'Thin-wall' approximations to vacuum decay rates

We examine the validity of Coleman's 'thin-wall' approximation to the euclidean action of the bounce solution by comparing its predictions with exact numerically integrated actions for potentials which yield thin- and thick-wall bubbles. In both cases, the original thin-wall approximation is found to be poor, rapidly diverging from the exact action as the difference in energy of the two vacuum states is increased from zero. We introduce a new approximation scheme, calculationally similar to the original thin-wall scheme, which gives greatly improved accuracy. (orig.)