Isospin purity of the isobaric analogue resonances for several open channels

Abstract

The isospin purity of the full and of the doorway state scattering functions in the internal region is investigated, under the assumption of no internal mixing. When several channels are open, it is shown that the isospin is pure at an energyE > (slightly larger then the resonance energy) only under a restrictive condition, namely that the reduced widths of the analogue state vanish in all channels but one. This may happen either because of isospin selection rules (for the neutron channels) or for reasons of nuclear structure (for some of the proton channels). Then, the corresponding (p, n) and (p, p′) cross sections vanish atE >. If several channels with non-vanishing reduced widths are open, the isospin of both the full and doorway state wave function is no longer pure atE >. If two proton channels are open, the doorway state contains three different types of admixtures in the internal region. Two, one of isospinT > and one of isospinT <, are excited according to a simple Breit-Wigner probability law. They are both independent of the entrance channel. The third one has isospinT <, depends upon the entrance channel and is excited according to an asymmetric enhancement factor identical toRobson's.