Pion - Nucleus Scattering and Systematics of the Delta - Nucleus Potential

A proper description of p ion-nuc leus scattering at energies near the (3,3) resonance requires that account be taken of the dynamics of the resonant p i o n n u cleon system. In particular the motion of this system through the nucleus and its strong interaction with the nuclear medium cannot be neglected [1,2]. Recently several groups [2 6] have incorporated these effects into calculations of pion scattering from light nuclei based on the isobar--hole model. In this model the p ion-nuc leon system is regarded in the (3,3) sp inisospin channel as a single particle, the A isobar. Published calculations of this kind which deal with the fully quantum mechanical problem of /x propagation in the presence of the A--nucleus interaction [3--6] are unfortunately quite complicated. Consequently no such calculations have been performed for nuclei of mass number A > 16. We present here a new technique of calculation within the isobar hole model which we have used to consider pion elastic scattering from closed-shell nuclei up to A = 40. An important result of these calculations is that the A--nucleus interaction is well described by a local potential whose central value is independent o f A . TiLts potential is analogous to the nuclear shell model potential for nucleons [71. Our technique of calculation differs from that of previous workers in that we do not calculate the p i o n nucleus T-matrix directly. Instead, an approach based on the p ion-nuc leus optical potential is used. This approach gives a significant reduction in computat ional labor and interfaces well with more conventional approaches to pion nucleus scattering. The resonant part of the optical potential may be written as