  The tunneling potential method to calculate the action for vacuum decay is an
alternative to the Euclidean bounce method that has a number of attractive
features. In this paper we extend the formalism to general spacetime dimension
$d>2$ and use it to give simple proofs of several results. For Minkowski or
Anti de Sitter false vacua, we show that gravity or higher barriers increase
vacuum lifetime and describe a very clean picture of gravitational quenching of
vacuum decay. We also derive the thin-wall limit of the action, show how
detailed balance for dS to dS transitions works in the new formalism and how to
obtain potentials for which the vacuum decay solution can be obtained
analytically.
