  We compute bounce solutions describing false vacuum decay in a Phi**4 model
in four dimensions with quantum back-reaction. The back-reaction of the quantum
fluctuations on the bounce profiles is computed in the one-loop and Hartree
approximations. This is to be compared with the usual semiclassical approach
where one computes the profile from the classical action and determines the
one-loop correction from this profile. The computation of the fluctuation
determinant is performed using a theorem on functional determinants, in
addition we here need the Green' s function of the fluctuation operator in oder
to compute the quantum back-reaction. As we are able to separate from the
determinant and from the Green' s function the leading perturbative orders, we
can regularize and renormalize analytically, in analogy of standard
perturbation theory. The iteration towards self-consistent solutions is found
to converge for some range of the parameters. Within this range the corrections
to the semiclassical action are at most a few percent, the corrections to the
transition rate can amount to several orders of magnitude. The strongest
deviations happen for large couplings, as to be expected. Beyond some limit,
there are no self-consistent bounce solutions.
