Superfluid of finite nuclei in density functional theory with finite range separable pairing interaction

A separable pairing interaction is introduced in the covariant density functional theory. The parameters of the separable force are adjusted to reproduce the pairing properties of the Gogny force in nuclear matter. It preserves translational invariance and has finite range. Applying well known techniques of Talmi and Moshinsky, this pairing interaction can be used in relativistic and in non-relativistic Hartree-Bogoliubov or Hartree-Fock-Bogoliubov calculation of finite nuclei. It avoids the complicated problem of a cutoff at large momenta or energies inherent in other zero range pairing forces. This finite range separable pairing force is applied to study the properties of the ground and excited states for spherical Sn-isotopes in the relativistic Hartree Bogoliubov and relativistic quasiparticle random phase approximation. The superfluid properties of the ground state for the axially deformed Sm-isotopes are also studied in the deformed RHB theory with the separable pairing force. It has been shown that with this force the pairing properties of ground states can be well depicted on almost the same footing as with the original Gogny pairing interaction. There are also many extensions of relativistic density functional theory beyond mean field, such as applications using projection onto subspaces with good symmetries, generator coordinate methods, or investigation of complex configurations in the framework of particle-vibrational coupling (PVC). All these methods require a more realistic description of pairing correlations in the future. (authors)