Related papers: Two-electron atom with a screened interaction
Electron-electron correlation forms the basis of difficulties encountered in many-body physics. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in the correlation. In an…
The analysis of correlation energy of the simplest first approximation of a variational method for the intrashell states of two-electron atoms is the purpose of the present work. This method allows to divide energy of atom on Coulomb and…
Electron-electron correlation forms the basis of difficulties encountered in many-body problems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In an…
We present a general approach for the solution of the three-body problem for a general interaction, and apply it to the case of the Coulomb interaction. This approach is exact, simple and fast. It makes use of integral equations derived…
We review our recent progress in the determination of the high-density correlation energy $\Ec$ in two-electron systems. Several two-electron systems are considered, such as the well known helium-like ions (helium), and the Hooke's law atom…
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 classical dynamics of two electrons in the Coulomb potential of an attractive nucleus is chaotic in large parts of the high-dimensional phase space. Quantum spectra of two-electron atoms, however, exhibit structures which clearly hint…
The hydrogen atom with the Coulomb interaction is one of the exactly solvable non-relativistic quantum models. Unlike many other exactly solvable models it describes a real physical object providing the formulas for energy levels and…
A simple one dimensional model is introduced describing a two particle "atom" approaching a point at which the interaction between the particles is lost. The wave function is obtained analytically and analyzed to display the entangled…
The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis…
We report analytic solutions of a recently discovered quasi-exactly solvable model consisting of two electrons, interacting {\em via} a Coulomb potential, but restricted to remain on the surface of a $\mathcal{D}$-dimensional sphere.…
Electron-electron interactions and correlations form the basis of difficulties encountered in the theoretical solution of problems dealing with multi-electron systems. Accurate treatment of the electron-electron problem is likely to unravel…
A harmonic oscillator model in four dimensions is presented for the helium atom to estimate the distance to the inner and outer electron from the nucleus, the angle between electrons and the energy levels. The method is algebraic and is not…
We show that a difference in time scales of vertical and lateral dynamics permits one to analyze the problem of interacting electrons confined in an axially symmetric three-dimensional potential with a lateral oscillator confinement by…
Electron-electron correlation forms the basis of difficulties encountered in multi-electron systems. Accurate treatment of the correlation problem is likely to unravel some nice physical properties of matter embedded in this correlation. In…
The concerted motion of two or more bound electrons governs atomic and molecular non-equilibrium processes and chemical reactions. It is thus a long-standing scientific dream to measure the dynamics of two bound correlated electrons in the…
The compressibility of a two-dimensional electron system with spin in a spatially correlated random potential and a quantizing magnetic field is investigated. Electron-electron interaction is treated with the Hartree-Fock method. Numerical…
We study a two dimensional electron system in a parabolic confining potential and constant magnetic field for the case of harmonic electron-electron interaction. We present analytic results for the electrochemical potential versus magnetic…
We study the three-body Coulomb problem in two dimensions and show how to calculate very accurately its quantum properties. The use of a convenient set of coordinates makes it possible to write the Schr\"{o}dinger equation only using…
Recent experiments on the laser-induced resonant annihilation provide a precise measurement of transition energies of antiprotonic helium atoms. Relativistic corrections of an order of $\alpha ^2$ to the pure Coulomb interaction will be…