  We compute the vacuum polarization energies (VPE) of solitons in a self-dual
impurity model in which the soliton profiles take the shape of a separated
kink-antikink pair. Classically the soliton energies are invariant under the
change of a continuous parameter that can be interpreted as the kink-antikink
separation. This is not the case for the VPE so that quantum effects decide on
the energetically most favorable separation. The considered configurations are
classically stable so that its quantum fluctuations have only real frequency
eigenvalues. Hence, in contrast to the kink-antikink configuration in the
$\phi^4$ model, the VPE is well defined for any value of the separation and we
gain insight into the quantum corrections to the kink-antikink potential
