Isovector correction to the Kerman, McManus, and Thaler formalism

In the derivation of the scaled, first order optical potential of Kerman, McManus, and Thaler it is assumed that all target nucleons have identical isospin character. This makes possible the scaling by (A-1)/A that is characteristic of the Kerman-McManus-Thaler formalism. In applications, the difference between the interactions of the projectile with target neutrons and protons is imposed upon the scaled optical potential. The nuclear scattering amplitude calculated in this way differs from the correct first order result which can be obtained by recognizing the isospin difference at the onset of the derivation. A new expression for the Kerman-McManus-Thaler optical potential is obtained. The result is the usual isospin weighted sum of the projectile-proton and projectile-neutron interactions, plus a correction to the scaled first order optical potential which is proportional to the square of the projectile-nucleon isovector interaction. Numerical estimates of the volumes and root mean square radii of this isovector correction are given for proton and pion projectiles. Relative to the usual first order term, the volume integral of this correction is found to be negligible in most cases, except for (3,3) resonant energy pion-nucleus scattering where it can contribute several percent