Compound Nucleus Formulation of Reaction Matrix Theory

Abstract

It is shown that multilevel resonance parameters for each element of the reaction matrix cannot be determined from available data. However, additional constraints may be introduced without affecting agreement with experiment. The Bohr compound nucleus hypothesis, which states that the modes of formation and decay of a compound nucleus are independent, is applied to the T-matrix and it is found, as in Newton's model, that the channel matrix can be inverted analytically to provide simple formulae for cross sections, for both the real Wigner?Eisenbud reaction matrix and Moldauer's complex reaction matrix. Wigner?Eisenbud theory leads directly to Newton's strong correlation model and its unacceptable consequences. Moldauer's theory does not, however, and can explain cross section behaviour adequately while being consistent with Bohr's hypothesis. Cross sections can be written as a sum of single level contributions, as in the Adler?Adler formulation. Finally, Moldauer's statistical theory is shown to be applicable, and expressions are derived for the ·averaged cross sections as functions of the complex Moldauer resonance parameters.