Variational eigenvalues for the S states of helium

Drake, G. W. F.; Yan, Zong-Chao

doi:10.1016/0009-2614(94)01085-4

Cited by 127 publications

(58 citation statements)

References 12 publications

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“…For the test helium calculations the energies are reproduced up to the seventh decimal digit with respect to the nonrelativistic limit [23]. This is an indication that our approach works well for a twoelectron system, giving reason to expect that it will also work well for a system with four electrons.…”

Section: Resultsmentioning

confidence: 88%

Accurate Born–Oppenheimer calculations of the low‐lying c³Σ and a³Σ excited states of helium dimer

Pavanello¹,

Cafiero²,

Bubin³

et al. 2008

Int J of Quantum Chemistry

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Accurate variational Born-Oppenheimer calculations of the two lowest excited ⌺ triplet states of the helium dimer at their respective equilibrium geometries are reported. The wave functions of the states are expanded in terms of explicitly correlated Gaussian functions with shifted centers. The obtained energies are the best variational estimates ever calculated for these states. One-electron densities are also presented and discussed. The results are compared with the experimental values and previous calculations.

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Section: Resultsmentioning

confidence: 88%

Accurate Born–Oppenheimer calculations of the low‐lying c³Σ and a³Σ excited states of helium dimer

Pavanello¹,

Cafiero²,

Bubin³

et al. 2008

Int J of Quantum Chemistry

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“…A comparison of results obtained for the celebrated benchmark case of the He atom is proposed in Table V . [241] 246 −2.9037243770340 Thakkar [242] 308 −2.9037243770341144 Drake [249] 1262 −2.90372437703411948 Goldman [245] 8066 −2.903724377034119594 Korobov [33] 2114 −2.903724377034119598296 Drake [46] 2358 −2.903724377034119598305 Baye [250] 18900 −2.9037243770340…”

Section: Optimisation Of the Parametersmentioning

confidence: 99%

Stability of few-charge systems in quantum mechanics

2005

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We consider non-relativistic systems in quantum mechanics interacting through the Coulomb potential, and discuss the existence of bound states which are stable against spontaneous dissociation into smaller atoms or ions. We review the studies that have been made of specific mass configurations and also the properties of the domain of stability in the space of masses or inverse masses. These rigorous results are supplemented by numerical investigations using accurate variational methods. A section is devoted to systems of three arbitrary charges and another to molecules in a world with two space-dimensions.

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“…slightly below the previous result in [10]. Expectation values of Dirac delta function without and with the mass polarization term are correspondingly:…”

mentioning

confidence: 95%

Hyperfine splitting of 2³S₁state in He³

Pachucki¹

2001

J. Phys. B: At. Mol. Opt. Phys.

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Relativistic corrections to the hyperfine splitting are calculated for the triplet 2 3 S 1 state of the helium isotope He 3 . High precision variational wave functions are employed, where the electron-electron correlations are well accounted for. Due to the unknown nuclear structure a comparison with the experimental result is performed via He 3+ hyperfine splitting. Surprisingly, the second order contribution due to Fermi interaction, in spite of the additional small factor m/M , is very significant. PACS numbers 31

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Variational eigenvalues for the S states of helium

Cited by 127 publications

References 12 publications

Accurate Born–Oppenheimer calculations of the low‐lying c³Σ and a³Σ excited states of helium dimer

Accurate Born–Oppenheimer calculations of the low‐lying c³Σ and a³Σ excited states of helium dimer

Stability of few-charge systems in quantum mechanics

Hyperfine splitting of 2³S₁state in He³

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Variational eigenvalues for the S states of helium

Cited by 127 publications

References 12 publications

Accurate Born–Oppenheimer calculations of the low‐lying c3Σ and a3Σ excited states of helium dimer

Accurate Born–Oppenheimer calculations of the low‐lying c3Σ and a3Σ excited states of helium dimer

Stability of few-charge systems in quantum mechanics

Hyperfine splitting of 23S1state in He3

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Accurate Born–Oppenheimer calculations of the low‐lying c³Σ and a³Σ excited states of helium dimer

Accurate Born–Oppenheimer calculations of the low‐lying c³Σ and a³Σ excited states of helium dimer

Hyperfine splitting of 2³S₁state in He³