On the analytical description of resonance tunnelling reactions

Abstract

The analytical description of resonance tunnelling reactions is considered within the context of the model introduced by Child. Semi-classical connection formulae based on an exact solution of the Schrödinger equation for a parabolic barrier are derived and their properties developed. These connection formulae are valid for incident energies which lie either above or below the barrier maximum and provide a direct connection between one classically allowed region and another. A complex energy formulation is introduced and used to characterize the quasi-stationary states which exist within the dip on the potential energy surface for the reaction. The resonance tunnelling phenomenon is developed in terms of the resonance energies and widths of these quasi-stationary levels. The reaction cross section is found to be given by an equation of the Breit-Wigner type.