The Δ excitations in nuclei induced by pion and photon scattering are analyzed within the isobar-hole model. The results are compared to those of intermediate energy charge exchange reactions. The similarities and differences between the various probes due to their kinematics and spin-structure are discussed. It is shown that the experimental cross sections for pion and photon induced reactions as well as for the inclusive charge exchange reactions can be consistently described within the isobar-hole model. Of special interest is the coherent pion decay of the Δ resonance which is studied by means of the exclusive reaction ${\mathrm{C}}^{12}$(${\mathrm{He}}^3$,t${\mathrm{\pi }}^{+}$)${\mathrm{C}}^{12}$ (g.s.), by elastic pion scattering, and by pion photoproduction. It turns out that the coherent pion decay of the ${\mathrm{C}}^{12}$(${\mathrm{He}}^3$,t${\mathrm{\pi }}^{+}$)${\mathrm{C}}^{12}$ (g.s.) reaction is intimately related to elastic pion scattering. Most interestingly, both the peak energy and the magnitude of the coherent pion production cross section depend very sensitively on the strength of the Δ-hole residual interaction. The observed energy shift is directly proportional to the nuclear density ρ. This shows that the coherent pions propagate through the nuclear interior. The coherent pion cross section can be used to determine the Landau-Migdal parameter ${\mathrm{g}}_{\mathrm{\Delta }\mathrm{\Delta }}^{\prime }$.

• Received 14 April 1994

DOI:https://doi.org/10.1103/PhysRevC.50.1637