Narrow Results

In this paper, we have investigated the Thomas–Fermi model for the electron gas in Rindler space. We have observed that if the uniform acceleration is along $+x$-direction, then there is $y-z$-symmetry in space. For the sake of mathematical simplicity, we have therefore assumed a two-dimensional spatial structure $(x-y)$ in Rindler space. It has been shown that in two-dimensional spatial coordinates, the electrons are distributed discontinuously but in a periodic manner in a number of rectangular strip-like domains along $\pm y$-direction. Some of them are having void structure, with no electrons inside such rectangular strips, while some are filled up with electrons. We call the latter type domain as the normal zone. We have also given physical interpretation for such exotic type electron distribution in Rindler space.

Thomas–Fermi model is considered here to make it cogent to capture the Planck-scale effect with the use of a generalization of uncertainty relation. Here generalization contains both linear and quadratic terms of momentum. We first reformulate the Thomas–Fermi model for the non-relativistic case. We have shown that it can also be reformulated for taking into account the relativistic effect. We study the dialectic screening for both the non-relativistic and relativistic cases and find out the Fermi length for both the cases explicitly.

We describe work being done at Baylor University investigating the possibility of new states of mesonic matter containing two or more quark–antiquark pairs. To put things in context, we begin by describing the lattice approach to hadronic physics. We point out there is a need for a quark model which can give an overall view of the quark interaction landscape. A new application of the Thomas–Fermi (TF) statistical quark model is described, similar to a previous application to baryons. The main usefulness of this model will be to detect systematic energy trends in the composition of the various particles. It could be a key to identifying families of bound states, rather than individual cases. Numerical results based upon a set of parameters derived from a phenomenological model of tetraquarks are given.

The widely used Thomas Fermi model always produces pressure which is less than or equal to that of the ideal Fermi gas. On the other hand the spherical cellular model, in certain regions of the temperature-density plane, can produce pressures which are greater than that of the ideal gas. This phenomenon is investigated.

Using the Thomas-Fermi method, the density distribution of N electrons confined within a three-dimensional anisotropic parabolic potential is studied. This system simulates the structure of the recently built artificial atoms or quantum dots where a bunch of electrons is trapped in a semiconductor material. In the limit of large N, an analytical solution is obtained. Qualitatively speaking, this solution consists of a constant-density interior and a uniform thin skin that covers it. The asymmetry of the external figure is related to that of the confining potential. The radius, density, eccentricity and skin depth of the system are given as a function of N and of the properties of the confining potential and of the matrix material.

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.

In a unified treatment we extrapolate results for neutral atoms with heavy nuclei to nuclear matter cores of stellar dimensions with mass numbers A ≈ (m_Planck/m_n)³ ~ 10⁵⁷. We give explicit analytic solutions for the relativistic Thomas–Fermi equation of N_n neutrons, N_p protons and N_e electrons in beta equilibrium, fulfilling global charge neutrality, with N_p = N_e. We give explicit expressions for the physical parameters including the Coulomb and the surface energies and we study as well the stability of such configurations. Analogous to heavy nuclei these macroscopic cores exhibit an overcritical electric field near their surface.

We prove in this paper that the minimizer of Lennard–Jones energy per particle among Bravais lattices is a triangular lattice, i.e. composed of equilateral triangles, in ℝ² for large density of points, while it is false for sufficiently small density. We show some characterization results for the global minimizer of this energy and finally we also prove that the minimizer of the Thomas–Fermi energy per particle in ℝ² among Bravais lattices with fixed density is triangular.

We consider a degenerate globally neutral system of stellar dimensions consisting of N_n neutrons, N_p protons and N_e electrons in beta equilibrium. Such a system at nuclear density having mass numbers A ≈ 10⁵⁷ can exhibit a charge distribution different from zero. We present the analysis in the framework of classical electrodynamics to investigate the magnetic field induced by this charge distribution when the system is allowed to rotate as a whole rigid body with constant angular velocity around the axis of symmetry.

The relativistic generalization of the Feynman, Metropolis and Teller treatment of compressed atoms is obtained. Each atomic configuration is confined by a Wigner-Seitz cell and is characterized by a positive electron Fermi energy. 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 , here expressed analytically in the ultra-relativistic approximation. The treatment is then extrapolated to compressed nuclear matter cores of stellar dimensions with A ≃ (m_Planck/m_n)³ ~ 10⁵⁷ or M_core ~ M_⊙. A new family of equilibrium configurations exists for selected values of the electron Fermi energy varying in the range . 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 , for .

We describe work being done at Baylor University investigating the possibility of new states of mesonic matter containing two or more quark–antiquark pairs. To put things in context, we begin by describing the lattice approach to hadronic physics. We point out there is a need for a quark model which can give an overall view of the quark interaction landscape. A new application of the Thomas–Fermi (TF) statistical quark model is described, similar to a previous application to baryons. The main usefulness of this model will be to detect systematic energy trends in the composition of the various particles. It could be a key to identifying families of bound states, rather than individual cases. Numerical results based upon a set of parameters derived from a phenomenological model of tetraquarks are given.

The widely used Thomas Fermi model always produces pressure which is less than or equal to that of the ideal Fermi gas. On the other hand the spherical cellular model, in certain regions of the temperature-density plane, can produce pressures which are greater than that of the ideal gas. This phenomenon is investigated.

The role of the Thomas-Fermi approach in Neutron Star matter cores is presented and discussed with special attention to solutions which are globally neutral and do not fulfil the traditional condition of local charge neutrality. A new stable and energetically favorable configuration is found. This new solution can be of relevance in understanding unsolved issues of gravitational collapse processes and their energetics.

Using the relativistic Thomas-Fermi equation we consider the two limiting cases of compressed atoms and compressed massive nuclear density cores. Each configuration is confined by a Wigner-Seitz cell and is characterized by a positive electron Fermi energy. In both cases there exists a limiting configuration with a maximum value of the electron Fermi energy reached when the Wigner—Seitz cell radius equals the radius of the core while the configuration with , reached when the Wigner-Seitz cell radius tends to infinity corresponds to the ground state of the system.

The traditional Tolman-Oppenheimer-Volkoff (TOV) equations of NSs assume local charge neutrality and electromagnetic structure is not accounted for. We show that such an assumption is inconsistent when all known interactions in NS equilibrium equations are present, including electromagnetism. We present the new Einstein-Maxwell-Thomas-Fermi (EMTF) set of equations, which must be solved under the constraint of global, but not local, charge neutrality. We discuss new gravito-electrodynamic effects and present their implications on the mass-radius relation and observational properties of neutron stars.