Δ excitations in nuclei and their decay properties

A formalism for the calculation of intermediate energy charge exchange reactions exciting the Δ resonance region in nuclei is presented. The nuclear structure part of the formalism is based on the isobar-hole model and the nuclear reaction part is treated within the distorted-wave impulse approximation (DWIA). In the nuclear structure part, all important nuclear medium effects are included, such as nucleon and isobar binding, two-body Δ isobar-nucleon hole correlations, and intermediate coupling to multiparticle-multihole channels. The latter coupling is treated phenomenologically through a Δ spreading potential. Explicit account is also taken of the nucleon knockout mode and the related nucleon particle-nucleon hole correlations. In order to perform the calculations, we first set up coupled-channel equations for the excited nucleon and Δ, which are slightly, but importantly, transformed into equations for localized functions only. We solve these equations by using the Lanczos method. The resultant formalism allows us to calculate cross sections for Δ excitation, quasielastic scattering, and low-lying Gamow-Teller excitations on the same footing. In this way a detailed study of the nuclear medium effects on the Δ isobar can be done. Particular attention is paid to the Δ-hole correlations in the spin-longitudinal (S⋅qT) channel. It is shown that the coherent pion production events in the exclusive ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$(p,n${\mathrm{\pi }}^{+}$ ${)}^{12}$C(g.s.) and ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$ ${(}^3$He,t${\mathrm{\pi }}^{+}$ ${)}^{12}$C(g.s.) reactions provide a unique signature on the nuclear pionic mode.