Relativistic and nonrelativistic models of the nuclear optical potential

Abstract

Recently it has been shown that the standard nonrelativistic theory of the nuclear optical potential is unable to explain the spin-dependent observables for proton-nucleus scattering for projectile energies from about 400 MeV to 1 GeV if one uses the impulse approximation to calculate the potential. On the other hand, a relativistic impulse approximation leads to a (relativistic) optical potential for use in the Dirac equation; the relativistic model is able to provide good fits to the spin observables in the energy range noted above. We discuss the relationship between the nonrelativistic and relativistic models of the optical potential and show that the nonrelativistic potential may, to a first approximation, be identified with one of two terms in an expression for the relativistic optical potential. This identification is not precise since the density matrices of the target are different in the relativistic and nonrelativistic theories. The second term in our expression for the relativistic optical potential is associated with projectile propagation in negative-energy states. It may be seen that this term and the corrections arising from the use of a relativistic density matrix for the target are responsible for the success of the relativistic model.