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Register a new userSymmetry restoration in the mean-field description of proton-neutron pairing
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We show that the symmetry-restored paired mean-field states (quasiparticle vacua) properly account for isoscalar versus isovector nuclear pairing properties. Full particle-number, spin, and isospin symmetries are restored in a simple SO(8) proton-neutron pairing model, and prospects to implement a similar approach in a realistic setting are delineated. Our results show that, provided all symmetries are restored, the pictures based on pair-condensate and quartet-condensate wave functions represent equivalent ways of looking at the physics of nuclear proton-neutron pairing.
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The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Examples are strongly interacting atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact many-body wave function is mapped onto a non-linear density-dependent one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. However, mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group theoretical techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. We present applications of the projection methods to simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the energy density functional theories are highlighted.
The onset of 1S0 proton spin-singlet pairing in neutron-star matter is studied in the framework of the BCS theory including medium polarization effects. The strong three-body coupling of the diproton pairs with the dense neutron environment and the self-energy effects severely reduce the gap magnitude, so to reshape the scenario of the proton superfluid phase inside the star. The vertex corrections due to the medium polarization are attractive in all isospin-asymmetry range at low density and tend to favor the pairing in that channel. However quantitative estimates of their effect on the energy gap do not give significant changes. Implications of the new scenario on the role of pairing in neutron-star cooling is briefly discussed.
The self-energy effect on the neutron-proton (np) pairing gap is investigated up to the third order within the framework of the extend Bruecker-Hartree-Fock (BHF) approach combined with the BCS theory. The self-energy up to the second-order contribution turns out to reduce strongly the effective energy gap, while the emph{renormalization} term enhances it significantly. In addition, the effect of the three-body force on the np pairing gap is shown to be negligible. To connect the present results with the np pairing in finite nuclei, an effective density-dependent zero-range pairing force is established with the parameters calibrated to the microscopically calculated energy gap.
Neutron-proton (np-) pairing is expected to play an important role in the N Z nuclei. In general, it can have isovector and isoscalar character. The existence of isovector np-pairing is well established. On the contrary, it is still debated whether there is an isoscalar np-pairing. The review of the situation with these two types of pairing with special emphasis on the isoscalar one is presented. It is concluded that there are no substantial evidences for the existence of isoscalar np-pairing.
Ground-state properties of exotic even-even nuclei with extreme neutron-to-proton ratios are described in the framework of the self-consistent mean-field theory with pairing formulated in coordinate space. This theory properly accounts for the influence of the particle continuum, which is particularly important for weakly bound systems. The pairing properties of nuclei far from stability are studied with several interactions emphasizing different aspects, such as the range and density dependence of the effective interaction. Measurable consequences of spatially extended pairing fields are presented, and the sensitivity of the theoretical predictions to model details is discussed.
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