Related papers: Strong Scott Conjecture
In heavy atoms and molecules, on the distances $a \gg Z^{-1}$ from all of the nuclei (with a charge $Z_m$) we prove that $\rho_\Psi (x)$ is approximated in $L^p$-norm, by the Thomas-Fermi density.
The strong Scott conjecture about the electron density at a distance 1/Z from an atomic nucleus of charge $Z$ and its generalization for molecules are proved. The density, suitably scaled, converges to an explicit limiting density as $Z \to…
We prove the convergence of the density on the scale $Z^{-1}$ to the density of the Bohr atom (with infinitely many electrons) (strong Scott conjecture) for a model that is known to describe heavy atoms accurately.
We consider a large neutral atom of atomic number $Z$, taking relativistic effects into account by assuming the dispersion relation $\sqrt{c^2p^2+c^4}$. We study the behavior of the one-particle ground state density on the length scale…
We derive an upper estimate for electronic density $\rho_\Psi (x)$ in heavy atoms and molecules. While not sharp, on the distances $\gtrsim Z^{-1}$ from the nuclei it is still better than the known estimate $CZ^3$ ($Z$ is the total charge…
We consider heavy neutral atoms of atomic number $Z$ modeled with kinetic energy $(c^2p^2+c^4)^{1/2}-c^2$ used already by Chandrasekhar. We study the behavior of the one-particle ground state density on the length scale $Z^{-1}$ in the…
A basic quantity in the characterization of relativistic particles is the proton-to-electron (p/e) energy density ratio. We derive a simple approximate expression suitable to estimate this quantity, U_p/U_e = (m_p/m_e)^(3-q)/2, valid when a…
We present a unified treatment of nuclear density cores recovering the classic results for neutral atoms with heavy nuclei having a mass number $A\approx 10^2--10^6$ and extrapolating these results to massive nuclear density cores with…
The neutron skin thickness $\Delta r_{\rm{np}}$ of heavy nuclei is essentially determined by the symmetry energy density slope $L({\rho })$ at $\rho_c = 0.11~{\rm {fm}^{-3}}\approx 2/3\rho_0$ ($\rho_0$ is nuclear saturation density),…
The Large Electron Positron Collider (LEP) established the Standard Model (SM) of particle physics with unprecedented precision, including all its radiative corrections. These led to predictions for the masses of the top quark and Higgs…
We compute the ab-initio electron density beyond the strict Born-Oppenheimer approximation in crystalline LiH and LiD with density functional methods. By taking into account the quantum mechanical nature of the nuclei, an aspect absent in…
The many-body system comprising a He nucleus, three electrons, and a positron has been studied using the exact diagonalization technique. The purpose has been to clarify to which extent the system can be considered as a distinguishable…
The purpose of this paper is to derive sharp asymptotics of the ground state energy for the heavy atoms and molecules in the relativistic settings, and, in particular, to derive relativistic Scott correction term and also Dirac, Schwinger…
We prove the first correction to the leading Thomas-Fermi energy for the ground state energy of atoms and molecules in a model where the kinetic energy of the electrons is treated relativistically. The leading Thomas-Fermi energy,…
We show by a statistical analysis of high-resolution scanning tunneling microscopy (STM) experiments, that the interpretation of the density of electron charge as a statistical quantity leads to a conflict with the Heisenberg uncertainty…
A new formula that relates the electron density at the nucleus of atoms,rho(0,Z), and the atomic number,Z, is proposed. This formula,rho(0,Z)=a(Z-bZ^(0.5))^3, contains two unknown parameters (a,b) that are derived using a least square…
In non-relativistic Brueckner calculations of nuclear matter, the self-consistent single particle potential is strongly momentum dependent. To simplify the calculations, a parabolic approximation is often used in the literature. The…
The asymptotic form of the energy density for a gas of particles surrounding a sphere of mass $M$ and radius $R$ is studied using Einstein's equations. It is shown that if the pressure of the gas $p$ varies linearly with the energy density…
We review some older and more recent results concerning the energy and particle distribution in ground states of heavy Coulomb systems. The reviewed results are asymptotic in nature: they describe properties of many-particle systems in the…
The lightest supersymmetric particle (LSP) is stable in an R-parity conserving theory. In this article the steps needed to calculate the present day mass density of such a particle are detailed. It is shown that there can be a…