Comparison between relativistic and nonrelativistic models of the nucleon-nucleon effective interaction. I. Normal-parity isoscalar transitions

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Relativistic density-dependent effective interactions for nucleon-nucleus scattering based upon a complete set of Lorentz-invariant NN amplitudes are used in calculations of elastic and inelastic scattering to normal-parity states of self-conjugate targets. Owing to distortion of Dirac spinors by the relativistic mean fields, the effective interaction appropriate for use in a Schr\odinger formalism incorporates relativistic density dependence, which is stronger for inelastic than elastic scattering. The dominant effect for normal-parity transitions is equivalent to a short-ranged repulsive contribution to the real central interaction that is proportional to density and nearly independent of energy. Pauli blocking of occupied intermediate states is included and gives results similar to the familiar Clementel-Villi damping of the absorptive potential. The relativistic effective interaction is compared with nonrelativistic G-matrix calculations and with empirical effective interactions fitted to data for proton elastic and inelastic scattering. Calculations for elastic and inelastic scattering are compared with data for 200, 318, and 500 MeV and we find that the agreement with data improves as the energy increases. The density dependence of the relativistic model is much stronger at low energies than either the G matrix or the empirical interaction; its repulsive contribution to the central interaction is too strong to give a good description of the data for 200 MeV. Near 500 MeV the relativistic interaction is closer to the empirical interaction and better agreement with the data is obtained, whereas the density dependence of nonrelativistic effective interactions is too small.