Meson theoretical basis for Dirac impulse approximation

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Abstract
Basic features of proton-nucleus optical potentials for use in the Dirac equation are discussed. The original form of the Dirac impulse approximation follows from using Fermi covariants (scalar, vector, tensor, pseudoscalar, and axial vector) to extend physical NN amplitudes into operators in the full Dirac space. Overly large scalar and vector optical potentials are shown to follow at low energy in this case due to forcing pion exchange contributions to be pseudoscalar. The pair contributions to proton-nucleus scattering are much too large at low energy. A variant of the impulse approximation is developed by replacing pseudoscalar covariants by pseudovector ones. Much reduced scalar and vector strengths are obtained at low energy in the pseudovector case. The pair contributions are similarly reduced to reasonable values. However, the large differences between optical potentials based on pseudoscalar and pseudovector covariants are not controlled by physical NN scattering data. These differences represent a basic ambiguity in NN amplitudes when the only constraint is positive energy scattering data. Using a complete and unambiguous set of NN Lorentz invariant amplitudes obtained from a relativistic one-meson-exchange model, the scalar and vector optical potential strengths are found to be reasonably constant over the range of 50 to 1000 MeV of proton energy. The meson theory results for nuclear matter are found to be comparable to those obtained when the pseudoscalar covariant is replaced by the pseudovector covariant in the original impulse approximation.