Elastic Scattering of Protons and Neutrons by Helium

Abstract

Proton-alpha elastic scattering experiments at 5.81 and 9.48 Mev are analyzed in terms of phase shifts, and the results, together with earlier ones at lower energies, are used to compute the logarithmic derivatives of the wave functions at a radius of 2.9\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}13}$ cm. These logarithmic derivaties, for ${P}_{\frac{1}{2}}$ and ${P}_{\frac{3}{2}}$ states, are found to be linear functions of the energy. From the behavior of the logarithmic derivatives the widths and positions of the ${P}_{\frac{1}{2}}$ and ${P}_{\frac{3}{2}}$ energy levels are determined, the most striking results being the large splitting of the two levels and the very broad width of the ${P}_{\frac{1}{2}}$ level. These results are compared with neutron-alpha experiments and are found to be in sufficiently good agreement to support the conclusions about the ${P}_{\frac{1}{2}}$ level which differ from those previously expected. Small negative $D$ wave phase shifts are found in the proton-alpha experiments which also show evidence of an inverted doublet spin-orbit splitting.