A Dirac-Hartree-Bogoliubov approximation for finite nuclei

We develop a complete Dirac-Hartree-Fock-Bogoliubov approximation to the ground state wave function and energy of finite nuclei. We apply it to spin-zero proton-proton and neutron-neutron pairing within the Dirac-Hartree-Bogoliubov approximation (we neglect the Fock term), using a zero-range approximation to the relativistic pairing tensor. We study the effects of the pairing on the properties of the even-even nuclei of the isotopic chains of Ca, Ni and Sn (spherical) and Kr and Sr (deformed), as well as the $N$=28 isotonic chain, and compare our results with experimental data and with other recent calculations.