  A separable form of pairing interaction in the $^{1}S_{0}$ channel has been
introduced and successfully applied in the description of both static and
dynamic properties of superfluid nuclei. By adjusting the parameters to
reproduce the pairing properties of the Gogny force in nuclear matter, this
separable pairing force is successful in depicting the pairing properties of
ground states and vibrational excitations of spherical nuclei on almost the
same footing as the original Gogny force. In this article, we extend these
investigations for Relativistic Hartree Bogoliubov theory in deformed nuclei
with axial symmetry (RHBZ) using the same separable pairing interaction. In
order to preserve translational invariance we construct one- and
two-dimensional Talmi-Moshinsky brackets for the cylindrical harmonic
oscillator basis. We show that the matrix elements of this force can then be
expanded in a series of separable terms. The convergence of this expansion is
investigated for various deformations. We observe a relatively fast
convergence. This allows for a considerable reduction in computing time as
compared to RHBZ-calculations with the full Gogny force in the pairing channel.
As an example we solve the RHBZ equations with this separable pairing force for
the ground states of the chain of Sm-isotopes. Good agreement with the
experimental data as well as with other theoretical results is achieved.
