Abstract
A formal expression is derived for an optical model potential based on an assumed two-body interaction between nucleons, which provides an exact description of the elastic scattering of a single nucleon by a closed shell (or closed shell ±1) nucleus. A second-quantized description is used for the many-fermion system, the true state vector being expanded in terms of a complete set of single-particle model wave functions. Elimination of the variables of all but the scattered nucleon yields a weighting function which satisfies a one-body Schrödinger equation, whose S-matrix elements are identical with those of the true S-matrix between states corresponding to elastic scattering. The effective optical model potential is identified from this Schrödinger equation, and is found, of course, to be complex and non-local. It contains all the effects of the exclusion principle, and is in the form of a linked-cluster perturbation expansion, so that the spurious divergence of Brillouin-Wigner perturbation theory for a large number of nucleons is absent.
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