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Register a new userNon-uniform Matter in Neutron Star Crusts Studied by the Variational Method with Thomas-Fermi Calculations
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The equation of state (EOS) for neutron star (NS) crusts is studied in the Thomas-Fermi (TF) approximation using the EOS for uniform nuclear matter obtained by the variational method with the realistic nuclear Hamiltonian. The parameters associated with the nuclear three-body force, which are introduced to describe the saturation properties, are finely adjusted so that the TF calculations for isolated atomic nuclei reproduce the experimental data on masses and charge distributions satisfactorily. The resulting root-mean-square deviation of the masses from the experimental data for mass-measured nuclei is about 3 MeV. With use of the nuclear EOS thus determined, the nuclei in the crust of NS at zero temperature are calculated. The predicted proton numbers of the nuclei in the crust of NS are close to the gross behavior of the results by Negele and Vautherin, while they are larger than those for the EOS by Shen et al. due to the difference in the symmetry energy. The density profile of NS is calculated with the constructed EOS.
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We investigate the nuclear pasta phases in neutron star crusts by conducting a large number of three-dimensional Hartree-Fock+BCS calculations at densities leading to the crust-core transition. We survey the shape parameter space of pasta at constant pressure. Spaghetti, waffles, lasagna, bi-continuous phases and cylindrical holes occupy local minima in the resulting Gibbs energy surfaces. The bi-continuous phase, in which both the neutron gas and nuclear matter extend continuously in all dimensions and therefore protons are delocalized, appears over a large range of depths. Our results support the idea that nuclear pasta is a glassy system. Multiple pasta configurations coexist in a given layer of the crust. At a characteristic temperature, of order $10^8$-$10^9$K, different phases become frozen into domains whose sizes we estimate to be 1-50 times the lattice spacing and over which the local density and electron fraction can vary. Above this temperature, there is very little long-range order and matter is an amorphous solid. Electron scattering off domain boundaries may contribute to the disorder resistivity of the pasta phases. Annealing of the domains may occur during cooling; repopulating of local minima during crustal heating might lead to temperature dependent transport properties in the deep layers of the crust. We identify 4 distinct regions: (1) nuclear pasta first appears as a local minima, but spherical nuclei are the ground state; (2) nuclear pasta become the absolute minimum, but spherical nuclei are still a local minimum (3) only nuclear pasta appears in local minima, and protons are still localized in at least one dimension (4) only pasta appears, and protons are delocalized. The whole pasta region can occupy up to 70% of the crust by mass and 40% by thickness, and the layer in which protons are delocalized could occupy 45% of the crust mass and 25% of its thickness.
Using the $hbar$-expansion of the Greens function of the Hartree-Fock-Bogoliubov equation, we extend the second-order Thomas-Fermi approximation to generalized superfluid Fermi systems by including the density-dependent effective mass and the spin-orbit potential. We first implement and examine the full correction terms over different energy intervals of the quasiparticle spectra in calculations of finite nuclei. Final applications of this generalized Thomas-Fermi method are intended for various inhomogeneous superfluid Fermi systems.
We develop the variational/parquet diagram approach to the structure of nuclear systems with strongly state-dependent interactions. For that purpose, we combine ideas of the general Jastrow-Feenberg variational method and the local parquet-diagram theory for bosons with state-dependent interactions (R. A. Smith and A. D. Jackson, Nucl. Phys. {bf 476}, 448 (1988)). The most tedious aspect of variational approaches, namely the symmetrization of an operator dependent variational wave function, is thereby avoided. We carry out calculations for neutron matter interacting via the Reid and Argonne $v_6$ models of the nucleon-nucleon interaction. While the equation of state is a rather robust quantity that comes out reasonably well even in very simplistic approaches, we show that effective interactions, which are the essential input for calculating dynamic properties, depend sensitively on the quality of the treatment of the many-body problem.
We apply parquet-diagram summation methods for the calculation of the superfluid gap in $S$-wave pairing in neutron matter for realistic nucleon-nucleon interactions such as the Argonne $v_6$ and the Reid $v_6$ potentials. It is shown that diagrammatic contributions that are outside the parquet class play an important role. These are, in variational theories, identified as so-called commutator contributions. Moreover, using a particle-hole propagator appropriate for a superfluid system results in the suppression of the spin-channel contribution to the induced interaction. Applying these corrections to the pairing interaction, our results agree quite well with Quantum Monte Carlo data.
We develop a manifestly microscopic method to deal with strongly interacting nuclear systems that have different interactions in spin-singlet and spin-triplet states. In a first step we analyze variational wave functions that have been suggested to describe such systems, and demonstrate that the so-called commutator contributions can have important effects whenever the interactions in the spin-singlet and the spin-triplet states are very different. We then identify these contributions as terms that correspond, in the language of perturbation theory, to non-parquet diagrams. We include these diagrams in a way that is suggested by the Jastrow-Feenberg approach and show that the corrections from non-parquet contributions are, at short distances, larger than all other many-body effects.
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