相关论文: On $1/Z$ expansion, the critical charge for two-el…
The $1/Z$-expansion for the Coulomb system of infinitely massive center of charge Z and two electrons is discussed. Numerical deficiency in Baker et al, {\em Phys. Rev. \bf A41}, 1247 (1990) is indicated which continue to raise doubts in…
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…
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 $Z_{B}^{\infty}\ =\ 0.904854$…
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…
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…
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 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…
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 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…
We prove that the ground state energy of an atom confined to two dimensions with an infinitely heavy nucleus of charge $Z>0$ and $N$ quantum electrons of charge -1 is $E(N,Z)=-{1/2}Z^2\ln Z+(E^{\TF}(\lambda)+{1/2}c^{\rm H})Z^2+o(Z^2)$ when…
The Schroedinger equation for two electrons in the field of a charged fixed center $Z$ is solved with the Lagrange mesh method for charges close to the critical charge $Z_{cr}$. We confirm the value of the nuclear critical charge $Z_{cr}$…
The Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B \textbf{30}, 825 (1997); \textbf{30}, 2747(E) (1997)] is exploited to derive a closed-form expression for the magnetizability of the…
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…
The ground-state energy and the density correlation function of the electron liquid in a thin one-dimensional wire are computed. The calculation is based on an approximate mapping of the problem with a realistic Coulomb interaction law onto…
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…
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…
Following detailed analysis of relativistic, QED and mass corrections for helium-like and lithium-like ions with static nuclei for $Z \leq 20$ the domain of applicability of Non-Relativistic QED (NRQED) is localized for ground state energy.…
Extensive variational computations are reported for the ground state energy of the non-relativistic two-electron atom. Several different sets of basis functions were systematically explored, starting with the original scheme of Hylleraas.…
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 to the Lamb shift of hydrogen-like ions is calculated for the $1s$, $2s$, and $2p_{1/2}$ states and nuclear charge numbers $Z = 30$-$100$. The calculation is performed to all orders in the nuclear binding…