Related papers: Two-electron atomic systems. A simple method for c…
The two-electron self-energy contribution to the ground state energy of heliumlike ions is calculated both for a point nucleus and an extended nucleus in a wide interval of Z. All the two-electron contributions are compiled to obtain most…
We treat a system (a molecule or a solid) in which electrons are coupled linearly to any number and type of harmonic oscillators and which is further subject to external forces of arbitrary symmetry. With the treatment restricted to the…
Various properties of the general two-center two-electron integral over the explicitly correlated exponential function are analyzed for the potential use in high precision calculations for diatomic molecules. A compact one dimensional…
We derive the photoionisation cross section in dipole approximation for many-electron atoms and ions for neutron star magnetic field strengths in the range of 10^7 to 10^9 T. Both bound and continuum states are treated in adiabatic…
We extend our analysis of two electrons on a sphere [Phys. Rev. A {\bf 79}, 062517 (2009); Phys. Rev. Lett. {\bf 103}, 123008 (2009)] to electrons on concentric spheres with different radii. The strengths and weaknesses of several…
A fully analytical approximation for the observable characteristics of many-electron atoms is developed via a complete and orthonormal hydrogen-like basis with a single-effective charge parameter for all electrons of a given atom. The basis…
A simple, seven-parameter trial function is proposed for a description of the ground state of the Lithium atom. It includes both spin functions. Inter-electronic distances appear in exponential form as well as in a pre-exponential factor,…
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…
A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…
The Fock expansion [1] describes the $S$-state wave function of the two-electron atomic system in the vicinity of the triple coalescence point. The present work constitutes the additional appendix to our paper [2] devoted to refinement and…
Calculations of the two-loop electron self-energy for the $n = 1$ and $n = 2$ states of hydrogen-like ions are reported, performed to all orders in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and…
The non-relativistic interacting electron gas in an external field of positively charged massive cores is dealt with in the scheme of second quantization. Ladder operators that change between stationary states of contiguous energy…
A sixth-order quadrupole boson Hamiltonian is used to describe the states $0^+$ and $2^+$ identified in several nuclei by various types of experiments. Two alternative descriptions of energy levels are proposed. One corresponds to a…
The rigorous two-center approach based on the dual-kinetically balanced finite-basis-set expansion is applied to one-electron, heteronuclear diatomic Bi-Au, U-Pb, and Cf-U quasimolecules. The obtained $1\sigma$ ground-state energies are…
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…
Most modern calculations of many-electron atoms use basis sets of atomic orbitals. An accurate account for the electronic correlations in heavy atoms is very difficult computational problem and optimization of the basis sets can reduce…
Exact ground-state properties are presented by combining the diagonalization in the Fock space (and taking all hopping integrals and all two-site interactions) with the ab initio optimization of the Wannier functions. Electrons are…
The structure of approximate two electron wavefunction is deeply investigated, both theoretically and numerically, in the strong-field driven ionization dynamics. Theoretical analyses clarify that for two electron singlet systems, the…
A new type of basis functions is proposed to describe a two-electron continuum which arises as a final state in electron-impact ionization and double photoionization of atomic systems. We name these functions, which are calculated in terms…
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$^-$,…