K-Matrix Theory of the Isobaric Analog Resonances

A theory of the isobaric analog resonances is formulated on the basis of the shell-model approach to reaction theory. By extending the $K$-matrix theory, originally formulated by MacDonald and Mekjian for a similar purpose, forms of $S$-matrix elements amenable to various direct numerical calculations are obtained. The formalism thus allows one to discuss most of the known characteristic features of the isobaric analog resonances, such as their asymmetric forms and the superposition of fine structures. It can also be used to extract the spectroscopic factors from the ($p, p_0$) and ($p, p^{\prime }$) data and to analyze the ($p, n$) data, all via isobaric analog resonances. Further discussions are presented on the use of the results of the present paper in the analyses of nucleon transfer reactions to or via the isobaric analog states.