Microscopic foundations of Dirac phenomenology.

Abstract

Recently we have seen a series of highly successful fits to data for nucleon-nucleus scattering which are based upon the use of the Dirac equation. In the phenomenological analysis the potential in the Dirac equation is usually limited to two terms, a (Lorentz) scalar and vector potential. In a recent work we have shown that there are eight scalar invariants that are needed to fully specify the relativistic interaction of an off-shell nucleon with an on-shell, spin zero nucleus. It appears that the phenomenological potentials are effective potentials in the sense that their values need to be adjusted to compensate for the use of a highly simplified phenomenological form. In this work we present calculations of the complete potential, including estimates of the eight terms noted above. Our preliminary results indicate that the values of the phenomenological potentials can be reproduced in a microscopic calculation and bear out our ideas concerning the significance of the phenomenological potentials. It is found that if one wishes to obtain the correct value for the spin-orbit potential strength, for example, in a microscopic calculation, one must consider the optical potential in its most general form. At projectile energies greater than 300 or 400 MeV we expect that only two of the eight terms noted above will be important and therefore the relativistic impulse approximation will provide a satisfactory basis for calculating the optical potential.