The fine structure of the isoharic analogue resonances

Abstract

The distribution of an isobaric analogue resonance over the numerous surrounding states of different isobaric spin is studied analytically in the frame of the Fano-Weidenmüller shell-model theory of nuclear reactions. The doorway state wave function is described byLane's coupled equations. The matrix element of the residual nuclear interaction between this doorway state and a complicated state of different isobaric spin exhibits a particular energy dependence. A sum rule is established: the sum of the fine structure widths is larger than the width of the doorway state, as calculated fromLane's model. The residual Coulomb interactions are neglected. When perturbation theory holds, the distribution of the fine structure peaks is shown to have a characteristic asymmetrical shape. The connection withRobson's R-matrix treatment is discussed.