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 V 0 { mM ij + hH ij + bB ij + w + S ℏ -2 ( s i + s j ). r ij × ( P i - P j )} exp (-β r ij 2 ) + ( e 2 / r ij ) ij , where ij = 1 if the nucleons are protons and zero otherwise. M ij , H ij and B ij are the normal Majorana, Heisenberg and Bartlett exchange operators, s i , s j and P i , P j 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 V 0 and β are taken to be -45 MeV and 0.2657 × 10 26 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 + 0.325 x , h = 0.258 - 0.325 x , w = 0.242 + 0.225 x , b = 0.242 - 0.225 x , 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.