Inclusion of virtual nuclear excitations in the formulation of the (e,e′N) reaction

A wave-function framework for the theory of the (e, e'N) reactions is presented in order to justify the use of coupled channel equations in the usual Feynman matrix element. The overall wave function containing the electron and nucleon coordinates is expanded in a basis set of eigenstates of the nuclear Hamiltonian, which contain both bound states as well as continuum states. The latter have an ingoing nucleon with a variable momentum Q incident on the daughter nucleus as a target, with as many outgoing channels as desirable. The Dirac equations for the electron part of the wave function acquire inhomogeneous terms, and require the use of distorted electron Green's functions for their solutions. The condition that the asymptotic wave function contains only the appropriate momentum Q(k) for the outgoing nucleon, which corresponds to the electron momentum k through energy conservation, is achieved through the use of the steepest descent saddle point method, commonly used in three-body calculations.