The Scattering of Nucleons by Alpha Particles - Determination of the Spin-Orbit Interaction

The p-phases for the scattering of neutrons by alpha-particles have been calculated by the resonating group structure method assuming an interaction between nucleons of the form V0{mMij + hHij + bBij + w + S -2(si + sj). rij × (Pi-Pj)} exp (-βrij2) + (e2/rij)ij, where ij = 1 if the nucleons are protons and zero otherwise. Mij, Hij and Bij are the normal Majorana, Heisenberg and Bartlett exchange operators, si, sj and Pi, Pj are the spin and orbital angular momentum of the two nucleons. m, h, w, b are constants which satisfy the conditions m + h + w + b = 1, m + w - (h + b) = x = 0.6 V0 and β are taken to be -45 MeV and 0.2657 × 1026 cm-2 respectively. The parameter S measures the relative strength of the spin-orbit interaction, and the aim of the work was to determine S to give the best fit with the observed scattering data. It is found that the mean p-phase shift is only given correctly when the exchange operator in the central interaction is close to the Serber form m = w = ¼(1 + x), h = b = ¼(1 - x). A good fit is obtained with the following constants: m = 0.258 + 0.325x,h = 0.258 - 0.325x,w = 0.242 + 0.225x,b = 0.242 - 0.225x, S = 0.1. The phase shifts were calculated from the integro-differential equation using the Pilot ACE electronic computer at the National Physical Laboratory Teddington. Values of the d-phases have also been obtained for neutron energies up to 16 MeV.