Three phenomenological descriptions of $p-p$ scattering have been proposed to date, two of which, the singular tensor-force model of Christian-Noyes and the L·S force model of Case-Pais, are characterized by a singular triplet potential. The Jastrow model introduces a hard core in the singlet interaction. The parameters of these various potentials were all determined, in part, by use of Born approximation estimates of triplet scattering cross sections at high energies. Inasmuch as the validity of such estimates is not clear in those cases where the interaction is singular, more exact calculations have been performed at 240 Mev with the singular potentials (and also, for comparative purposes, with the well-behaved triplet interaction of Jastrow) using Schwinger's variational method and/or numerical integration procedures. Such calculations have also been performed at 450 Mev for the singular tensor-force model. To insure the existence of solutions, a zero cutoff has been introduced in the singular potentials at distances of the order of the nucleon Compton wavelength.

It is found that, in all instances where the potential is singular, the Born approximation and the use of Born approximation trial functions in a variational treatment are completely unreliable. More exact calculations of the differential scattering cross sections than those in Born approximation introduce large anisotropies in the case of the singular interactions and, in particular, in the case of the L·S potential. The hard-core model, on the other hand, is in qualitative agreement with experiment.

Also discussed are the results of calculations of polarization effects in a double $p-p$ scattering and their implications for the various potentials considered.

• Received 18 August 1952

DOI:https://doi.org/10.1103/PhysRev.88.1099