Related papers: The maximal excess charge in M\"uller density-matr…
We consider a Thomas-Fermi mean-field model for large neutral atoms. That is, Schr\"odinger operators $H_Z^{\text{TF}}=-\Delta-\Phi_Z^{\text{TF}}$ in three-dimensional space, where $Z$ is the nuclear charge of the atom and…
We study a two-dimensional electron system in a magnetic field with a fermion hardcore interaction and without disorder. Projecting the Hamiltonian onto the n-th Landau level, we show that the Hartree-Fock theory is exact in the limit n…
An electron density functional approach for the calculation of the nuclear multipole moments is presented. The electronic matrix elements entering the experimentally observed hyperfine electron-nucleus interaction constants in atoms are…
Hartree-Fock atom in a strong electric static field is considered. It is demonstrated that exchange between outer and inner electrons, taken into account by the so-called Fock term affects strongly the long-range behavior of the inner…
We compute the ground-state properties of finite systems of neutrons in an external harmonic trap, interacting via the Minnesota potential, using the "exact-exchange" form of orbital-dependent density functional theory. We compare our…
Electrons in strong magnetic fields can be described by one-dimensional models in which the Coulomb potential and interactions are replaced by regularizations associated with the lowest Landau band. For a large class of models of these…
We consider the Thomas--Fermi--Dirac--von~Weizs{\"a}cker model for a system composed of infinitely many nuclei placed on a periodic lattice and electrons with a periodic density. We prove that if the Dirac constant is small enough, the…
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…
Both electron and its neutrino possess not only the anomalous magnetic moment but also each of the existing types of electric charges and their dipole moments. Any of them can interact with field of emission leading to the elastic…
It is well known that $N$-electron atoms undergoes unbinding for a critical charge of the nucleus $Z_c$, i.e. the atom has eigenstates for the case $Z> Z_c$ and it has no bound states for $Z<Z_c$. In the present paper we derive upper bound…
Atomic nuclei can be spontaneously deformed into non-spherical shapes as many-nucleon systems. We discuss to what extent a similar deformation takes place in many-electron systems. To this end, we employ several many-body methods, such as…
This work merges two different types of many-electron ensembles, namely the Theophilou-Gross-Oliveira-Kohn ensembles of ground and neutrally-excited states, and the more recent $N$-centered ensembles of neutral and charged ground states. On…
The model of binding alpha-particles in nuclei is suggested. It is shown good (with the accuracy of 1-2%) description of the experimental binding energies in light and medium nuclear systems. Our preliminary calculations show enhancement of…
The M1 transitions between low-lying T=1 and T=0 states in deformed odd-odd N=Z nuclei are analyzed in the frames of the rotor-plus-particle model. Using the representation of an explicit coupling of angular momenta we show that strong…
We examine the Friedel sum rule which states that the "excess charge" due to a single impurity potential in a metal is equal to a sum of phase shifts for scatterings of electrons by the impurity. For finite volume, the ``excess charge" is…
We present a modified Thomas-Fermi theory that describes the increase of the hyperfine coupling constants of endohedrally enclosed atoms. We use the March boundary conditions corresponding to a positively charged spherical shell surrounding…
The structure of infinite nuclear matter is studied with two of the Zimanyi - Moszkowski (ZM) models in the framework of a relativistic approximation which takes into account Hartree terms and beyond and is compared with the results which…
In this paper we study the large-Z behaviour of the ground state energy of atoms with electrons having relativistic kinetic energy sqrt(p^2c^2+m^2c^4)-mc^2. We prove that to leading order in Z the energy is the same as in 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 suggest to include the density of electron charge explicitly in the electron potential of density functional theory, rather than implicitly via exchange-correlation functionals. The advantages of the approach are conceptual and…