Explain the discrepancy between homonuclear RAIM predissociation lifetimes

Determine the cause of the discrepancy between the predissociation lifetimes calculated with the present time-independent scattering approach and those obtained by Duspayev et al. using a time-dependent complex-absorbing-potential method for homonuclear Rb$^*$Rb$^+$ Rydberg atom–ion molecules, including the possible roles of numerical inaccuracies in the highly sensitive $P_{23}$ non-adiabatic coupling and deviations from exponential decay.

Background

The paper reports that its calculated predissociation lifetimes for homonuclear Rb$^*$Rb$^+$ Rydberg atom–ion molecules are generally one to two orders of magnitude larger than the lifetimes reported in Duspayev et al. The discrepancy is especially significant because the coupled-channel results are extremely sensitive to the peak value of the nearly singular $P_{23}$ derivative coupling: an error of approximately one percent can substantially alter the predicted lifetimes.

The authors identify two possible explanations but do not resolve the issue. First, a small numerical error in $P_{23}$ could account for the difference. Second, the molecular population may exhibit power-law rather than exponential decay because of interference during predissociation, whereas the earlier time-dependent analysis assumed exponential decay. Establishing which mechanism explains the disagreement remains unresolved.