physicists to deal with the problem by the formalism of two body scattering theory. The alpha–neutron system was analyzed using a modified Hylleraas potential as the nuclear interaction component, while the alpha–proton system incorporated an additional pure Coulomb potential to model the electromagnetic interaction. It is argued that the traditional phase function method (PFM) does not hold good for pure Coulomb and Coulomb-like interaction and needs modification. For brevity, it is conjectured here that local Coulomb-like potential is equally applicable for the traditional phase function method which will be examine through some model calculations. The scattering phase shifts for $${}^{2}S_{1/2}$$ , $${}^{2}P_{1/2}$$ , $${}^{2}P_{3/2}$$ , $${}^{2}D_{3/2}$$ and $${}^{2}D_{5/2}$$ states of both the alpha–neutron and alpha–proton systems at a laboratory energy of 12.5 MeV were computed using the Phase Function Method. The calculated phase shifts were then compared to previously reported data, revealing a strong agreement that emphasizes the validity and effectiveness of the present methodological approach.