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

The lowest 1Se 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 E(M) and width Γ(M) in the interval 0<~M<~30 are reported. The principal finding of these calculations is that the function Γ(M) 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 M→∞ is analyzed. This analysis extends the range of M up to M=300 and confirms that Γ(M) 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 Γ(M) agree excellently with the calculated results