  We compute bounce solutions describing false vacuum decay in a Phi**4 model
in two dimensions in the Hartree approximation, thus going beyond the usual
one-loop corrections to the decay rate. We use zero energy mode functions of
the fluctuation operator for the numerical computation of the functional
determinant and the Green's function. We thus avoid the necessity of
discretizing the spectrum, as it is necessary when one uses numerical
techniques based on eigenfunctions. Regularization is performed in analogy of
standard perturbation theory; the renormalization of the Hartree approximation
is based on the two-particle point-irreducible (2PPI) scheme. The iteration
towards the self-consistent solution is found to converge for some range of the
parameters. Within this range we find the corrections to the leading one-loop
approximation to be relatively small, not exceeding one order of magnitude in
the total transition rate.
