Relativistic mean field plus exact pairing approach to open shell nuclei

Background: Pairing correlations play a critical role in determining numerous properties of open-shell nuclei. Traditionally, they are included in a mean-field description of atomic nuclei through the approximate Bardeen-Cooper-Schrieffer or Hartree-Fock-Bogoliubov formalism. Purpose: We propose a new hybrid ''relativistic-mean-field-plus-pairing'' approach in which pairing is treated exactly so the number of particles is conserved. To verify the reliability of the formalism, we apply it to the study of both ground-state properties and isoscalar monopole excitations of the Tin isotopes. Methods: Accurately-calibrated relativistic mean-field models supplemented by an exact treatment of pairing correlations are used to compute ground-state observables along the isotopic chain in Tin. In turn, ground-state densities are used as input to the calculation of giant monopole resonances through a constrained-relativistic approach. Results: We compute a variety of ground-state observables sensitive to pairing correlations as well as the evolution of giant monopole energies along the isotopic chain in Tin. Whereas ground-state properties are consistent with experiment, we find that pairing correlations have a minor effect on the giant monopole energies. Conclusions: A new mean-field-plus-pairing approach is introduced to compute properties of open-shell nuclei. The formalism provides an efficient and powerful alternative to the computation of both ground-state properties and monopole energies of open-shell nuclei. We find ground-state properties to be well reproduced in this approach. However, as many have concluded before us, we find that pairing correlations are unlikely to provide an answer to the question of ''why is Tin so soft?''