  We evaluate the one-loop prefactor in the false vacuum decay rate in a theory
of a self interacting scalar field in 3+1 dimensions. We use a numerical
method, established some time ago, which is based on a well-known theorem on
functional determinants. The proper handling of zero modes and of
renormalization is discussed. The numerical results in particular show that
quantum corrections become smaller away from the thin-wall case. In the
thin-wall limit the numerical results are found to join into those obtained by
a gradient expansion.
