Field-theoretical approach to the π-nucleon scattering in nuclear matter

On the line of the Heisenberg picture of the QFT, making use of the standard reduction techniques and assuming a low-density approximation for the nuclear medium, a set of integral equations are derived for the effective π-nucleon scattering amplitude in nuclear matter. In the static limit the effects of the nuclear medium arise from the Pauli blocking for the states of the intermediate nucleon and this results in the equations through the actual occupation numbers of the nucleons in nuclear matter. The equations are solved in closed form and corrections to the free-scattering amplitude are obtained which depend linearly on the nuclear density. (author)