Related papers: On 1/Z expansion for two-electron systems
The $1/Z$-expansion for the ground state energy of the Coulomb system of an infinitely massive center of charge Z and two electrons (two electron ionic sequence) is studied. A critical analysis of the $1/Z$ coefficients presented in Baker…
Let us consider some Coulomb systems of several infinitely massive centers of charge Z and one-two electrons: $(Z,e)$, $(2Z,e)$, $(3Z,e)$, $(4Z,e)$, $(2Z,e,e)$, $(3Z,e,e)$. It is shown that the physical, integer charges $Z=1,2,...$ do not…
Results of our recent highly accurate computations of the Coulomb two-center systems with the unit electrical charges $X^{+} X^{+} e^{-}$ and $X^{+} Y^{+} e^{-}$ are discussed. In particular, we have determined (to very high accuracy) the…
The second (unphysical) critical charge in the 3-body quantum Coulomb system of a nucleus of positive charge $Z$ and mass $m_p$, and two electrons, predicted by F~Stillinger has been calculated to be equal to $Z_{B}^{\infty}\ =\ 0.904854$…
We consider a model of three electrons and one hole confined in a two-dimensional (2D) plane, interacting with one another through Coulomb forces. Using a Ritz variational method we find an upper bound of \approx -0.0112me^4/8\pi^2 \epsilon…
In non-relativistic quantum mechanics we study the Coulomb systems of infinitely massive center of charge Z and two-three electrons: $(Z,e,e)$ and $(Z,e,e,e)$. It is shown that in both cases the total energy curve in $Z$ is smooth, without…
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…
Accurate mass-interpolation and mass-asymptotic formulas are derived for one- and two-center three-body ions with unit charges. The derived formulas are applied to predict accurate numerical values of the total energies of the ground…
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…
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…
We propose a simple and efficient real-space approach for the calculation of the ground-state energies of Wigner crystals in 1, 2, and 3 dimensions. To be precise, we calculate the first two terms in the asymptotic expansion of the total…
The total energies of a large number of diatomic (or two-center) one-electron $A^{+} B^{+} e^{-}$ ions with unit electrical charges are determined numerically to high accuracy. Based on these results we derive some accurate…
We provide the first counterexample showing that the ground state energy of electrons in an external Coulomb potential is not always a convex function of the number of electrons. This convexity has been conjectured for decades and plays an…
Accurate QED calculations of the interelectron interaction corrections for the $(1s2p)2 {}^1 P_1$, $(1s2p)2 {}^3 P_1$ two-electron configurations for ions with nuclear charge numbers $10\le Z \le 92$ are performed within the line profile…
The two-loop self-energy correction is evaluated to all orders in Z alpha for the ground-state Lamb shift of H-like ions with Z >= 20, where Z is the nuclear charge number and alpha is the fine structure constant. The results obtained are…
We consider systems of two and three electrons in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the electron plane of motion. We show that the energy levels corresponding to states with high angular…
Elaborating on a previous letter, we use a new approach to compute energy levels of a non-relativistic bound-state of two constituents, with masses m and M, by systematic expansions - one in powers of m/M and another in powers of (1-m/M).…
A novel Gaussian-Sinc mixed basis set for the calculation of the one-electron electronic structure within a uniform magnetic field in three dimensions is presented. The one-electron system is used to demonstrate the utility of this new…
Ground-state energies of the one- and two-electron uranium dimers are calculated for internuclear distances in the range D=40--1000 fm and compared with the previous calculations. The generalization of the dual-kinetic-balance approach for…
Accurate QED evaluations of the one- and two-photon interelectron interaction for low lying two- and three-electron configurations for ions with nuclear charge numbers $60\le Z \le 93$ are performed. The three-photon interaction is also…