New approach to solving the problem of composite-particle scattering on nuclei

An essentially new approach to solving the problem of elastic and inelastic scattering of a composite particle on stable nuclei is described. Within this approach, all channels of virtual breakup and stripping in the intermediate states are included in a nonlocal complex-valued interaction operator with the aid of the projection-operator technique.The three-particle continuum spectrum of the Hamiltonian for intermediate states in Q space is calculated within the orthogonalizing-pseudopotential method by introducing a pseudo-Hamiltonian, which is diagonalized in a full space in terms of a relevant oscillator basis. As was shown by a number of authors, the use of special quadratures makes it possible to reduce integration over the continuous spectrum of intermediate states to summation over a discretized continuum. On the basis of the formalism developed in this study, a closed Schrödinger equation with a nonlocal complex potential for partial waves is derived for describing elastic scattering of a composite particle by a target, and an explicit approximate formula for the amplitude of three-particle breakup is obtained on the same basis. This method has a number of obvious advantages over currently well-known approaches of the type of the discretized-continuum coupled-channel method, where solving the problem in question reduces to solving a cumbersome set of coupled equations.