Extending the kawai-kerman-mcvoy statistical theory of nuclear reactions to intermediate structure via doorways

Kawai, Kerman, and McVoy have shown that a statistical treatment of many open channels that are coupled by direct reactions leads to modifications of the Hauser-Feshbach expression for energy-averaged cross section [Ann. of Phys. 75, 156 (1973)]. The energy averaging interval for this cross section is on the order of the width of single particle resonances, ≈ 1 MeV, revealing only a gross structure in the cross section. When the energy-averaging interval is decreased down to a width of a doorway state, ≈ 0.1 MeV, a so-called intermediate structure may be observed in cross sections. We extend the Kawai-Kerman-McVoy theory into the intermediate structure by leveraging a theory of doorway states developed by Feshbach, Kerman, and Lemmer [Ann. of Phys. 41, 230 (1967)]. As a by-product of the extension, an alternative derivation of the central result of the Kawai-Kerman-McVoy theory is suggested. We quantify the effect of the approximations used in derivation by performing numerical computations for a large set of compound nuclear states.