On the Constitution of Metallic Sodium. II

Wigner, E. P.; Seitz, Frederick

doi:10.1103/physrev.46.509

Cited by 536 publications

(138 citation statements)

References 19 publications

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“…VMC retrieves more than 99.5% of the DMC correlation energy in the density range studied (r s = 0. [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. The effects of backflow on the nodes increase with r s , even though the additional percentage of the correlation energy retrieved in VMC decreases with r s , implying that the energies of dilute HEGs are less sensitive to the nodal structure of the trial wave function than those of denser systems.…”

Section: Discussionmentioning

confidence: 99%

Inhomogeneous backflow transformations in quantum Monte Carlo calculations

et al. 2006

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An inhomogeneous backflow transformation for many-particle wave functions is presented and applied to electrons in atoms, molecules, and solids. We report variational and diffusion quantum Monte Carlo (VMC and DMC) energies for various systems and study the computational cost of using backflow wave functions. We find that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations. The backflow transformations significantly improve the wave functions and their nodal surfaces.

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Section: Discussionmentioning

confidence: 99%

Inhomogeneous backflow transformations in quantum Monte Carlo calculations

et al. 2006

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“…However equations (2) with the boundary conditions (4) are numerically very complicated to solve. The approximation introduced a long time ago by Wigner and Seitz in the study of metallic sodium [3,4] has been widely applied in the context of neutron star crust, as described below.…”

Section: A Band Theory Of Solidsmentioning

confidence: 99%

Validity of the Wigner-Seitz approximation in neutron star crust

et al. 2007

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Since the seminal work of Negele and Vautherin, the Wigner-Seitz approximation has been widely applied to study the inner crust of neutron stars formed of nuclear clusters immersed in a neutron sea. In this article, the validity of this approximation is discussed in the framework of the band theory of solids. For a typical cell of 200 Zr, present in the external layers of the inner crust, it is shown that the ground state properties of the neutron gas are rather well reproduced by the Wigner-Seitz approximation, while its dynamical properties depend on the energy scale of the process of interest or on the temperature. It is concluded that the Wigner-Seitz approximation is well suited for describing the inner crust of young neutron stars and the collapsing core of massive stars during supernovae explosions. However the band theory is required for low temperature transport properties as, for instance, the effective neutron mass giving rise to entrainment effects. In the standard model of neutron stars [1], the crust is believed to be formed of nuclear clusters in a body centered cubic lattice stabilized by Coulomb forces and considered infinite and pure (made of only one type of nuclei at a given density). In the inner crust, at densities above ∼ 4.10 11 g.cm −3 and below ∼ 10 14 g.cm −3 , the "neutron drip" regime is reached and the clusters are surrounded by a neutron fluid. A formal comparison can be made with electrons in ordinary solids present on earth: part of the neutrons participate to the nuclear clusters which form the lattice (equivalent to electrons bounded to atoms) while part of the neutrons are delocalized over the whole crystal (equivalent to valence electrons). As a consequence, the band theory of solids developed in condensed matter [2] can be applied to describe the crust of neutron star. But due to the highly specific numerical issues of band theory, nuclear physicists have preferred to use an approximation due to Wigner and Seitz (W-S) [3,4], where the crust is divided into independent and spherical cells. Since the work of Negele and Vautherin [5], the W-S approximation has been used to predict the structure of the crust, the pairing properties, the thermal effects, or the low lying energy excitation spectrum [6,7,8,9,10,11,12]. Only recently, band theory calculations have been carried out in order to study the hydrodynamical properties of the neutron fluid and in particular the neutron effective mass giving rise to entrainment effects [13,14,15], although these calculations are not yet self-consistent. While the W-S approximation is well justified below the "neutron drip" regime, its validity beyond remains to be assessed.In this article, we investigate the limitations of the W-S approximation in the ρ ∼ 7.10 11 g.cm −3 density layer of the inner crust, composed of a crystal of zirconium like clusters [5] surrounded by the neutron gas. In Sect. I, before discussing the W-S approximation, we briefly review the band theory of solids. Then we compare in Sect. II the results of the band theory...

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“…A t ambient pressure the alkali metals are simple metals; i.e., they can be described as nearly-free-electron metals that are characterized by a weak interaction between their single valence electron and the atomic core (1,2). At ambient conditions the alkali metals all crystallize in the close-packed body-centered cubic (bcc) structure.…”

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confidence: 99%

Structure of sodium above 100 GPa by single-crystal x-ray diffraction

McMahon

Gregoryanz

Lundegaard

et al. 2007

Proc. Natl. Acad. Sci. U.S.A.

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At pressures above a megabar (100 GPa), sodium crystallizes in a number of complex crystal structures with unusually low melting temperatures, reaching as low as 300 K at 118 GPa. We have utilized this unique behavior at extreme pressures to grow a single crystal of sodium at 108 GPa, and have investigated the complex crystal structure at this pressure using high-intensity x-rays from the new Diamond synchrotron source, in combination with a pressure cell with wide angular apertures. We confirm that, at 108 GPa, sodium is isostructural with the cI16 phase of lithium, and we have refined the full crystal structure of this phase. The results demonstrate the extension of single-crystal structure refinement beyond 100 GPa and raise the prospect of successfully determining the structures of yet more complex phases reported in sodium and other elements at extreme pressures.alkali metals ͉ crystal structure ͉ high pressure A t ambient pressure the alkali metals are simple metals; i.e., they can be described as nearly-free-electron metals that are characterized by a weak interaction between their single valence electron and the atomic core (1, 2). At ambient conditions the alkali metals all crystallize in the close-packed body-centered cubic (bcc) structure. However, under sufficient compression, they undergo a series of structural phase transitions. At pressures ranging from 2.2 GPa in cesium to 65 GPa in sodium, they transform from the bcc to the face-centered-cubic ( fcc) structure (3-5). Further compression leads to the formation of a wide variety of lower-symmetry and often very complex crystal structures (6, 7), which range from distorted variants of the bcc structure in lithium and sodium (5,8,9) to an incommensurate composite or ''host-guest'' crystal structure in rubidium (10, 11). The discovery of a whole series of these symmetry-lowering transitions over the last decade-not only in the alkali metals, but also in various other elements (6, 7, 9)-had been unexpected because it often involves a reduction in coordination number, which is opposite to the usual trend for pressureinduced phase transitions. The experimental discoveries have been complemented by computational studies, but the physical mechanisms that lead to the formation of the complex phases are not yet fully understood, and their physical properties not yet known in detail.Because of the low x-ray scattering power and relatively high transition pressures of sodium, it is only recently that it has become possible to investigate its high-pressure behavior. A number of high-pressure phases have been identified above 100 GPa (ref. 12 and M. Hanfland, K. Syassen, N. E. Christensen, and D. L. Novikov, unpublished data-see ref. 5), and the melting line was discovered to be very unusual: it first rises close to 1,000 K at Ϸ30 GPa and then falls to room temperature (Ϸ300 K) at 118 GPa (12) (see Fig. 1). Previous x-ray diffraction studies have shown that, with increasing pressure at room temperature, sodium transforms first from the bcc phase to fcc at 65 GP...

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On the Constitution of Metallic Sodium. II

Cited by 536 publications

References 19 publications

Inhomogeneous backflow transformations in quantum Monte Carlo calculations

Inhomogeneous backflow transformations in quantum Monte Carlo calculations

Validity of the Wigner-Seitz approximation in neutron star crust

Structure of sodium above 100 GPa by single-crystal x-ray diffraction

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