Coulomb interaction in multiple scattering theory

The treatment of the Coulomb interaction in the multiple scattering theories of Kerman-McManus-Thaler and Watson is examined in detail. By neglecting virtual Coulomb excitations, the lowest order Coulomb term in the Watson optical potential is shown to be a convolution of the point Coulomb interaction with the distributed nuclear charge, while the equivalent Kerman-McManus-Thaler Coulomb potential is obtained from an averaged, single-particle Coulombic $T$ matrix. The Kerman-McManus-Thaler Coulomb potential is expressed as the Watson Coulomb term plus additional Coulomb-nuclear and Coulomb-Coulomb cross terms, and the omission of the extra terms in usual Kerman-McManus-Thaler applications leads to negative infinite total reaction cross section predictions and incorrect pure Coulomb scattering limits. Approximations are presented which eliminate these anomalies. Using the two-potential formula, the full projectile-nucleus $T$ matrix is separated into two terms, one resulting from the distributed nuclear charge and the other being a Coulomb distorted nuclear $T$ matrix. It is shown that the error resulting from the omission of the Kerman-McManus-Thaler Coulomb terms is effectively removed when the pure Coulomb $T$ matrix in Kerman-McManus-Thaler is replaced by the analogous quantity in the Watson approach. Using the various approximations, theoretical angular distributions are obtained for 800 MeV $p$+${}_{}{}^{208}{}_{}{}^{}\mathrm{Pb}$ elastic scattering and compared with experimental data.