Improved (1s)2 variational model for helium

• Authors: B. Reed
• Languages of publication: EN

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).

Keywords

EN

Variational technique; helium ground state; 31. 15pf; 31.25Eb

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2005
• Volume: 3
• Issue: 1
• Pages: 1-7

Dates

published

1 - 3 - 2005

online

1 - 3 - 2005

Contributors

author

B. Reed

• Department of Physics, Alma College, 48801, Alma, MI, USA

References

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Identifiers

DOI

10.2478/BF02476500