  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?''
