  The Barnes slave boson approach to the $U=\infty$ single impurity Anderson
model extended by a non-local Coulomb interaction is revisited. We demonstrate
first that the radial gauge representation facilitates the treatment of such a
non-local interaction by performing the \emph{exact} evaluation of the path
integrals representing the partition function, the impurity hole density and
the impurity hole density autocorrelation function for a two-site cluster. The
free energy is also obtained on the same footing. Next, the exact results are
compared to their approximations at saddle-point level, and it is shown that
the saddle point evaluation recovers the exact answer in the limit of strong
non-local Coulomb interaction, while the agreement between both schemes remains
satisfactory in a large parameter range.
