Families of strictly equivalent potentials for the elastic wavefunction

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It is shown that there exists a manifold infinite family of single-particle potential operators which all yield the exact elastic component of the many-body scattering wavefunction. These operators may have different analytical properties in the complex energy plane. Correspondingly, the real and imaginary parts of these potentials are connected by dispersion relations in which the disoersion integrals may run over different energy domains. Among these potentials, the mass operator is the most closely related to the phenomenological mean field, mainly because it also yields information on the bound states of the ( A − 1)-nucleon system. Moreover, the mass operator fulfills a simple dispersion relation similar to that used in recent practical applications; the other operators fulfill more complicated dispersion relations. Nuclear matter is discussed in detail. In that case, explicit expressions are derived in the framework of second-order perturbation theory.