BCS-BEC crossover in nuclear matter with the relativistic Hartree-Bogoliubov theory

Based on the relativistic Hartree-Bogoliubov theory, the influence of the pairing interaction strength on the di-neutron correlations and the crossover from superfluidity of neutron Cooper pairs in the $^{1}S_{0}$ channel to Bose-Einstein condensation of di-neutron pairs is systematically investigated in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in the particle-particle channel with an effective factor to simulate the medium effects and take into account the possible ambiguity of pairing force, and the effective interaction PK1 is used in the particle-hole channel. If the effective factor is larger than 1.10, a di-neutron BEC state appears in the low-density limit, and if it is smaller than 0.85, the neutron Cooper pairs are found totally in the weak coupling BCS region. The reference values of several characteristic quantities which characterize the BCS-BEC crossover are obtained respectively from the dimensionless parameter $1/(k_{\rm Fn}a)$ with $a$ the scattering length and $k_{\rm{Fn}}$ the neutron Fermi momentum, the zero-momentum transfer density correlation function D(0) and the effective chemical potential $\nu_{\rm n}$.Comment: 8 pages, 4 figures, 2 tables, Accepted Thursday Jun 14, 2012 for Physical Review

Pairing Properties of Symmetric Nuclear Matter in Relativistic Mean Field Theory

The properties of pairing correlations in symmetric nuclear matter are studied in the relativistic mean field (RMF) theory with the effective interaction PK1. Considering well-known problem that the pairing gap at Fermi surface calculated with RMF effective interactions are three times larger than that with Gogny force, an effective factor in the particle-particle channel is introduced. For the RMF calculation with PK1, an effective factor 0.76 give a maximum pairing gap 3.2 MeV at Fermi momentum 0.9 fm$^{-1}$, which are consistent with the result with Gogny force.Comment: 14 pages, 6 figures

Deformation effect on the center-of-mass correction energy in nuclei ranging from Oxygen to Calcium

The microscopic center-of-mass (c.m.) correction energies for nuclei ranging from Oxygen to Calcium are systematically calculated by both spherical and axially deformed relativistic mean-field (RMF) models with the effective interaction PK1. The microscopic c.m. correction energies strongly depend on the isospin as well as deformation and deviate from the phenomenological ones. The deformation effect is discussed in detail by comparing the deformed with the spherical RMF calculation. It is found that the direct and exchange terms of the c.m. correction energies are strongly correlated with the density distribution of nuclei and are suppressed in the deformed case.Comment: 7 pages, 3 figures, accepted by Chin.Phys.Let

Deformation effect on the center-of-mass correction energy in nuclei ranging from Oxygen to Calcium

The microscopic center-of-mass (c.m.) correction energies for nuclei ranging from Oxygen to Calcium are systematically calculated by both spherical and axially deformed relativistic mean-field (RMF) models with the effective interaction PK1. The microscopic c.m. correction energies strongly depend on the isospin as well as deformation and deviate from the phenomenological ones. The deformation effect is discussed in detail by comparing the deformed with the spherical RMF calculation. It is found that the direct and exchange terms of the c.m. correction energies are strongly correlated with the density distribution of nuclei and are suppressed in the deformed case.Comment: 7 pages, 3 figures, accepted by Chin.Phys.Let

Applicability of Relativistic Point-Coupling Models to Neutron Star Physics

Comparing with a wide range of covariant energy density functional models based on the finite-range meson-exchange representation, the relativistic mean-field models with the zero-range contact interaction, namely the relativistic point-coupling models, are still infrequent to be utilized in establishing nuclear equation of state (EoS) and investigating neutron star properties, although comprehensive applications and achievements of them in describing many nuclear properties both in ground and exited states are mature. In this work, the EoS of neutron star matter is established constructively in the framework of the relativistic point-coupling models to study neutron star physics. Taking two selected functionals DD-PC1 and PC-PK1 as examples, nuclear symmetry energies and several neutron star properties including proton fractions, mass-radius relations, the core-crust transition density, the fraction of crustal moment of inertia and dimensionless tidal deformabilities are discussed. A suppression of pressure of neutron star matter found in the functional PC-PK1 at high densities results in the difficulty of its prediction when approaching to the maximum mass of neutron stars. In addition, the divergences between two selected functionals in describing neutron star quantities mentioned above are still large, ascribing to the less constrained behavior of these functionals at high densities. Then it is expected that the constraints on the dense matter EoS from precise and massive modern astronomical observations, such as the tidal-deformabilities taken from gravitational-wave events, would be essential to improve the parameterizing of the relativistic point-coupling models.Comment: To appear in the AIP Proceedings of the Xiamen-CUSTIPEN Workshop on the EOS of Dense Neutron-Rich Matter in the Era of Gravitational Wave Astronomy, Jan. 3-7, Xiamen, Chin