The compound nucleus (CN) has received considerable attention -- both theoretical and experimental -- in the recent years because of its seeming ability to enhance the effects of the weak interaction to a few percent (see for example [1] and references therein). In the present study we consider the breaking of symmetries caused by K-body forces in the compound process in general. The adequate quantity to characterize symmetry nonconservation in many-body systems is the spreading width due to the underlying interaction [2]. Although in most applications a two-body force is used, we treat the case of arbitrary K since it will allow for some insight into the energy dependence of the spreading width. This provides a generalization of the results presented in [3] and the communication of some details omitted therein.
In the statistical theory of CN reactions the matrix elements of the interaction are assumed to show the characteristics of the Gaussian orthogonal ensemble (GOE). The crucial point is that statistical assumptions of this kind can only be made about the defining matrix elements, i.e. the matrix elements in K-body space. However, the quantity of physical interest is the matrix element in A-body space. The connection between the properties of the K-body matrix elements and those in A-body space is called the propagation of the defining matrix elements [4]. In the present article a solution for this problem is offered which consists of the transition to the exciton picture (with the accompanying simplification of the basis states and complication in the description of the interaction), the propagation into the subspace of fixed exciton number, and the averaging over subspaces, which implies the return to the body picture. This procedure is necessary because our formalism makes use of the dilute gas approximation (DGA) which -- in contrast to the body picture -- is very good in the exciton representation of the system. In the final sections then, the general expression, which involves a convolution of partial and total densities of states, is evaluated by inserting well known analytical formulae for the level densities, the results are discussed, and limitations of our approach are indicated.