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

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.

Figure 1

Error in the correlation energy (a) $E_c=E\left(G\right)-E(G=0)$ and overlaps (b) for the states (26) relative to the QCM state (25), versus the interaction strength $G$ (in units of the level spacing). The results are for two protons and four neutrons on eight equidistant levels. To indicate the results we use the notations: “${\mathrm{\Gamma }}_x{Q}_x$” for the state ${\mathrm{\Gamma }}^{†}\left(x\right)Q^{†}\left(x\right)|0\rangle$ of Eq. (25) with equal pair and quartet amplitudes $x=y$; “${\mathrm{\Gamma }}_x{\left[{\mathrm{\Gamma }}_x{\mathrm{\Gamma }}_y\right]}_0$” for state ${\mathrm{\Gamma }}_1^{†}\left(x\right){\left[{\mathrm{\Gamma }}^{†}\left(x\right){\mathrm{\Gamma }}^{†}\left(y\right)\right]}^{T=0}|0\rangle$; “$P_{NT}{|\mathrm{BCS}\rangle }_{1,2}$” for the projected BCS states of Eqs. (26a) and (26b).