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

Abstract

The lowest ${}^{1}{S}^{e}$ 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 $\mathcal{E}(M)$ and width $\ensuremath{\Gamma}(M)$ in the interval $0<~M<~30$ are reported. The principal finding of these calculations is that the function $\ensuremath{\Gamma}(M)$ 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 $\stackrel{\ensuremath{\rightarrow}}{M}\ensuremath{\infty}$ is analyzed. This analysis extends the range of M up to $M=300$ and confirms that $\ensuremath{\Gamma}(M)$ 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 $\ensuremath{\Gamma}(M)$ agree excellently with the calculated results.