Related papers: Electrons on sphere in the helium-like atomic syst…
We investigate, both analytically and numerically, the behavior of the electron gas on a sphere in the presence of point-like impurities. We find a criterion when the disorder can be regarded as small one and the main effect is the…
Different kinds of averaging of the wavefunctions/densities of the two-electron atomic systems are investigated. Using the Pekeris-like method, the ground state wave functions $\Psi$ of the helium-like atoms with nucleus charge $1\leq…
A model of the non-concentric spherical core-shell quantum dot under the influence of an externally applied electric field was proposed. It was established that the energy spectrum of both the electron and the hole depends on the intensity…
In the context of two-dimensional spacetime within a helium atom, both 1s electrons are characterized by wave functions that observe duality equation. They are symmetric, orthogonal and interwoven, forming a dynamic rope structure at any…
A detailed analysis on the effect of spherical impenetrable confinement on the structural properties of two-electron ions in S-states have been done. The energy values of 1sns [n = 2-4] (3Se) states of helium-like ions (Z = 2-5) are…
The collinear eZe configuration of helium, with the electrons on opposite sides of the nucleus, is studied in the presence of an external electromagnetic (laser or microwave) field. We show that the classically unstable "asymmetric stretch"…
We consider the correlation functions in a gas of electrons moving within a thin layer on the surface of nanosize sphere. A closed form of expressions for the RKKY indirect exchange, superconducting Cooper loop and `density-density'…
This is the second of two papers devoted to tight-binding electronic spectra on graphs with the topology of the sphere. We investigate the problem of an electron subject to a spin-orbit interaction generated by the radial electric field of…
The angular coefficients $\psi_{k,p}(\alpha,\theta)$ of the Fock expansion characterizing the S-state wave function of the two-electron atomic system, are calculated in hyperspherical angular coordinates $\alpha$ and $\theta$. To solve the…
The toolbox for imaging molecules is well-equipped today. Some techniques visualize the geometrical structure, others the electron density or electron orbitals. Molecules are many-body systems for which the correlation between the…
We give a detailed account of an $\it{ab}$ $\it{initio}$ spectral approach for the calculation of energy spectra of two active electron atoms in a system of hyperspherical coordinates. In this system of coordinates, the Hamiltonian has the…
Isolated electrons resting near a helium surface have a spectrum close to that of a quantum-defect atom. A precisely solvable model with Rydberg spectrum is sugguested and discussed.
We present a thorough analysis of the electron density distribution (shape) of two electrons, confined in the three-dimensional harmonic oscillator potential, as a function of the perpendicular magnetic field.Explicit algebraic expressions…
The quantum mechanics of two-electron systems is reviewed, starting with the ground state of the helium atom and helium-like ions, with central charge $Z\ge 2$. For Z=1, demonstrating the stability of the negative hydrogen ion, H$^-$,…
The impact of the strongly attractive electromagnetic field of heavy nuclei on electrons in quasi-elastic (e,e') scattering is often accounted for by the effective momentum approximation. This method is a plane wave Born approximation which…
We study the spectra and response of two electrons moving on a surface of a sphere and interacting via harmonic potential, to external static and laser fields. The spectrum of such system law is analysed in the light of varying coupling…
The article discusses how the pattern of elastic scattering of an electron on a pair of identical atomic spheres will look if we abandon the standard in the molecular physics assumption that, outside the molecular sphere, in the external…
The entanglement properties of two-electron atomic systems have been the subject of considerable research activity in recent years. These studies are still somewhat fragmentary, focusing on numerical computations on particular states of…
An analytical solution of the quantum problem of an electron on a spherical segment with angular confinement potential of the form of rectangular impenetrable walls is presented. It is shown that the problem is reduced to finding solution…
Simulations for the density and potential profiles of the ions in the planar electrical double layer of a model electrolyte or an ionic liquid are reported. The ions of a real electrolyte or an ionic liquid are usually not spheres; in ionic…