scholarly journals Cluster structure of the inner crust of neutron stars in the Hartree-Fock-Bogoliubov approach

2011 ◽  
Vol 84 (6) ◽  
Author(s):  
F. Grill ◽  
J. Margueron ◽  
N. Sandulescu
Keyword(s):  
Neutron Stars ◽  
Cluster Structure ◽  
Hartree Fock

THE INNER CRUST OF NEUTRON STARS IN RELATIVISTIC MEAN FIELD APPROACH

2008 ◽  
Vol 17 (09) ◽  
pp. 1765-1773 ◽  
Author(s):  
JIGUANG CAO ◽  
ZHONGYU MA ◽  
NGUYEN VAN GIAI
Keyword(s):  
Boundary Conditions ◽  
Neutron Stars ◽  
Mean Field ◽  
Bcs Theory ◽  
Neutron Density ◽  
Field Approach ◽  
Hartree Fock ◽  
Relativistic Mean Field ◽  
Density Distributions ◽  
Rmf Model

The microscopic properties and superfluidity of the inner crust in neutron stars are investigated in the framework of the relativistic mean field(RMF) model and BCS theory. The Wigner-Seitz(W-S) cell of inner crust is composed of neutron-rich nuclei immersed in a sea of dilute, homogeneous neutron gas. The pairing properties of nucleons in the W-S cells are treated in BCS theory with Gogny interaction. In this work, we emphasize on the choice of the boundary conditions in the RMF approach and superfluidity of the inner crust. Three kinds of boundary conditions are suggested. The properties of the W-S cells with the three kinds of boundary conditions are investigated. The neutron density distributions in the RMF and Hartree-Fock-Bogoliubov(HFB) models are compared.

scholarly journals 1S0 Pairing Gaps, Chemical Potentials and Entrainment Matrix in Superfluid Neutron-Star Cores for the Brussels–Montreal Functionals

Universe ◽  
2021 ◽  
Vol 7 (12) ◽  
pp. 470
Author(s):  
Valentin Allard ◽  
Nicolas Chamel
Keyword(s):  
Neutron Star ◽  
Equation Of State ◽  
Neutron Stars ◽  
Physical Meaning ◽  
Outer Core ◽  
Time Dependent ◽  
Hartree Fock ◽  
Chemical Potentials ◽  
Bogoliubov Equations ◽  
Flow Velocities

Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for npeμ in beta-equilibrium using the Brussels–Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.

scholarly journals Estimation of Electrical Conductivity and Magnetization Parameter of Neutron Star Crusts and Applied to the High-Braking-Index Pulsar PSR J1640-4631

Universe ◽  
2020 ◽  
Vol 6 (5) ◽  
pp. 63
Author(s):  
Hui Wang ◽  
Zhi-Fu Gao ◽  
Huan-Yu Jia ◽  
Na Wang ◽  
Xiang-Dong Li
Keyword(s):  
Magnetic Field ◽  
Neutron Star ◽  
Neutron Stars ◽  
General Expression ◽  
Equations Of State ◽  
Rotation Period ◽  
Ohmic Dissipation ◽  
Hartree Fock ◽  
Induction Equation ◽  
The Magnetic Field

Young pulsars are thought to be highly magnetized neutron stars (NSs). The crustal magnetic field of a NS usually decays at different timescales in the forms of Hall drift and Ohmic dissipation. The magnetization parameter ω B τ is defined as the ratio of the Ohmic timescale τ O h m to the Hall drift timescale τ H a l l . During the first several million years, the inner temperature of the newly born neutron star cools from T = 10 9 K to T = 1.0 × 10 8 K, and the crustal conductivity increases by three orders of magnitude. In this work, we adopt a unified equations of state for cold non-accreting neutron stars with the Hartree–Fock–Bogoliubov method, developed by Pearson et al. (2018), and choose two fiducial dipole magnetic fields of B = 1.0 × 10 13 G and B = 1.0 × 10 14 G, four different temperatures, T, and two different impurity concentration parameters, Q, and then calculate the conductivity of the inner crust of NSs and give a general expression of magnetization parameter for young pulsars: ω B τ ≃ ( 1 − 50 ) B 0 / ( 10 13 G) by using numerical simulations. It was found when B ≤ 10 15 G, due to the quantum effects, the conductivity increases slightly with the increase in the magnetic field, the enhanced magnetic field has a small effect on the matter in the low-density regions of the crust, and almost has no influence the matter in the high-density regions. Then, we apply the general expression of the magnetization parameter to the high braking-index pulsar PSR J1640-4631. By combining the observed arrival time parameters of PSR J1640-4631 with the magnetic induction equation, we estimated the initial rotation period P 0 , the initial dipole magnetic field B 0 , the Ohm dissipation timescale τ O h m and Hall drift timescale τ H a l l . We model the magnetic field evolution and the braking-index evolution of the pulsar and compare the results with its observations. It is expected that the results of this paper can be applied to more young pulsars.

MULTICONFIGURATION HARTREE–FOCK THEORY FOR PSEUDORELATIVISTIC SYSTEMS: THE TIME-DEPENDENT CASE

2013 ◽  
Vol 24 (03) ◽  
pp. 599-626 ◽  
Author(s):  
HICHEM HAJAIEJ ◽  
PETER A. MARKOWICH ◽  
SABER TRABELSI
Keyword(s):  
Molecular Dynamics ◽  
Initial Data ◽  
Neutron Stars ◽  
Time Dependent ◽  
System Of Equations ◽  
Critical Number ◽  
Dependent Case ◽  
Hartree Fock ◽  
The Third ◽  
Time Solution

In [Setting and analysis of the multi-configuration time-dependent Hartree–Fock equations, Arch. Ration. Mech. Anal.198 (2010) 273–330] the third author has studied in collaboration with Bardos, Catto and Mauser the nonrelativistic multiconfiguration time-dependent Hartree–Fock system of equations arising in the modeling of molecular dynamics. In this paper, we extend the previous work to the case of pseudorelativistic atoms. We show the existence and the uniqueness of global-in-time solution to the underlying system under technical assumptions on the energy of the initial data and the charge of the nucleus. Moreover, we prove that the result can be extended to the case of neutron stars when the number of electrons is less than a critical number N cr .

scholarly journals Equation of state of dense nuclear matter and neutron star structure from nuclear chiral interactions

2018 ◽  
Vol 609 ◽  
pp. A128 ◽  
Author(s):  
Ignazio Bombaci ◽  
Domenico Logoteta
Keyword(s):  
Neutron Star ◽  
Equation Of State ◽  
Neutron Stars ◽  
Nuclear Matter ◽  
Symmetric Nuclear Matter ◽  
Heavy Nuclei ◽  
Hartree Fock ◽  
Binary Neutron Star ◽  
Dense Nuclear Matter ◽  
Three Body

Aims. We report a new microscopic equation of state (EOS) of dense symmetric nuclear matter, pure neutron matter, and asymmetric and β-stable nuclear matter at zero temperature using recent realistic two-body and three-body nuclear interactions derived in the framework of chiral perturbation theory (ChPT) and including the Δ(1232) isobar intermediate state. This EOS is provided in tabular form and in parametrized form ready for use in numerical general relativity simulations of binary neutron star merging. Here we use our new EOS for β-stable nuclear matter to compute various structural properties of non-rotating neutron stars. Methods. The EOS is derived using the Brueckner–Bethe–Goldstone quantum many-body theory in the Brueckner–Hartree–Fock approximation. Neutron star properties are next computed solving numerically the Tolman–Oppenheimer–Volkov structure equations. Results. Our EOS models are able to reproduce the empirical saturation point of symmetric nuclear matter, the symmetry energy Esym, and its slope parameter L at the empirical saturation density n0. In addition, our EOS models are compatible with experimental data from collisions between heavy nuclei at energies ranging from a few tens of MeV up to several hundreds of MeV per nucleon. These experiments provide a selective test for constraining the nuclear EOS up to ~4n0. Our EOS models are consistent with present measured neutron star masses and particularly with the mass M = 2.01 ± 0.04 M⊙ of the neutron stars in PSR J0348+0432.

scholarly journals Proximity effect of pair correlation in the inner crust of neutron stars

2020 ◽  
Author(s):  
Toshiyuki Okihashi ◽  
Masayuki Matsuo
Keyword(s):  
Neutron Stars ◽  
Proximity Effect ◽  
Pair Correlation ◽  
Baryon Density ◽  
Coordinate Space ◽  
Hartree Fock ◽  
Bogoliubov Theory ◽  
Seitz Cell ◽  
Deep Layers ◽  
Nuclear Cluster

Abstract We study proximity effect of pair correlation in the inner crust of neutron stars by means of the Skyrme-Hartree-Fock-Bogoliubov theory formulated in the coordinate space. We describe a system composed of a nuclear cluster immersed in neutron superuid, which is confined in a spherical box. Using a density-dependent effective pairing interaction which reproduces both the pair gap of neutron matter obtained in ab initio calculations and that of finite nuclei, we analyze how the pair condensate in neutron superuid is affected by the presence of the nuclear cluster. It is found that the proximity effect is characterized by the coherence length of neutron superuid measured from the edge position of the nuclear cluster. The calculation predicts that the proximity effect has a strong density dependence. In the middle layers of the inner crust with baryon density 5 × 10-4 fm-3 ≲ ρb ≲ 2 × 10-2 fm-3, the proximity effect is well limited in the vicinity of the nuclear cluster, i.e. in a sufficiently smaller area than the Wigner-Seitz cell. On the contrary, the proximity effect is predicted to extend to the whole volume of the Wigner-Seitz cell in shallow layers of the inner crust with ρb ≲ 2 × 10-4 fm-3, and in deep layers with ρb ≲ 5 × 10-2 fm-3.

scholarly journals Unified Equation of State for Neutron Stars Based on the Gogny Interaction

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1613
Author(s):  
Xavier Viñas ◽  
Claudia Gonzalez-Boquera ◽  
Mario Centelles ◽  
Chiranjib Mondal ◽  
Luis M. Robledo
Keyword(s):  
Equation Of State ◽  
Neutron Stars ◽  
Density Functional ◽  
Mean Field ◽  
Nuclear Interaction ◽  
Energy Density Functional ◽  
Hartree Fock ◽  
The Moment ◽  
Finite Nuclei ◽  
Pairing Field

The effective Gogny interactions of the D1 family were established by D. Gogny more than forty years ago with the aim to describe simultaneously the mean field and the pairing field corresponding to the nuclear interaction. The most popular Gogny parametrizations, namely D1S, D1N and D1M, describe accurately the ground-state properties of spherical and deformed finite nuclei all across the mass table obtained with Hartree–Fock–Bogoliubov (HFB) calculations. However, these forces produce a rather soft equation of state (EoS) in neutron matter, which leads to predict maximum masses of neutron stars well below the observed value of two solar masses. To remove this limitation, we built new Gogny parametrizations by modifying the density dependence of the symmetry energy predicted by the force in such a way that they can be applied to the neutron star domain and can also reproduce the properties of finite nuclei as good as their predecessors. These new parametrizations allow us to obtain stiffer EoS’s based on the Gogny interactions, which predict maximum masses of neutron stars around two solar masses. Moreover, other global properties of the star, such as the moment of inertia and the tidal deformability, are in harmony with those obtained with other well tested EoSs based on the SLy4 Skyrme force or the Barcelona–Catania–Paris–Madrid (BCPM) energy density functional. Properties of the core-crust transition predicted by these Gogny EoSs are also analyzed. Using these new Gogny forces, the EoS in the inner crust is obtained with the Wigner–Seitz approximation in the Variational Wigner–Kirkwood approach along with the Strutinsky integral method, which allows one to estimate in a perturbative way the proton shell and pairing corrections. For the outer crust, the EoS is determined basically by the nuclear masses, which are taken from the experiments, wherever they are available, or by HFB calculations performed with these new forces if the experimental masses are not known.

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