Energy levels of a helium atom

Aznabayev, D.; Bekbaev, A. K.; Ishmukhamedov, I. S.; Korobov, V. I.

doi:10.1134/s1547477115050040

Cited by 12 publications

(23 citation statements)

References 11 publications

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“…The nonrelativistic energies of the (singlet) (1s) 2 ground state and of the first-excited triplet 1s2s state of the helium atom in 3D are known with an excellent precision: in Ref. [44] they are calculated with 20 significant digits. We only write here the first of them:…”

Section: Exact Results In 3dmentioning

confidence: 99%

Electron exchange energy of neutral donors inside a quantum well

et al. 2018

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We calculated the exchange energy of a pair of donor-bound electrons placed in the middle of an infinite quantum well (QW). In order to obtain this energy for any interdonor distance and for any QW thickness, we have first adapted to a QW the method developed by Gor'kov and Pitaevskii [L. P. Gor'kov and L. P. Pitaevskii, Dokl. Akad. Nauk SSSR 151, 822 (1963)] for a three-dimensional (3D) distribution of donors, and calculated the asymptotic form of the exchange energy. Second we have calculated the exchange energy of a "helium atom" in a QW; and third, inspired by the interpolation procedure proposed by Ponomarev et al. [I.V. Ponomarev et al., Phys. Rev. B 60, 5485 (1999)], we have obtained an interpolated expression for any interdonor distance. The obtained exchange energy is written in units of effective hartree, and the distance between the donors, as well as the width of the QW, are expressed in units of effective Bohr radius. We calculated the exchange energy for some commonly studied semiconductor materials, and discussed also the relationship between the exchange energy and the spin relaxation time for a donor concentration close to the insulator-metal transition.

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Section: Exact Results In 3dmentioning

confidence: 99%

Electron exchange energy of neutral donors inside a quantum well

et al. 2018

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“…See, for example, Harris et al [ 44 ] for how to handle these cases §§§§ . While this recursion is potentially unstable due to the negative signs in the recursion, the conditions on L lead to a severely limited range of L, which restricts the places where differencing errors can occur to the well‐studied l < 0 case [ 42,50 ] and this recursion which appears to be the same as the Efros [ 49 ] recursion used effectively for He by Aznabayev et al [ 51 ]…”

Section: Methods Of Calculationmentioning

confidence: 99%

“…The results are presented in Table 1 to an accuracy that all three methods agreed upon. All of the calculations in this work were performed by the second method, that is, evaluating I 0 using Equations ) and () and then using the recursion formula Equation ) to recur to higher L values because the same or similar Efros [ 49 ] recursion has been used very effectively for He by Aznabayev et al [ 51 ]…”

Section: Methods Of Calculationmentioning

confidence: 99%

Exponentially correlated Hylleraas‐configuration interaction nonrelativistic energy of the ¹S ground state of the helium atom

Sims

Padhy²,

Ruiz

2020

Int J of Quantum Chemistry

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A generalization of the Hylleraas‐configuration interaction method (Hy‐CI) first proposed in a previous study, the exponentially correlated Hylleraas‐configuration interaction method (E‐Hy‐CI) in which the single rij of an Hy‐CI wave function is generalized to a form of the generic type , is explored. This type of correlation, suggested by Hirshfelder in 1960, has the right behavior in the vicinity of both the rij cusp as rij goes to 0 and as rij goes to infinity; this work explores whether wave functions containing both linear and exponential rij factors converge more rapidly than either one alone. The method of calculation of the two‐electron E‐Hy‐CI kinetic energy and electron repulsion integrals in a stable and efficient way using recursion relations is discussed, and the relevant formulas are given. The convergence of the E‐Hy‐CI wave function expansion is compared with that of the Hy‐CI wave function without exponential correlation factors, demonstrating both convergence acceleration and an improvement in the accuracy for the same basis. This makes the application of the E‐Hy‐CI method to systems with N > 4, for which this formalism with at most a single factor per term leads to solvable integrals, very promising. E‐Hy‐CI method variational calculations with up to 10,080 expansion terms are reported for the ground 1S state of the neutral helium atom, with a resultant nonrelativistic energy of −2.9037 2437 7034 1195 9831 1084 hartree for the best expansion.

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“…All calculations for the Helium atom were conducted in atomic units. Since we have taken the results of [54] as benchmark results for atomic Helium energies, infinite (10 15 a.u. in practice) Helium core mass was used in the calculations as in [54].…”

Section: Examplesmentioning

confidence: 99%

Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation via Spline Collocation and Tensor Product Preconditioning

Gradusov¹

2021

CICP

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The computational approach for solving the Faddeev-Merkuriev equations in total orbital momentum representation is presented. These equations describe a system of three quantum charged particles and are widely used in bound state and scattering calculations. The approach is based on the spline collocation method and exploits intensively the tensor product form of discretized operators and preconditioner, which leads to a drastic economy in both computer resources and time.

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Energy levels of a helium atom

Cited by 12 publications

References 11 publications

Electron exchange energy of neutral donors inside a quantum well

Electron exchange energy of neutral donors inside a quantum well

Exponentially correlated Hylleraas‐configuration interaction nonrelativistic energy of the ¹S ground state of the helium atom

Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation via Spline Collocation and Tensor Product Preconditioning

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Energy levels of a helium atom

Cited by 12 publications

References 11 publications

Electron exchange energy of neutral donors inside a quantum well

Electron exchange energy of neutral donors inside a quantum well

Exponentially correlated Hylleraas‐configuration interaction nonrelativistic energy of the 1S ground state of the helium atom

Solving the Faddeev-Merkuriev Equations in Total Orbital Momentum Representation via Spline Collocation and Tensor Product Preconditioning

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Exponentially correlated Hylleraas‐configuration interaction nonrelativistic energy of the ¹S ground state of the helium atom