A model for the study of the interference of the direct and compound-nucleus reaction mechanisms

Abstract

A model is proposed for the investigation of the interference of direct and compound-nucleus reaction mechanisms in the inelastic scattering of nucleons. The continuum eigenfunction is considered to consist of a sum of two types of components: Product functions represent the nonlocalized open-channel or scattering components. Closed-channel or compound-nucleus components are represented by localized functions. The direct reaction mechanism is characterized by the set of matrix elements of the nucleon-nucleus interaction that couple two open-channel components. The compound-nucleus reaction mechanism is characterized by the matrix elements that couple open- and closed-channel components. The formal development of the above model is essentially a simple application of Feshbach's unified theory of nuclear reactions. However an additional “surface-transition model” is employed, in which the coupling of the various open- and closed-channel components is restricted to occur at one value of the nucleon-nucleus separation. Within this model, the effective Schrödinger equation is completely solvable and an analytic expression for the collision matrix is derived. This expression indicates clearly the dynamical interference between the reaction mechanisms; namely, it indicates the nonlinear manner in which the two mechanisms contribute to the collision matrix. The collision matrix is further investigated in two situations. The case of an isolated compound-nucleus state is considered and the departures from the form of a direct term plus Breit-Wigner term are examined. The case of a dense set of overlapping compound-nucleus states is also treated. Here the energy-averaged collision function is compared to that which would arise in the absence of any compound mechanism. Insight is gained into the relation between such energy averages and the use of complex potentials in reaction theory. Implications of the dynamical interference for studies of statistical fluctuations is noted.