Analog state resonances

A theory of analog state resonances is presented based on a K-matrix formulation of the shell-model theory of nuclear reactions. After deriving the detailed structure of the analog state and the “configurational states” of Lane and Soper, we discuss the “internal” mixing of the analog state to the configurational states. A shell-model description of “external” mixing is then given. In contradiction to earlier suggestions that internal mixing is unimportant, we conclude that internal mixing cannot be neglected. We also derive the distribution of partial widths for the fine structure resonances. The structure of the fine structure states is discussed, and the various coupling mechanisms that can exist between the analog state and these states are established. The internal and external mixing of these different isospin states is treated on an equal footing, and the effect on each on the distribution of widths is discussed. Expressions for the average cross section for the one- and many-open channel cases are derived. A numerical discussion of the p 3 2 analog resonance in 41K is given.