Time-independent energy-sudden transformationa)

Abstract

The time-independent energy sudden (ES) representation is defined through application of the energy shift operator S=exp[−(h−ωn)∂/∂ε], where h is the internal (molecular) Hamiltonian. Our introduction of S follows from an earlier study by Chang, Eno, and Rabitz where exp[−iht], which ‘‘factors out’’ internal motion, was used to define the time-dependent ES representation. Exact integral equations for the scattering wave function within the ES representation are derived, the leading terms being the approximate ES wave function. Corrections to the ES wave function are nonsingular and involve the generalized potential increment V=S−1VS−V, where V is the interaction potential. Boundary conditions and transition amplitudes are discussed, as is the connection between wave functions in the ES and the original representations.