Variational principles for breakup amplitudes: Three charged clusters

Abstract

Variational principles for three-body reaction amplitudes are derived which allow for colliding systems that are charged and composite and are applicable for energies lying below the threshold for breakup into four subsystems. The starting point of the analysis is a formulation of the collision dynamics based on coupled integral equations of the Faddeev type that are applicable in the presence of long-range Coulomb interactions. A variational identity (which becomes a variational approximation with the introduction of trial functions) for the amplitude for the breakup of a bound pair by a third particle is derived within the integral equation formulation. The expression is then converted to a differential form of the Kohn type involving wave functions in configuration space. Knowledge of the asymptotic form of the wave function representing the time-reversed final state, in which three unbound particles are incident, is not required in performing this derivation. The variational principle is enhanced by the existence of a subsidiary minimum principle satisfied by that component of the wave function describing virtual excitations of one or more of the three clusters that make up the scattering system.