Proton-neutron pairing and alpha-type condensation in nuclei

We summarize a recent work (N. Sandulescu et al, arXiv: 1507.04144) on isoscalar and isovector proton-neutron pairing treated in a formalism which conserves exactly the particle number and the isospin. The formalism is designed for self-conjugate (N = Z) systems of nucleons moving in an axially deformed mean field and interacting through the most general isovector and isoscalar pairing interactions. The ground state of these systems is described by a superposition of two types of condensates, i.e., condensates of isovector quartets, built by two isovector pairs coupled to the total isospin T = 0, and condensates of isoscalar proton-neutron pairs. The comparison with the exact solutions of realistic isovector-isoscalar pairing Hamiltonians shows that this formalism is able to describe accurately the pairing correlations energies. It is also shown that, contrary to the majority of HFB calculations, in the present formalism the isovector and isoscalar pairing correlations coexist together for any pairing interactions.