Interference effects in the decay of resonance states in three-body Coulomb systems

Abstract

The lowest [Formula Presented] resonance state in a family of symmetric three-body Coulomb systems is systematically studied as a function of the mass-ratio M for the constituting particles. The Siegert pseudostate method for calculating resonances is described and accurate results obtained by this method for the resonance position [Formula Presented] and width [Formula Presented] in the interval [Formula Presented] are reported. The principal finding of these calculations is that the function [Formula Presented] oscillates, almost vanishing for certain values of M, which indicates the existence of an interference mechanism in the resonance decay dynamics. To clarify this mechanism, a simplified model obtained from the three-body Coulomb problem in the limit [Formula Presented] is analyzed. This analysis extends the range of M up to [Formula Presented] and confirms that [Formula Presented] continues to oscillate with an increasing period and decreasing envelope as M grows. Simultaneously it points to semiclassical theory as an appropriate framework for explaining the oscillations. On the basis of Demkov’s construction, the oscillations are interpreted as a result of interference between two paths of the resonance decay on the Riemann surface of adiabatic potential energy, i.e., as a manifestation of the Stueckelberg phase. It is shown that the implications of this interpretation for the period and envelope of the oscillations of [Formula Presented] agree excellently with the calculated results. © 1999 The American Physical Society.