  We study the Euclidean bounce action interpolating between a false and a true
vacuum for a scalar field theory with various types of potential. We focus on
the cases of a triangular, a square and a quadratic barrier, where the bounce
action has already been computed analytically in four dimensions. We generalize
the result to d dimensions, providing an analytic formula in each case.
Furthermore we show that our results reduce to the ones computed from the thin
wall approximation, when the true and the false vacuum are close in energy.
When the true vacuum cannot be reached in a finite amount of Euclidean time we
study the damped oscillations of the solution by analytical continuation to
Lorentzian spacetime.
