Elastic scattering of protons byO16,Ca40, andPb208at 200, 500, and 800 MeV: Relativistic and nonrelativistic analyses based on the impulse approximation

Systematics of Dirac impulse approximation predictions for cross sections and spin observables in elastic proton scattering by ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, and ${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ at energies of 200, 500, and 800 MeV are presented. The analysis is based on an optical potential constructed from complete sets of Lorentz-invariant NN amplitudes. The NN amplitudes are determined from a relativistic meson exchange model of the nuclear force. Comparisons are made with the original form of the Dirac impulse approximation, which is based on five Fermi terms to represent the NN interaction, and with the Schrödinger form of the impulse approximation. For the Dirac analyses, there is implicit coupling to virtual nucleon-antinucleon states. In order to illustrate these contributions, the Dirac equation is recast in the form of the Schrödinger equation and the resulting Schrödinger potentials are separated into ‘‘no-pair’’ and virtual-pair parts. The resulting virtual-pair part of the central potential is typically 25 MeV at the center of the nucleus for 200–800 MeV protons. A reasonable description of the experimental data is obtained over a broad energy range and over a wide variation of nuclear size when the analysis is based on complete sets of Lorentz-invariant amplitudes.