Effective interaction for inelastic proton scattering based on the relativistic impulse approximation.

Abstract

A density-dependent effective interaction is derived from a complete set of Lorentz-invariant NN amplitudes. Its use in a Schr\"odinger formalism produces results equivalent to use of the relativistic impulse approximation together with the Dirac equation. The effective interaction is defined for elastic scattering as a matrix element of the Lorentz-invariant nucleon-nucleon interaction, which differs from the free t matrix in that distortions are present in three of the Dirac spinors. A similar reduction of the relativistic distorted-wave impulse approximation for inelastic scattering is performed to obtain an inelastic effective interaction, which differs from the free t matrix in that distortions are present in all four of the Dirac spinors. A local-density approximation is used to evaluate the effective interactions. For elastic scattering, using the elastic effective interaction in the Schr\"odinger equation leads to a reasonable reproduction of the relativistic impulse approximation results. The effective interaction is similar to a phenomenological effective interaction obtained by fitting experimental data for elastic and inelastic scattering. The inelastic effective interaction can be used in conventional nonrelativistic analyses based on the distorted-wave impulse approximation and it provides a simple method for incorporating relativistic effects. The full spin and isospin dpendence of the inelastic effective interaction is developed.