On the theory of the phase shifts for resonance tunnelling reactions

Abstract

Semi-classical expressions for the elastic and reactive phase shifts for the double humped barrier characteristic of resonance tunnelling reactions are derived and their properties developed. The phase shifts are reduced to a Breit-Wigner resonance form by the application of two kinds of complex boundary conditions. The first boundary condition is the usual ‘outgoing waves only’ one, whilst the second is a ‘forward moving waves only’ boundary condition. This latter boundary condition gives rise to a novel form of complex energy: E = E_nL + i(γ_nL /2) where E_nL is the resonance energy and the width γ_nL may be positive, negative or zero. The sign and magnitude of γ_nL have a natural interpretation in terms of the flux of particles through the two potential barriers that surround the dip in the activation barrier for the reaction.