Self-consistentπNtmatrix

The $\pi N$ interaction in the nuclear medium is shown to be substantially altered by local field effects, including dressing of internal pion lines by the optical potential. The local field effect arises due to scattering of pions in the intermediate states of the $\pi Nt$ matrix from other nucleons in the medium. We develop an organization of pion scattering theory based on Goldstone diagrams which includes all possible contributions but emphasizes the dressing of propagators in $\pi Nt$-matrix intermediate states involving one pion and one nucleon only. Pion absorption and rescattering are treated on an equal footing. Self-consistency is introduced through the demand that the optical potential which dresses internal propagators be the same as the optical potential which is implied by the $t$ matrix so corrected. For calculational purposes, the general theory is simplified to the case of the $\pi Nt$ matrix in a Fermi gas. The input data consist of the free $\pi Nt$ matrix, an off-shell form factor, the $\pi N$ coupling constant, a binding energy, and a Fermi momentum $k_F$. Nucleon recoil effects are retained, as they have previously been found to be important. Numerical results are presented for the quantity $W(k,\omega )$ which is related to the Klein-Gordon optical potential for nuclear matter. The results show substantial modification of the $\pi N$ resonance by the nuclear medium. In particular, the resonance is broadened and the treatment of pion absorption provides sensible results for the imaginary part of the self-energy near threshold. Our calculations show the self-consistency is not crucial to the results, as dressing of propagators by the first-order optical potential is adequate. Nucleon recoil is significant. The results show that local field effects are important in $\pi$-nucleus interactions.