  We present a general numerical method for computing precisely the false
vacuum decay rate, including the prefactor due to quantum fluctuations about
the classical bounce solution, in a self-interacting scalar field theory
modeling the process of nucleation in four dimensional spacetime. This
technique does not rely on the thin-wall approximation. The method is based on
the Gelfand-Yaglom approach to determinants of differential operators, suitably
extended to higher dimensions using angular momentum cutoff regularization. A
related approach has been discussed recently by Baacke and Lavrelashvili, but
we implement the regularization and renormalization in a different manner, and
compare directly with analytic computations made in the thin-wall
approximation. We also derive a simple new formula for the zero mode
contribution to the fluctuation prefactor, expressed entirely in terms of the
asymptotic behavior of the classical bounce solution.
