DYNAMICAL EQUATIONS AND APPROXIMATION METHODS

Abstract

Publisher Summary This chapter presents dynamical equations and approximation methods. An exact procedure has been given for correctly incorporating Coulomb forces in calculations of scattering from a charged bound state below the break-up threshold. For the case of proton–deuteron scattering, a formulation based on the quasi-particle approach is reported and on a screening technique similar to that of Veselova. The strong nucleon–nucleon interaction is assumed to be separable, and Coulomb interaction is treated exactly. The chapter presents another generalized separable expansion based on the Noyes–Kowalski model and the Bateman method. It has the attractive feature that the unphysical poles, which appear in both the Noyes–Kowalski model and in the Bateman method, can be made to vanish simultaneously by an appropriate choice of a set of Bateman parameters. The expansion is applicable to all energies in contrast to the situation in applications of Bateman method. The chapter discusses several physical properties of the two-body system, which are invariant under the phase-shift equivalent transformation. The Fredholm determinant and several other quantities are invariant in addition to the known invariants such as scattering phase shifts.