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A separable form of pairing interaction in the $^{1}S_{0}$ channel has beenintroduced and successfully applied in the description of both static anddynamic properties of superfluid nuclei. By adjusting the parameters toreproduce the pairing properties of the Gogny force in nuclear matter, thisseparable pairing force is successful in depicting the pairing properties ofground states and vibrational excitations of spherical nuclei on almost thesame footing as the original Gogny force. In this article, we extend theseinvestigations for Relativistic Hartree Bogoliubov theory in deformed nucleiwith axial symmetry (RHBZ) using the same separable pairing interaction. Inorder to preserve translational invariance we construct one- andtwo-dimensional Talmi-Moshinsky brackets for the cylindrical harmonicoscillator basis. We show that the matrix elements of this force can then beexpanded in a series of separable terms. The convergence of this expansion isinvestigated for various deformations. We observe a relatively fastconvergence. This allows for a considerable reduction in computing time ascompared 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 forthe ground states of the chain of Sm-isotopes. Good agreement with theexperimental data as well as with other theoretical results is achieved.

Axially deformed relativistic Hartree Bogoliubov with separable pairing force