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Transfer of excitation energy between the upper states of the helium atom

S. A. Bagaev, O. V. Oginets, Valerii B Smirnov +1 more

Optics and SpectroscopyJun 1, 19790 citations

Bound states of interacting helium atoms

Stefan V. Mashkevich, S. I. Vilchynskyy

arXiv:cond-mat/9911176Journal of Molecular LiquidsSep 1, 20011 citation

CALCULATION OF THE ENERGY OF ONE-AND TWO-ELECTRON ATOMS IN SPACES OF THREE OR FEWER DIMENSIONS

skobelev skobelev

Abstract: The well-known variation method of calculating the total energy of a two-electron atom is generalized to the case of any set of quantum numbers of electrons in spaces of three or fewer dimensions, yielding the corresponding expressions for energy and screening constant. From these results, the particular cases of the basic and the lowest excited states follow, as earlier considered by us and other authors. We clarify the correct use of these results. Moreover, we generalize the standard relations connecting the average values of kinetic and potential energy with the total energy of an electron in a nucleus field in three dimension for any quantum state and extend it to subspaces of one and two dimensions in a three-dimensional space. The results of this work could be a useful addition to a university course on quantum mechanics.Abstract: The well-known variation method of calculating the total energy of a two-electron atom is generalized to the case of any set of quantum numbers of electrons in spaces of three or fewer dimensions, yielding the corresponding expressions for energy and screening constant. From these results, the particular cases of the basic and the lowest excited states follow, as earlier considered by us and other authors. We clarify the correct use of these results. Moreover, we generalize the standard relations connecting the average values of kinetic and potential energy with the total energy of an electron in a nucleus field in three dimension for any quantum state and extend it to subspaces of one and two dimensions in a three-dimensional space. The results of this work could be a useful addition to a university course on quantum mechanics.

Nov 28, 20180 citations

Energies and Asymptotic Analysis for Helium Rydberg States

G. W. F. Drake

Advances in atomic, molecular, and optical physicsJan 1, 199342 citations

Helium Atom Excitations by the GW and Bethe-Salpeter Many-Body Formalism

Jing Li, Markus Holzmann, Ivan Duchemin +2 more

The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the ab initio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.The helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schrödinger equation is known for helium ground and excited states, and it represents a benchmark for any many-body methodology. Here, we check the ab initio many-body GW approximation and the Bethe-Salpeter equation (BSE) against the exact solution for helium. Starting from the Hartree-Fock method, we show that the GW and the BSE yield impressively accurate results on excitation energies and oscillator strength, systematically improving the time-dependent Hartree-Fock method. These findings suggest that the accuracy of the BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.

arXiv:1611.07456Physical Review LettersApr 17, 201729 citations

Equivalence of a One-Dimensional Fermion Model and the Two-Dimensional Coulomb Gas

S. T. Chui, Patrick A. Lee

We show that the one-dimensional Luttinger model generalized to include spin and backward scattering is equivalent to a two-dimensional Coulomb gas. Scaling equations are derived and correlation functions are given simple physical interpretation in terms of the Coulomb gas; e.g., existence of an energy gap can be understood in terms of Debye screening. We conclude that an energy gap exists for ${U}_{\ensuremath{\parallel}}<|{U}_{\ensuremath{\perp}}|$ so that triplet excitations are nondivergent, and we provide physical arguments to support the exponents proposed by Luther and Emery for singlet excitations for general coupling constant.We show that the one-dimensional Luttinger model generalized to include spin and backward scattering is equivalent to a two-dimensional Coulomb gas. Scaling equations are derived and correlation functions are given simple physical interpretation in terms of the Coulomb gas; e.g., existence of an energy gap can be understood in terms of Debye screening. We conclude that an energy gap exists for ${U}_{\ensuremath{\parallel}}<|{U}_{\ensuremath{\perp}}|$ so that triplet excitations are nondivergent, and we provide physical arguments to support the exponents proposed by Luther and Emery for singlet excitations for general coupling constant.

Physical Review LettersAug 4, 1975137 citations

Energy and Screening Constants of a One-Dimensional Helium Atom in Excited States

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