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

The lowest S-1(e) resonance state in a family of symmetric three-body Coulo mb 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 th e resonance position epsilon(M) and width Gamma(M) in the interval 0 less t han or equal to M less than or equal to 30 are reported. The principal find ing of these calculations is that the function Gamma(M) oscillates, almost vanishing for certain values of M, which indicates the existence of an inte rference mechanism in the resonance decay dynamics. To clarify this mechani sm, a simplified model obtained from the three-body Coulomb problem in the limit M-->infinity is analyzed. This analysis extends the range of M up to M=300 and confirms that Gamma(M) continues to oscillate with an increasing period and decreasing envelope as M grows. Simultaneously it points to semi classical theory as an appropriate framework for explaining the oscillation s. 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 interpre tation for the period and envelope of the oscillations of Gamma(M)agree exc ellently with the calculated results. [S1050-2947(99)09912-6].