Neutron-proton pairing correlations in atomic nuclei: description of pairing coexistence with mean-field methods plus restoration of broken symmetries

The long-standing problem of neutron–proton pairing correlations is revisited by employing the Hartree–Fock–Bogoliubov formalism with neutron–proton mixing in both the particle–hole and particle–particle channels and symmetry-restoration techniques with the Variation After Projection framework. We compare numerical calculations performed within these methods with an exact pairing model based on the SO(8) algebra. We show that the symmetry-restored paired mean-field states (quasiparticle vacua) properly account for isoscalar versus isovector nuclear pairing properties within this model, whose relevant symmetries are full particle-number, spin, and isospin. Theoretical predictions of the reduced matrix elements of the deuteron transfer, the potential experimental probe to observe neutron-proton condensates in nuclei, are presented. Prospects to implement a similar approach in a realistic setting are delineated, calculating the matrix elements of a realistic separable interaction in the pairing channel, implementing them in the numerical software HFODD and evaluating them computing the pairing gaps for certain isotopic chains.