Bridging the quartet and pair pictures of isovector proton-neutron pairing

Abstract

The formal implications of a quartet coherent state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many body correlation functions. The intrinsic structure of the quartet coherent state is detailed, as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations.

Structure of the quartetting ground state of $N=Z$ nuclei

“…In order to compare the various possible choices for the ground state structure discussed in sec. 2.3, we have performed realistic calculations for N = Z nuclei with valence nucleons outside the closed cores 16 O, 40 Ca and 100 Sn. Following Ref.…”

“…[4,5,13,14,15], and recently in Ref. [16], in the more general context of a multi-level isovector pairing model. The particle number and isospin projection of a protonneutron BCS pair condensate state naturally generates the collective quartet structure of the ground state ansatz postulated in Ref.…”

“…Remarkably, the QCM approach turns out to be perfectly equivalent to the projected BCS (P N T BCS) approach, involving both particle number and isospin restorations, for the isovector pairing case [16].…”

“…corresponds to the particle number and isospin projection of the BCS state (see the next subsection and also Ref. [16] for more details),…”

“…The integral over all directions in isospin space of the γ-coherent state is shown in Ref. [16] to generate the collective quartet state,…”