Semiclassical threshold law when the Wannier exponent diverges

Abstract

Using semiclassical methods we investigate the threshold behavior for three-particle breakup of a system with one particle of charge $Z$ and two other particles of charge $\ensuremath{-}q$. For the particular case where the ratio of the charges of the third particle to the wing particles is $Z/q=1/4$, the Wannier exponent for breakup diverges and the threshold law changes from a power law to an exponential law of the form $\mathrm{exp}(\ensuremath{-}\ensuremath{\lambda}/\sqrt{E})$. The threshold behavior is tested above the region of divergence and it is found that for $Z/q<0.3$ a power law does not hold. Ionizing trajectories show that the dynamics within the near zone can become crucial to the energy dependence of the cross section. Cases are found to arise where more than one trajectory contributes to the same final state giving rise to semiclassical interference effects.