Direct nuclear reactions and interaction in the initial and final states

Abstract

A formal scheme is developed to take into account the interactions in the initial and final states in direct nuclear reactions. The unitari of the S-matrix and analytical properties of the amplitude of the reaction as function of energy are used. The solution of the singular integral equation for the partial amplitude of the reaction is found. The result is not affected if the amplitude has an essential singularity of the type e − ikR connected with the nuclear size. The solution of the problem is factorized into two factors, one of which ( ϱ ll′ ( E) = ϱ l ( E) ϱ l′ ( E)) contains all singularities connected with the interaction in the initial and final states, while the singularities of the other factor are determined by the mechanism of the reaction. The function ϱ l ( E) for rectangular well is calculated. The problem of the bound states of the system is considered. The solution found for the partial amplitude of the reaction satisfies the physical requirements and has the correct behaviour near the threshold. The solution also takes into account the resonance effects of the compound nucleus in a direct nuclear reaction. A method of boundary problem equivalent to the dispersion method but more easily vizualizable presented.