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## Open Physics

2005 | 3 | 1 | 1-7
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### Improved (1s)2 variational model for helium

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Abstracts
EN
The ground-state energy of neutral helium is estimated variationally with a trial wavefunction of the form ϕ≈e
−γ(rA/a
o)ne−γ(rB/a
o)n. This model represents a modification of traditional textbook examinations of this problem via inclusion of the power “n” as a second nonlinear variational parameter in addition to the usual effective nuclear charge γ and leads to an upper-limit on the ground state energy of −2.86107 Eh (Eh=1 hartree) in comparison with the traditional (n=1) result of −2.84766 Eh. This result represents a reduction of the percentage overestimate from the true ground-state energy (−2.90373 Eh) of from 1.93 to 1.47. In comparison with the maximum accuracy obtainable from an uncorrelated trial wavefunction, −2.86168 Eh, the present trial wavefunction reduces the percentage overestimate from 0.49 (n=1) to 0.021. The optimum values of (n, γ) are determined to be ≈(0.897, 1.825).
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1-7
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published
1 - 3 - 2005
online
1 - 3 - 2005
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• Department of Physics, Alma College, 48801, Alma, MI, USA, reed@alma.edu
References
• [1] E. Hylleraas and J. Midtdal: “Ground State Energy of Two-Electron Atoms”,Phys. Rev., Vol. 103, (1956), pp. 829–830. http://dx.doi.org/10.1103/PhysRev.103.829[Crossref]
• [2] L. Pauling and E.B. Wilson, Jr.:Introduction to Quantum Mechanics With Applications to Chemistry, Dover, New York, 1985, sect. 29.
• [3] H.A. Bethe and E.E. Salpeter:Quantum Mechanics of One and Two-Electron Atoms, Academic Press, New York, 1957), sect. II.
• [4] C.L. Pekeris: “Ground State of Two-Electron Atoms”,Phys. Rev., Vol. 112, (1958), pp. 1649–1658. http://dx.doi.org/10.1103/PhysRev.112.1649[Crossref]
• [5] C.L. Pekeris: “11S and 23S States of Helium”,Phys. Rev., Vol. 115, (1959), pp. 1216–1221. http://dx.doi.org/10.1103/PhysRev.115.1216[Crossref]
• [6] S.P. Goldman: “Uncoupling correlated calculations in atomic physics: Very high accuracy and ease”,Phys. Rev., Vol. A 57, (1998), pp. R677-R680.
• [7] F.L. Pilar:Elementary Quantum Chemistry, 2nd Ed., Dover, New York, 2001, Ch. 6.
• [8] T. Koga: “Radial correlation limits of helium and heliumlike atoms”,Z. Phys. D.,Vol.,37, (1996),pp.301–303. http://dx.doi.org/10.1007/s004600050044[Crossref]
• [9] G. Arfken:Mathematical Methods for Physicists, 3rd. Ed., Academic Press, Orlando, 1985, Ch, 10.
• [10] I.S. Gradshteyn and I.M. Ryzhik:Table of Integrals, Series, and Products, 5th Ed., Academic Press, New York, 1994, p. 364.
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