The Scattering of Nucleons by Alpha Particles - the s-Phases

The s-phase shifts for scattering of neutrons and of protons by alpha particles have been calculated over the energy range 0-4 Mev. A central interaction between nucleons of gaussian form has been assumed, the constants being consistent with the binding energy of the deuteron and alpha particle. The resonating group structure method has been employed to provide integro-differential equations for the wave functions which describe the scattering. These equations are internally consistent in that the functions used to describe the resonating groups are only assumed to satisfy the usual variational integral condition in terms of the alpha particle binding energy. The s-phases were determined by accurate numerical solutions of the equations. Very good agreement was obtained with the phases derived from analysis of observed data both for neutron and for proton scattering, provided the internucleonic forces were taken to be of symmetrical exchange character. The work is a necessary preliminary to an investigation of the p-phases in terms of an internucleonic spin-orbit interaction.