Pions in nuclear matter—an approach to the pion-nucleus optical potential

Abstract

The optical potential for pions propagating in nuclear matter is investigated from a many-body point of view. An exact expression for the optical potential is obtained in terms of the nuclear matter density-density correlation function. Explicit calculations of the pion self-energy, which is simply related to the optical potential, are performed via an expansion in the nuclear density n 0 . The familiar result of multiple scattering theory, 4π n 0f 0 where f 0 is the pion-nucleon scattering length, is recovered in lowest order. The terms quadratic in n 0 account for the long range Pauli correlation corrections to the pion-nucleon scattering process (quenching), as well as dispersion and absorption contributions coming from nucleon-nucleon collisions in the medium. The latter terms are proportional to off-shell nucleon-nucleon scattering amplitudes. Our treatment is compared and contrasted with that of Ericson and Ericson. In particular, we are able to establish what approxmations in the nuclear many-body problem lead to their form of s-wave potential that includes long-range correlation effects, as well as their p-wave potential that has a nonlinear density dependence (the Lorentz-Lorenz effect). Estimates of the dispersion and absorption terms are made using two simple models to describe interacting nuclear matter.