Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model

Li Yan Tang, Yong-Bo Tang, Ting-Yun Shi, James Mitroy

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    The Dirac-Coulomb equation for the helium atom is studied under the restrictions of the Poet-Temkin model which replaces the 1/r12 interaction by the simplified 1/r> form. The effective reduction in the dimensionality made it possible to obtain binding energies for the singlet and triplet states in this model problem with a relative precision from 10-8 to 10-10. The energies for the singlet state were consistent with a previous configuration interaction calculation [H. Tatewaki and Y. Watanabe, Chem. Phys. 389, 58 (2011)]. Manifestations of Brown-Ravenhall disease were noted at higher values of nuclear charge and ultimately limited the accuracy of the Poet-Temkin model energy. The energies from a no-pair configuration interaction (CI) calculation (the negative-energy states for the appropriate hydrogen-like ion were excluded from the CI expansion) were found to be different from the unrestricted B-spline calculation. � 2013 AIP Publishing LLC.
    Original languageEnglish
    Pages (from-to)134112-1-134112-8
    Number of pages8
    JournalJournal of Chemical Physics
    Volume139
    DOIs
    Publication statusPublished - 3 Oct 2013

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    Helium
    helium ions
    Ions
    configuration interaction
    Binding energy
    Splines
    Electron energy levels
    energy
    Hydrogen
    helium atoms
    splines
    hydrogen ions
    atomic energy levels
    Atoms
    constrictions
    binding energy
    expansion
    interactions

    Cite this

    Tang, Li Yan ; Tang, Yong-Bo ; Shi, Ting-Yun ; Mitroy, James. / Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model. In: Journal of Chemical Physics. 2013 ; Vol. 139. pp. 134112-1-134112-8.
    @article{8318afec766a44b696f682147c6cde48,
    title = "Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model",
    abstract = "The Dirac-Coulomb equation for the helium atom is studied under the restrictions of the Poet-Temkin model which replaces the 1/r12 interaction by the simplified 1/r> form. The effective reduction in the dimensionality made it possible to obtain binding energies for the singlet and triplet states in this model problem with a relative precision from 10-8 to 10-10. The energies for the singlet state were consistent with a previous configuration interaction calculation [H. Tatewaki and Y. Watanabe, Chem. Phys. 389, 58 (2011)]. Manifestations of Brown-Ravenhall disease were noted at higher values of nuclear charge and ultimately limited the accuracy of the Poet-Temkin model energy. The energies from a no-pair configuration interaction (CI) calculation (the negative-energy states for the appropriate hydrogen-like ion were excluded from the CI expansion) were found to be different from the unrestricted B-spline calculation. � 2013 AIP Publishing LLC.",
    keywords = "Configuration-interaction calculations, Dirac-Coulomb equation, Helium-like ion, Hydrogenlike ion, Model problems, Negative-energy state, Nuclear charges, Singlet and triplet state, Binding energy, Helium",
    author = "Tang, {Li Yan} and Yong-Bo Tang and Ting-Yun Shi and James Mitroy",
    year = "2013",
    month = "10",
    day = "3",
    doi = "10.1063/1.4823486",
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    Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model. / Tang, Li Yan; Tang, Yong-Bo; Shi, Ting-Yun; Mitroy, James.

    In: Journal of Chemical Physics, Vol. 139, 03.10.2013, p. 134112-1-134112-8.

    Research output: Contribution to journalArticleResearchpeer-review

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    T1 - Solution of the Dirac Coulomb equation for helium-like ions in the Poet-Temkin model

    AU - Tang, Li Yan

    AU - Tang, Yong-Bo

    AU - Shi, Ting-Yun

    AU - Mitroy, James

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    N2 - The Dirac-Coulomb equation for the helium atom is studied under the restrictions of the Poet-Temkin model which replaces the 1/r12 interaction by the simplified 1/r> form. The effective reduction in the dimensionality made it possible to obtain binding energies for the singlet and triplet states in this model problem with a relative precision from 10-8 to 10-10. The energies for the singlet state were consistent with a previous configuration interaction calculation [H. Tatewaki and Y. Watanabe, Chem. Phys. 389, 58 (2011)]. Manifestations of Brown-Ravenhall disease were noted at higher values of nuclear charge and ultimately limited the accuracy of the Poet-Temkin model energy. The energies from a no-pair configuration interaction (CI) calculation (the negative-energy states for the appropriate hydrogen-like ion were excluded from the CI expansion) were found to be different from the unrestricted B-spline calculation. � 2013 AIP Publishing LLC.

    AB - The Dirac-Coulomb equation for the helium atom is studied under the restrictions of the Poet-Temkin model which replaces the 1/r12 interaction by the simplified 1/r> form. The effective reduction in the dimensionality made it possible to obtain binding energies for the singlet and triplet states in this model problem with a relative precision from 10-8 to 10-10. The energies for the singlet state were consistent with a previous configuration interaction calculation [H. Tatewaki and Y. Watanabe, Chem. Phys. 389, 58 (2011)]. Manifestations of Brown-Ravenhall disease were noted at higher values of nuclear charge and ultimately limited the accuracy of the Poet-Temkin model energy. The energies from a no-pair configuration interaction (CI) calculation (the negative-energy states for the appropriate hydrogen-like ion were excluded from the CI expansion) were found to be different from the unrestricted B-spline calculation. � 2013 AIP Publishing LLC.

    KW - Configuration-interaction calculations

    KW - Dirac-Coulomb equation

    KW - Helium-like ion

    KW - Hydrogenlike ion

    KW - Model problems

    KW - Negative-energy state

    KW - Nuclear charges

    KW - Singlet and triplet state

    KW - Binding energy

    KW - Helium

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