Related papers: Atoms in the anionic domain, Z < N
The study of a positive or negative charge when an atom loses or gains an electron is a custom in both physical and chemical sciences. However, the related principles and phenomena become confusing when studying the concepts of ionization.…
We consider a large neutral atom of atomic number $Z$, modeled by a pseudo-relativistic Hamiltonian of Chandrasekhar. We study its suitably rescaled one-particle ground state density on the Thomas--Fermi length scale $Z^{-1/3}$. Using an…
We prove that in Thomas-Fermi-Dirac-von Weizs\"acker theory, a nucleus of charge $Z>0$ can bind at most $Z+C$ electrons, where $C$ is a universal constant. This result is obtained through a comparison with Thomas-Fermi theory which, as a…
We study the non-uniform nuclear matter using the self-consistent Thomas--Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped…
We study minimum energy configurations of $N$ particles in $\R^3$ of charge -1 (`electrons') in the potential of $M$ particles of charges $Z_\alpha>0$ (`atomic nuclei'). In a suitable large-N limit, we determine the asymptotic electron…
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…
We reconsider the problem of the spontaneous emission of light by an excited atomic state. We scrutinize the survival probability of this excited state for very short times, in the so-called Zeno regime, for which we show that the dynamics…
By extrapolating the energies of non-relativistic 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, even as…
The critical nuclear charge Zc required for a heliumlike atom to have at least one bound state was recently determined with high accuracy from variational calculations. Analysis of the wave functions further suggested that the bound state…
It is established within the Thomas -- Fermi model that a bound state of a proton with a heavy atom should exist. On the one hand, the electrons of the atom screen the proton's field. This decreases the repulsion force between the proton…
This paper is concerned with the Schr\"odinger equation for atoms and ions with N=1 to 10 electrons. In the asymptotic limit of large nuclear charge $Z$, we determine explicitly the low-lying energy levels and eigenstates. The asymptotic…
In a Thomas-Fermi model, calculations are presented for nuclei beyond the nuclear drip line at zero temperature. These nuclei are in equilibrium by the presence of an external gas, as may be envisaged in the astrophysical scenario. We find…
Theoretical energy levels of the $n = 1$ and $n = 2$ states of hydrogenlike atoms with the nuclear charge numbers $1 \le Z \le 110$ are tabulated. The tabulation is based on ab initio quantum electrodynamical calculations performed to all…
The thermodynamic properties of nuclei are studied in a mean field model using a Skryme interaction. Properties of two component systems are investigated over the complete range of proton fraction from a system of pure neutrons to a system…
We show an atom of atomic number $Z$ described by the time-dependent Thomas-Fermi equation or the Vlasov equation cannot bind more than $4Z$ electrons.
We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb…
The "catastrophe" in solving the Dirac equation for an electron in the field of a point electric charge, which emerges for the charge numbers Z > 137, is removed in this work by effective accounting of finite dimensions of nuclei. For this…
Experimental nuclear level densities at excitation energies below the neutron threshold follow closely a constant-temperature shape. This dependence is unexpected and poorly understood. In this work, a fundamental explanation of the…
The study shows how to define "exactly" the average ion charge $Z_{\rm I}$ in the electron-ion model for plasmas and liquid metals: this definition comes out of the condition that a plasma consisting of electrons and nuclei can be described…
We discuss how the thermalization of an elementary quantum system is modified when the system is placed in an environment out of thermal equilibrium. To this aim we provide a detailed investigation of the dynamics of an atomic system placed…