Padé Approximants and Inner Projections in the Brillouin-Wigner Perturbation Scheme for He-like Ions

G. L. Bendazzoli; O. Goscinski; G. Orlandi

doi:10.1103/PhysRevA.2.2

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Padé Approximants and Inner Projections in the Brillouin-Wigner Perturbation Scheme for He-like Ions

G. L. Bendazzoli^*, O. Goscinski, and G. Orlandi^†

Department of Quantum Chemistry, University of Uppsala, Uppsala, Sweden

^*Present address: Istituto di Chimica Fisica e Spettroscopia, v. Risorgimento 4, Bologna, Italy.
^†Present address: Istituto Chimico G. Ciamician, v. Selini 2, Bologna, Italy.

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Phys. Rev. A 2, 2 – Published 1 July, 1970

DOI: https://doi.org/10.1103/PhysRevA.2.2

Abstract

The continued-fraction expansions in terms of Brillouin-Wigner perturbation energies are evaluated for the He-like series. They show remarkable convergence and stability properties. Both Padé approximants and perturbation energies are computed with formulas derived by the inner-projection technique.

References (23)

L. Brillouin, J. Phys. Radium 4, 1 (1933) E. P. Wigner, Anz. Ungar. Akad. Wiss. 53, 475 (1935)
P. Goldhammer and E. Feenberg, Phys. Rev. 101, 1233 (1956)
R. C. Young, L. C. Biedenharn, and E. Feenberg, Phys. Rev. 106, 1151 (1957)
B. A. Lippman, Phys. Rev. 103, 1149 (1956)
P.-O. Löwdin, Phys. Rev. 139, A357 (1965)
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H. Padé, Thèse Ann. Ecole Nor. 9, Suppl. 1 (1892) G. A. Baker, Jr., Advan. Theoret. Phys. 1, 1 (1965)
O. Goscinski and E. Brändas, in Proceedings of the Vilnius International Symposium, June, 1969 (unpublished) J. Nuttal, Phys. Rev. 157, 1312 (1967)
E. Brändas and O. Goscinski, Phys. Rev. A 1, 552 (1970)
P.-O. Löwdin, in Perturbation Mechanics, edited by C. H. Wilcox (Wiley, New York, 1966), p. 255
O. Goscinski and E. Brändas, Intern. J. Quantum Chem. (to be published)
W. J. Meath and J. O. Hirschfelder, J. Chem. Phys. 41, 1628 (1964)
P. Lindner and P.-O. Löwdin, Intern. J. Quantum Chem. 2S, 161 (1968)
P.-O. Löwdin, J. Chem. Phys. 43, S175 (1965)
J. Midtdal, Phys. Math. Univ. Oslo 32, (1966)
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A. T. Amos (unpublished)
E. Feenberg, Phys. Rev. 103, 1116 (1956)

[c1] L. Brillouin, J. Phys. Radium 4, 1 (1933) E. P. Wigner, Anz. Ungar. Akad. Wiss. 53, 475 (1935)

[c2] P. Goldhammer and E. Feenberg, Phys. Rev. 101, 1233 (1956)

[c3] R. C. Young, L. C. Biedenharn, and E. Feenberg, Phys. Rev. 106, 1151 (1957)

[c4] B. A. Lippman, Phys. Rev. 103, 1149 (1956)

[c5] P.-O. Löwdin, Phys. Rev. 139, A357 (1965)

[c6] O. Goscinski, Intern. J. Quantum Chem. 1, 769 (1967)

[c7] H. Padé, Thèse Ann. Ecole Nor. 9, Suppl. 1 (1892) G. A. Baker, Jr., Advan. Theoret. Phys. 1, 1 (1965)

[c8] O. Goscinski and E. Brändas, in Proceedings of the Vilnius International Symposium, June, 1969 (unpublished) J. Nuttal, Phys. Rev. 157, 1312 (1967)

[c9] E. Brändas and O. Goscinski, Phys. Rev. A 1, 552 (1970)

[c10] P.-O. Löwdin, in Perturbation Mechanics, edited by C. H. Wilcox (Wiley, New York, 1966), p. 255

[c11] O. Goscinski and E. Brändas, Intern. J. Quantum Chem. (to be published)

[c12] W. J. Meath and J. O. Hirschfelder, J. Chem. Phys. 41, 1628 (1964)

[c13] P. Lindner and P.-O. Löwdin, Intern. J. Quantum Chem. 2S, 161 (1968)

[c14] P.-O. Löwdin, J. Chem. Phys. 43, S175 (1965)

[c15] J. Midtdal, Phys. Math. Univ. Oslo 32, (1966)

[c16] E. A. Hylleraas, Z. Physik 54, 347 (1929)

[c17] T. Kinoshita, Phys. Rev. 105, 1490 (1957)

[c18] C. W. Scherr, F. C. Sanders, and R. E. Knight, [10], p. 97 (p. 101)

[c19] J. Hadamard, J. Math. 4, 101 (1892)

[c20] H. Rutishauer, Mitt. Inst. Angew. Math., No. 7 (Birkhauser Verlag, Stuttgart, 1957)

[c21] R. Ahlrichs, Intern. J. Quantum Chem. 4, 149 (1970)

[c22] A. T. Amos (unpublished)

[c23] E. Feenberg, Phys. Rev. 103, 1116 (1956)

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Padé Approximants and Inner Projections in the Brillouin-Wigner Perturbation Scheme for He-like Ions

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