Can cosmic-ray catalysed vacuum decay dominate over tunnelling?

We consider the question of whether cosmic-ray catalysed false-vacuum decay can be phenomenologically more important than spontaneous decay via quantum tunnelling. We extend the zero bubble wall width Landau-WKB analysis of catalysed false-vacuum decay to include the leading order effects of finite wall width and derive an expression for the thin-wall bubble action. Using this we calculate the exponential suppression factor for the catalysed decay rate at the critical bubble energy, corresponding to the largest probability of catalysed decay. We show that, in general, cosmic-ray catalysed decay is more important than spontaneous decay for sufficiently thin-walled bubbles (wall thickness less than about 30% of the initial bubble radius), but that spontaneous decay will dominate for the case of thick-walled bubbles. Since any perturbative model with a cosmologically significant false-vacuum decay rate will produce thick-walled bubbles, we can conclude that cosmic-ray catalysed false-vacuum decay will never dominate over tunnelling in imposing phenomenological constraints on perturbative particle physics models. (orig.)