Unique Definition of the Quasistationary State for Resonant Processes

Abstract

The quasistationary-state formalism for describing all manner of resonant collision processes and the diabatic states of molecules is made unique by defining the hitherto arbitrary quasistationary-state energy uniquely. The unique quasistationary-state energy $E_r$ (together with its wave function) is defined by a pair of eigenvalue equations which require that it remain unshifted by coupling to the continuum. Two alternate and equivalent definitions are also given, and the results are generalized first to the many-resonance case and secondly in the unusual direction of negative energies, where the quasistationary state produces a resonance among the discrete set of Rydberg levels. This last generalization is necessary for the principal present application of the states, i.e., to the diabatic states mediating molecular transitions, since the energy of these diabatic states moves freely between the continuum and the negative-energy region of the Rydberg states.