Thomas-Fermi Model Research Articles

ON COMPRESSED NUCLEAR MATTER: FROM NUCLEI TO NEUTRON STARS

We address the description of neutron-proton-electron degenerate matter in beta equilibrium subjected to compression both in the case of confined nucleons into a nucleus as well as in the case of deconfined nucleons. We follow a step-by-step generalization of the classical Thomas–Fermi model to special and general relativistic regimes, which leads to a unified treatment of beta equilibrated neutron-proton-electron degenerate matter applicable from the case of nuclei all the way up to the case of white-dwarfs and neutron stars. New gravito-electrodynamical effects, missed in the traditional approach for the description of neutron star configurations, are found as a consequence of the new set of general relativistic equilibrium equations.

Nonexistence of a “local suppression” in the ionization of hydrogen atoms by a low-frequency laser field of arbitrary strength

Further development of an analytical model for the tunneling ionization of atoms using a low-frequency laser field of arbitrary strength, including the strong-field region, is presented. The model uses a very accurate approximation of the true ionization barrier–potential in the Schrödinger equation by the effective parabolic barrier–potential based on the algorithm suggested by Miller and Good and later employed by Kulyagin and Taranukhin (KT) for calculating the ionization rate, W(F), of hydrogen atoms from the ground state by a linearly polarized laser field. We point out and eliminate a number of principal errors made by KT and calculate W(F) much more accurately. We demonstrate that the dependence of the ionization rate on the strength of the linearly polarized laser field is monotonic and does not show any effect of the stabilization (“local ionization suppression”) claimed by KT. Our results for W(F) are in good agreement with the results of quantum fully numerical simulations. The analytical method, further developed in the present paper, can be extended without difficulty to calculations of the tunneling ionization for a number of other quantum systems. The most immediate extensions are to hydrogen atoms in an elliptically polarized laser field and atoms described by the Thomas–Fermi model.

Testing neutrino magnetic moment in ionization of atoms by neutrino impact

The atomic ionization processes induced by scattering of neutrinos play key roles in the experimental searches for a neutrino magnetic moment. Current experiments with reactor (anti)neutrinos employ germanium detectors having energy threshold comparable to typical binding energies of atomic electrons, which fact must be taken into account in the interpretation of the data. Our theoretical analysis shows that the so-called stepping approximation to the neutrino-impact ionization is well applicable for the lowest bound Coulomb states, and it becomes exact in the semiclassical limit. Numerical evidence is presented using the Thomas-Fermi model for the germanium atom.

INNER CRUSTS OF NEUTRON STARS IN STRONGLY QUANTIZING MAGNETIC FIELDS

We study the properties and stability of nuclei in the inner crust of neutron stars in the presence of strong magnetic fields $\sim 10^{17}$ G. Nuclei coexist with a neutron gas and reside in a uniform gas of electrons in the inner crust. This problem is investigated within the Thomas-Fermi model. We extract the properties of nuclei based on the subtraction procedure of Bonche, Levit and Vautherin. The phase space modification of electrons due to Landau quantisation in the presence of strong magnetic fields leads to the enhancement of electron as well as proton fractions at lower densities $\sim 0.001$ fm$^{-3}$. We find the equilibrium nucleus at each average baryon density by minimising the free energy and show that, in the presence of strong magnetic fields, it is lower than that in the field free case. The size of the spherical cell that encloses a nucleus along with the neutron and electron gases becomes smaller in strong magnetic fields compared with the zero field case. Nuclei with larger mass and atomic numbers are obtained in the presence of strong magnetic fields as compared with cases of zero field.

Surface energy density of metal nanostructures by Thomas-Fermi model

This letter examines the surface energy density of metal nanostructures with different morphologies by taking into account the effects of the electrostatic screening on the systems. The results show that the surface energy density is higher on concave nanostructures than on convex ones. The finding implies voids are more effective for the physisorption process than particles and wires.

Applications of density matrix in the fractional quantum mechanics: Thomas–Fermi model and Hohenberg–Kohn theorems revisited

The many-body space fractional quantum system is studied using the density matrix method. We give the new results of the Thomas–Fermi model, obtain the quantum pressure of the free electron gas. We also show the validity of the Hohenberg–Kohn theorems in the space fractional quantum mechanics and generalize the density functional theory to the fractional quantum mechanics.

Gradient corrections to the kinetic energy density functional of a two-dimensional Fermi gas at finite temperature

We examine the leading-order semiclassical gradient corrections to the noninteracting kinetic-energy density functional of a two-dimensional Fermi gas by applying the extended Thomas-Fermi theory at finite temperature. We find a nonzero von Weizs\"acker-like gradient correction, which in the high-temperature limit goes over to the functional form $(\ensuremath{\hbar}{}^{2}/24m)(\ensuremath{\nabla}\ensuremath{\rho}){}^{2}/\ensuremath{\rho}$. Our work provides a theoretical justification for the inclusion of gradient corrections in applications of density-functional theory to inhomogeneous two-dimensional Fermi systems at any finite temperature.

Density functional theory on phase space

AbstractForty‐five years after the point de départ [Hohenberg and Kohn, Phys Rev, 1964, 136, B864] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the electron density still eludes us—and possibly will do so forever [Schuch and Verstraete, Nat Phys, 2009, 5, 732]. In what follows we examine a formulation in the same spirit with phase space variables. The validity of Hohenberg–Kohn–Levy‐type theorems on phase space is recalled. We study the representability problem for reduced Wigner functions, and proceed to analyze properties of the new functional. Along the way, new results on states in the phase space formalism of quantum mechanics are established. Natural Wigner orbital theory is developed in depth, with the final aim of constructing accurate correlation‐exchange functionals on phase space. A new proof of the overbinding property of the Müller functional is given. This exact theory supplies its home at long last to that illustrious ancestor, the Thomas–Fermi model. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012

Relativistic Thomas-Fermi treatment of compressed atoms and compressed nuclear matter cores of stellar dimensions

The Feynman, Metropolis and Teller treatment of compressed atoms is extended to the relativistic regimes. Each atomic configuration is confined by a Wigner-Seitz cell and is characterized by a positive electron Fermi energy. The non-relativistic treatment assumes a point-like nucleus and infinite values of the electron Fermi energy can be attained. In the relativistic treatment there exists a limiting configuration, reached when the Wigner-Seitz cell radius equals the radius of the nucleus, with a maximum value of the electron Fermi energy $(E_e^F)_{max}$, here expressed analytically in the ultra-relativistic approximation. The corrections given by the relativistic Thomas-Fermi-Dirac exchange term are also evaluated and shown to be generally small and negligible in the relativistic high density regime. The dependence of the relativistic electron Fermi energies by compression for selected nuclei are compared and contrasted to the non-relativistic ones and to the ones obtained in the uniform approximation. The relativistic Feynman, Metropolis, Teller approach here presented overcomes some difficulties in the Salpeter approximation generally adopted for compressed matter in physics and astrophysics. The treatment is then extrapolated to compressed nuclear matter cores of stellar dimensions with $A\simeq (m_{\rm Planck}/m_n)^3 \sim 10^{57}$ or $M_{core}\sim M_{\odot}$. A new family of equilibrium configurations exists for selected values of the electron Fermi energy varying in the range $0 < E_e^F \leq (E_e^F)_{max}$. Such configurations fulfill global but not local charge neutrality. They have electric fields on the core surface, increasing for decreasing values of the electron Fermi energy reaching values much larger than the critical value $E_c = m_e^2c^3/(e\hbar)$, for $E_e^F=0$. We compare and contrast our results with the ones of Thomas-Fermi model in strange stars.

A theoretical study of the magnetically deformed inner crust matter of magnetars

We have studied various physical properties of magnetically deformed atoms and the associated matter, replacing the atoms by the deformed Wigner-Seitz (WS) cells at the crustal region of strongly magnetized neutron stars (magnetars). A relativistic version of the Thomas-Fermi (TF) model in the presence of a strong magnetic field in cylindrical coordinates is used to study the properties of such matter.

Surface potentials of few-layer graphene films in high vacuum and ambient conditions

The surface potentials of few-layer graphene (FLG) films in high vacuum and ambient conditions have been investigated by employing electrostatic force microscopy. It is found that the surface potential of FLG films in ambient air has a constant large depression compared to that measured in a high vacuum. Our experimental results indicate that the shift is most likely caused by the presence of ambient adsorbates on the outmost graphene surfaces. The surface potentials increase with the number of graphene layers and approach the bulk value for five or more graphene layers in high vacuum as well as in ambient air. Since the contribution of the surface adsorbates is a constant value, we further show that the thickness dependence of the surface potential can be sufficiently explained by the nonlinear Thomas–Fermi Theory in both conditions.

Shocks and Solitons in Ultradense Degenerate Electron-Positron-Ion Plasmas

The formation and propagation of shocks and solitons are investigated in an unmagnetized, ultradense plasma containing degenerate Fermi gas of electrons and positrons, and classical ion gas by employing Thomas-Fermi model. For this purpose, a deformed Korteweg-de Vries-Berger (dKdVB) equation is derived using the reductive perturbative technique for cold, adiabatic, and isothermal ions. Localized analytical solutions of dKdVB equation in planar geometry are obtained for dispersion as well as dissipation dominant cases. For nonplanar (cylindrical and spherical) geometry, time varying numerical shock wave solution of dKdVB equation is found. Its dispersion dominant case leading to the soliton solution is also discussed. The effect of ion temperature, positron concentration and dissipation is found significant on these nonlinear structures. The relevance of the results to the systems of scientific interest is pointed out.

Mass predictions of exotic nuclei within a macroscopic-microscopic model

Different Liquid Drop Model mass formulae have been studied. They include a Coulomb diffuseness correction Z2/A term and pairing and shell energies of the Thomas-Fermi model. The influence of the selected charge radius, the curvature energy and different forms of the Wigner term has been investigated. Their coefficients have been determined by a least square fitting procedure to 2027 experimental atomic masses. The different fits lead to a surface energy coefficient of 17-18 MeV. A large equivalent rms radius (r0 = 1.22 − 1.24 fm) or a shorter central radius may be used. A rms deviation of 0.54 MeV can be reached between the experimental and theoretical masses. The remaining differences come from the determination of the shell and pairing energies. Mass predictions are given for exotic nuclei.

Communication: Ionization potentials in the limit of large atomic number

By extrapolating the energies of nonrelativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row of the periodic table, even as Z → ∞. The local density approximation for the exchange contribution becomes more accurate (or even exact) in this limit. Extended Thomas-Fermi theory matches the shell average of both the ionization potential and density change.

Gradient corrections to the local-density approximation for trapped superfluid Fermi gases

Two species superfluid Fermi gas is investigated on the BCS side up to the Feshbach resonance. Using the Greens's function technique gradient corrections are calculated to the generalized Thomas-Fermi theory including Cooper pairing. Their relative magnitude is found to be measured by the small parameter $(d/R_{TF})^4$, where $d$ is the oscillator length of the trap potential and $R_{TF}$ is the radial extension of the density $n$ in the Thomas-Fermi approximation. In particular at the Feshbach resonance the universal %constant $A_{TF}$ has the %correction in the center $A=A_{TF}+A_2(d/R_{TF})^4+\...$ corrections to the local density approximation are calculated and a universal prefactor $\kappa_W=7/27$ is derived for the von Weizs\"acker type correction $\kappa_W(\hbar^2/2m)(\nabla^2 n^{1/2}/n^{1/2})$.

Pseudopotential and full-electron DFT calculations of thermodynamic properties ofelectrons in metals and semiempirical equations of state

In the present work, we compare the thermal contribution of electrons to thermodynamicfunctions of metals in different models at high densities and electron temperatures. One ofthe theoretical approaches, the full-potential linear-muffin-tin-orbital method, treats allelectrons in the framework of density functional theory (DFT). The other approach,VASP, uses projector-augmented-wave pseudopotentials for the core electronsand considers the valent electrons also in the context of DFT. We analyze thelimitations of the pseudopotential approach and compare the DFT results with afinite-temperature Thomas–Fermi model and two semiempirical equations of state.

Experimental and theoretical Compton profiles of Be, C and Al

The results of Compton profile measurements, Fermi momentum determinations, and theoretical values obtained from a linear combination of Slater-type orbital (STO) for core electrons in beryllium; carbon and aluminium are presented. In addition, a Thomas–Fermi model is used to estimate the contribution of valence electrons to the Compton profile. Measurements were performed using monoenergetic photons of 59.54 keV provided by a low-intensity Am-241 γ-ray source. Scattered photons were detected at 90° from the beam direction using a p-type coaxial high-purity germanium detector (HPGe). The experimental results are in good agreement with theoretical calculations.

Electrosphere of macroscopic “quark nuclei”: A source for diffuse MeV emissions from dark matter

Using a Thomas-Fermi model, we calculate the structure of the electrosphere of the quark antimatter nuggets postulated to comprise much of the dark matter. This provides a single self-consistent density profile from ultrarelativistic densities to the nonrelativistic Boltzmann regime that use to present microscopically justified calculations of several properties of the nuggets, including their net charge, and the ratio of MeV to 511 keV emissions from electron annihilation. We find that the calculated parameters agree with previous phenomenological estimates based on the observational supposition that the nuggets are a source of several unexplained diffuse emissions from the Galaxy. As no phenomenological parameters are required to describe these observations, the calculation provides another nontrivial verification of the dark-matter proposal. The structure of the electrosphere is quite general and will also be valid at the surface of strange-quark stars, should they exist.

ChemInform Abstract: Endohedral Effect in Inclusion Complexes of the C60 Cluster

An approximate theory of bonding in endohedral complexes that are formed by atoms, ions, and molecules trapped inside the C60 cage is formulated. It is found that the electrostatic potential at the cage center (the endohedral potential) determines such electronic properties of the endohedral complexes as the complexation energy, ionization potentials, and the stability with respect to internal electron transfer. The origins of the endohedral effect, i.e., the positive valuedness of the endohedral potential, are investigated with the help of the Thomas–Fermi theory. The theoretical predictions are demonstrated to be in good agreement with the numerical results of ab initio electronic structure calculations.

Shock Compression of a Fifth Period Element: Liquid Xenon to 840 GPa

Current equation of state (EOS) models for xenon show substantial differences in the Hugoniot above 100 GPa, prompting the need for an improved understanding of xenon's behavior at extreme conditions. We performed shock compression experiments on liquid xenon to determine the Hugoniot up to 840 GPa, using these results to validate density functional theory (DFT) simulations. Despite the nearly fivefold compression, we find that the limiting Thomas-Fermi theory, exact in the high density limit, does not accurately describe the system. Combining the experimental data and DFT calculations, we developed a free-energy-based, multiphase EOS capable of describing xenon over a wide range of pressures and temperatures.