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Volumn 59, Issue 2, 1999, Pages 1109-1124

Large-dimension limit of higher-angular-momentum states of two-electron atoms

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EID: 0012620030     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.59.1109     Document Type: Article
Times cited : (16)

References (261)
  • 1
    • 0003490890 scopus 로고    scopus 로고
    • Kluwer, Dordrecht
    • Dimensional Scaling in Chemical Physics, edited by D. R. Herschbach, J. Avery, and O. Goscinski (Kluwer, Dordrecht, 1993).
    • (1993) Dimensional Scaling in Chemical Physics
  • 3
    • 85037210747 scopus 로고    scopus 로고
    • New Methods in Quantum Theory, edited by C. A. Tsipis, V. S. Popov, D. R. Herschbach, and J. Avery Vol. 8 of NATO Advanced Science Institutes Series, Partnership Sub-Series 3 (Kluwer, Dordrecht, 1996)
    • New Methods in Quantum Theory, edited by C. A. Tsipis, V. S. Popov, D. R. Herschbach, and J. Avery Vol. 8 of NATO Advanced Science Institutes Series, Partnership Sub-Series 3 (Kluwer, Dordrecht, 1996).
  • 9
    • 36049054483 scopus 로고
    • Phys. Rev.H. E. Stanley, 176, 718 (1968)
    • (1968) , vol.176 , pp. 718
    • Stanley, H.E.1
  • 18
    • 84953681835 scopus 로고    scopus 로고
    • Recent Developments in Gauge Theories, Vol. 59 of NATO Advanced Study Institute Series B: Physics, edited by G. t’Hooft et al. (Plenum, New York, 1980)
    • E. Witten, Phys. Today 33(7), 38 (1980);Recent Developments in Gauge Theories, Vol. 59 of NATO Advanced Study Institute Series B: Physics, edited by G. t’Hooft et al. (Plenum, New York, 1980).
    • Phys. Today , vol.33 , pp. 38
    • Witten, E.1
  • 21
    • 85037251223 scopus 로고    scopus 로고
    • J. G. Loeser and D. R. Herschbach in New Methods in Quantum Theory (Ref
    • J. G. Loeser and D. R. Herschbach in New Methods in Quantum Theory (Ref. 3), pp. 1–32.
  • 50
    • 0002908707 scopus 로고
    • V. S. Popov, Phys. Lett. A 173, 63 (1993). The above papers use the (Formula presented) expansion, where (Formula presented) is the principal quantum number. However, this is equivalent to perturbation theory about the (Formula presented) limit, since (Formula presented), and the parabolic quantum numbers (Formula presented) and (Formula presented) are held fixed. As in Ref. 65, angular momentum and dimensionality enter into the one-electron Schrödinger equation in equivalent and interchangeable ways 19, and so the (Formula presented) expansion is also equivalent to dimensional perturbation theory about the (Formula presented) limit.
    • (1993) Phys. Lett. A , vol.173 , pp. 63
    • Popov, V.S.1
  • 63
    • 85037255668 scopus 로고    scopus 로고
    • D. Z. Goodson and D. K. Watson in Dimensional Scaling in Chemical Physics (Ref
    • D. Z. Goodson and D. K. Watson in Dimensional Scaling in Chemical Physics (Ref. 1), pp. 359–374.
  • 65
    • 85037185351 scopus 로고    scopus 로고
    • V. S. Popov in New Methods in Quantum Theory (Ref
    • V. S. Popov in New Methods in Quantum Theory (Ref. 3), pp. 149–182.
  • 81
    • 85037227503 scopus 로고    scopus 로고
    • J. G. Loeser in New Methods in Quantum Theory (Ref
    • J. G. Loeser in New Methods in Quantum Theory (Ref. 3), pp. 33–54.
  • 83
    • 0001049217 scopus 로고
    • C. M. Bender, L. D. Mlodinow, and N. Papanicolaou, Phys. Rev. A 25, 1305 (1982). An expansion is developed about the (Formula presented) limit in powers of (Formula presented). Since angular momentum and dimensionality enter into the one-electron Schrödinger equation in equivalent and interchangeable ways 19, this expansion is equivalent to dimensional perturbation theory about the (Formula presented) limit.
    • (1982) Phys. Rev. A , vol.25 , pp. 1305
    • Bender, C.M.1    Mlodinow, L.D.2    Papanicolaou, N.3
  • 90
    • 1142303090 scopus 로고
    • Dimensional Scaling in Chemical Physics (Ref
    • V. M. Vaǐnberg, V. S. Popov, and A. V. Sergeev, Zh. Éksp. Teor. Fiz. 98, 847 (1990) [Sov. Phys. JETP 71, 470 (1990)];and in Dimensional Scaling in Chemical Physics (Ref. 1), pp. 217–229.
    • (1990) Sov. Phys. JETP , vol.71 , pp. 470
    • Vaǐnberg, V.M.1    Popov, V.S.2    Sergeev, A.V.3
  • 98
  • 106
    • 0001585728 scopus 로고
    • Phys. Rev. AA. Z. Tang and F. T. Chan, 35, 911 (1987)
    • (1987) , vol.35 , pp. 911
    • Tang, A.Z.1    Chan, F.T.2
  • 109
    • 0000300246 scopus 로고
    • Phys. Rev. AY. P. Varshni38, 1595 (1988)
    • (1988) , vol.38 , pp. 1595
    • Varshni, Y.P.1
  • 110
    • 25044445993 scopus 로고
    • Phys. Rev. AY. P. Varshni40, 2180 (1989)
    • (1989) , vol.40 , pp. 2180
    • Varshni, Y.P.1
  • 113
    • 0001194145 scopus 로고
    • Phys. Rev. AR. Sever and C. Tezcan, 36, 1045 (1987)
    • (1987) , vol.36 , pp. 1045
    • Sever, R.1    Tezcan, C.2
  • 114
    • 0011470230 scopus 로고
    • Phys. Rev. AE. Papp, 36, 3550 (1987)
    • (1987) , vol.36 , pp. 3550
    • Papp, E.1
  • 115
    • 25044451556 scopus 로고
    • Phys. Rev. AE. Papp38, 2158 (1988)
    • (1988) , vol.38 , pp. 2158
    • Papp, E.1
  • 131
    • 33745503492 scopus 로고
    • J. Phys. AA. Chatterjee19, 3707 (1986)
    • (1986) , vol.19 , pp. 3707
    • Chatterjee, A.1
  • 133
    • 0011495521 scopus 로고
    • Phys. Rev. AŞ. Erkoç and R. Sever, 33, 588 (1986)
    • (1986) , vol.33 , pp. 588
    • Erkoç, Ş.1    Sever, R.2
  • 139
    • 0011452973 scopus 로고
    • Phys. Rev. AR. Sever and C. Tezcan, 35, 2725 (1987)
    • (1987) , vol.35 , pp. 2725
    • Sever, R.1    Tezcan, C.2
  • 140
    • 4243973555 scopus 로고
    • Phys. Rev. AR. SeverC. Tezcan37, 3158 (1988)
    • (1988) , vol.37 , pp. 3158
    • Sever, R.1    Tezcan, C.2
  • 148
    • 0003484762 scopus 로고
    • Kluwer, Dordrecht and in Dimensional Scaling in Chemical Physics (Ref
    • J. Avery, Hyperspherical Harmonics (Kluwer, Dordrecht, 1989);and in Dimensional Scaling in Chemical Physics (Ref. 1), pp. 139–164.
    • (1989) Hyperspherical Harmonics
    • Avery, J.1
  • 156
    • 0001378360 scopus 로고
    • J. Mol. Spectrosc.J. Louck and W. H. Shaffer, 4, 285 (1960)
    • (1960) , vol.4 , pp. 285
    • Louck, J.1    Shaffer, W.H.2
  • 157
    • 0037685647 scopus 로고
    • J. Mol. Spectrosc.J. Louck, 4, 298 (1960)
    • (1960) , vol.4 , pp. 298
    • Louck, J.1
  • 158
    • 0345998574 scopus 로고
    • J. Mol. Spectrosc.J. Louck4, 334 (1960).
    • (1960) , vol.4 , pp. 334
    • Louck, J.1
  • 169
    • 84911751868 scopus 로고
    • V. D. Mur and V. S. Popov, Pis’ma Zh. Éksp. Teor. Fiz. 45, 323 (1987) [JETP Lett. 45, 410 (1987)];
    • (1987) JETP Lett. , vol.45 , pp. 410
    • Mur, V.D.1    Popov, V.S.2
  • 209
    • 85037182449 scopus 로고    scopus 로고
    • M. O. Moelout and D. Z. Goodson (private communication). A tenth-order dimensional perturbation theory calculation of the lithium atom.
    • Moelout, M.O.1    Goodson, D.Z.2
  • 211
    • 0011511741 scopus 로고
    • Phys. Rev. AN. H. March, 30, 2936 (1984)
    • (1984) , vol.30 , pp. 2936
    • March, N.H.1
  • 212
    • 25044476156 scopus 로고
    • Phys. Rev. AN. H. March34, 5106 (1986)
    • (1986) , vol.34 , pp. 5106
    • March, N.H.1
  • 214
    • 0042151197 scopus 로고
    • J. Math. Phys. (N.Y.)D. A. Morales, 35, 3916 (1994).
    • (1994) , vol.35 , pp. 3916
    • Morales, D.A.1
  • 230
    • 85037188540 scopus 로고    scopus 로고
    • J. D. Morgan III, in Dimensional Scaling in Chemical Physics, (Ref
    • J. D. Morgan III, in Dimensional Scaling in Chemical Physics, (Ref. 131), p. 354.
  • 231
    • 0004109271 scopus 로고
    • Princeton University Press, Princeton
    • H. Weyl, The Classical Groups (Princeton University Press, Princeton, 1939).
    • (1939) The Classical Groups
    • Weyl, H.1
  • 232
    • 85037227217 scopus 로고    scopus 로고
    • H. Boerner, Representations of Groups (North-Holland, Amsterdam,1963). Although it does not explicitly discuss the application of the method of irreducible tensors to O(Formula presented), the discussion of the general principles is quite accessible.
    • Boerner, H.1
  • 238
    • 85037215997 scopus 로고    scopus 로고
    • A simplified, heuristic account of this work for the two-electron problem by the present authors may be found in Dimensional Scaling in Chemical Physics (Ref
    • A simplified, heuristic account of this work for the two-electron problem by the present authors may be found in Dimensional Scaling in Chemical Physics (Ref. 1), pp. 375–388.
  • 242
    • 85037222285 scopus 로고    scopus 로고
    • The power series expansion is often written (see, e.g., Refs
    • The power series expansion is often written (see, e.g., Refs. 3135), (Formula presented) In this case (Formula presented) is no longer the zeroth-order energy, but the coefficient of the first-order energy correction. However, due to the singular nature of the expansion point, this energy contribution does derive from the zeroth-order wave function (Formula presented) [see Eq. (43)].
  • 246
    • 85037196057 scopus 로고    scopus 로고
    • See also A. A. Suvernev and D. Z. Goodson, Chem. Phys. Lett. (to be published); and (unpublished)
    • See also A. A. Suvernev and D. Z. Goodson, Chem. Phys. Lett. (to be published);and (unpublished).
  • 249
    • 4243634756 scopus 로고
    • Phys. Rev. Lett.M. E. Kellman73, 2543 (1994).
    • (1994) , vol.73 , pp. 2543
    • Kellman, M.E.1
  • 251
    • 0001858325 scopus 로고
    • Review of Fundamental Processes and Applications of Atoms and Ions, edited by C.D. Lin (World Scientific, Singapore, 1993), pp. 357–401
    • C. D. Lin, Adv. At. Mol. Phys. 22, 77 (1986);and in Review of Fundamental Processes and Applications of Atoms and Ions, edited by C.D. Lin (World Scientific, Singapore, 1993), pp. 357–401;
    • (1986) Adv. At. Mol. Phys. , vol.22 , pp. 77
    • Lin, C.D.1
  • 252
    • 0040832977 scopus 로고
    • Phys. Rep. 257, 1 (1995)
    • (1995) Phys. Rep. , vol.257 , pp. 1
  • 255
    • 0343186403 scopus 로고
    • Dimensional Scaling in Chemical Physics (Ref
    • R. S. Berry, Contemp. Phys. 30, 1 (1989);and in Dimensional Scaling in Chemical Physics (Ref. 1), pp. 485–498.
    • (1989) Contemp. Phys. , vol.30 , pp. 1
    • Berry, R.S.1
  • 258
    • 0001549528 scopus 로고
    • Dimensional Scaling in Chemical Physics (Ref
    • J. M. Rost and J. S. Briggs, J. Phys. B 24, 4293 (1991);and in Dimensional Scaling in Chemical Physics (Ref. 1), pp. 471–484, and references therein.
    • (1991) J. Phys. B , vol.24 , pp. 4293
    • Rost, J.M.1    Briggs, J.S.2
  • 260
    • 85037246081 scopus 로고    scopus 로고
    • H. Weyl, The Classical Groups [Ref
    • H. Weyl, The Classical Groups [Ref. 135, Theorem (5.7.A) p. 154].


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