Theory of (p, p′) and (p, n) reactions through the isobaric analogue resonances: (I). Isospin purity of the doorway function in the internal region

Abstract

Results known for the case of a single open proton channel from the analysis of Lane's model are extended to the case of several open proton channels using a particle-hole description of the isobaric analogue state. This description is equivalent to Lane's model in the one open channel case. External and internal Coulomb mixing are discussed. It is shown that - in the case of two open proton channels - the wave function at resonance has three types of Coulomb admixtures in the internal region; one due to internal mixing and one due to external mixing, both of which are the same for all channels. The amplitudes of both these admixtures display a Breit-Wigner resonance. The third admixture depends on the incident channel. Aside from displaying a resonance behaviour, this amplitude vanishes at a (real) energy E > slightly above resonance. In the case when several proton channels are open, this offers a basis for explaining the asymmetries observed in (p, n) total cross sections and sometimes in (p, p′) cross sections. Ambiguities in the generalization of Lane's model to inelastic proton scattering are discussed.