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Atoms in Astrophysics pp 173–220Cite as

Application of Quantam Defect Theory

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Abstract

We follow the evolution of quantum defect theory and its applications from the 1960’s to the present. The merits and practical usefulness of quantum defect methods are discussed. On most topics, we only give a general discussion and refer the reader to the literature, but some illustrative examples are given in great detail.

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References

  1. D. R. Hartree, The Calculation of Atomic Structure, Wiley, New York, 1957.

    Google Scholar 

  2. F. B. Ham, in Solid State Physics, Vol. 1, F. Seitz and D. Turnbull, Eds., Academic, New York, 1955, pp. 127–192.

    Google Scholar 

  3. M. J. Seaton, The quantum defect method, Mon. Not. R. Astron. Soc. 118, 504–518 (1958).

    MathSciNet  ADS  MATH  Google Scholar 

  4. M. J. Seaton, Quantum defect theory I. General formulation, Proc. Phys. Soc. 88, 801–814 (1966).

    Google Scholar 

  5. M. J. Seaton, Quantum defect theory II. Illustrative one-channel and two-channel problems, Proc. Phys. Soc. 88, 815–832 (1966).

    Google Scholar 

  6. O. Bely, Quantum defect theory III. Electron scattering by He +, Proc. Phys. Soc. 88, 833–842 (1966).

    Google Scholar 

  7. D. L. Moores, Quantum defect theory IV. The absorption of radiation by calcium atoms, Proc. Phys. Soc. 88, 843–859 (1966).

    Article  ADS  Google Scholar 

  8. D. L. Moores, Quantum defect theory V. Autonionizing and bound states of the neutral beryllium atom, Proc. Phys. Soc. 91, 830–841 (1967).

    Article  ADS  Google Scholar 

  9. N. A. Doughty, M. J. Seaton, and V. B. Sheorey, Quantum defect theory VI. Extrapolations along isoelectronic sequences, J. Phys. B 1, 802–812 (1968).

    Article  ADS  Google Scholar 

  10. M. J. Seaton, Quantum defect theory VII. Analysis of resonance structures, J. Phys. B 2, 5–11 (1969).

    Article  ADS  Google Scholar 

  11. P. de A. P. Martins and M. J. Seaton, Quantum defect theory VIII. Resonances in the collision strengths for O+2p 3 2 D 3/2 - 2 D 5/2 , J. Phys. B 2, 333–340 (1969).

    Article  ADS  Google Scholar 

  12. D. W. Norcross and M. J. Seaton, Quantum defect theory IX. Complex quantum defects for the e-Be+system, J. Phys. B 3, 579–584 (1970).

    Article  ADS  Google Scholar 

  13. J. Dubau and J. Wells, Quantum defect theory X. Photoionization, J. Phys. B 6, 1452–1460 (1973).

    Article  ADS  Google Scholar 

  14. M. J. Seaton, Quantum defect theory XI. Clarification of some aspects of the theory, J. Phys. B 11, 4067–4093 (1978).

    Article  ADS  Google Scholar 

  15. J. Dubau, Quantum defect theory XII. Complex quantum defects for the He++e-system, J. Phys. B 11, 4095–4107 (1978).

    Article  ADS  Google Scholar 

  16. J. Dubau and M. J. Seaton, Quantum defect theory XIII. Further discussion of photoionization, J. Phys. Bsubmitted.

    Google Scholar 

  17. O. Bely, D. L. Moores, and M. J. Seaton, “Many-channel quantum defect theory in atomic collision processes,” in Proceedings of the Third International Conference on the Physics of Electronic and Atomic Collisions London 1963. M. R. C. Mowell, Ed., North Holland, Amsterdam, 1964, pp. 304–311.

    Google Scholar 

  18. M. Gailitis, Behavior of cross sections near threshold of a new reaction in the case of a Coulomb attraction field, Sov. Phys.-JETP 17, 1328–133 (1963).

    Google Scholar 

  19. U. Fano, Quantum defect theory of /-uncoupling in H2as an example of channel interaction treatment, Phys. Rev. A 2 353–365 (1970).

    Article  MathSciNet  ADS  Google Scholar 

  20. U. Fano, Unified treatment of perturbed series, continuous spectra and collisions, J. Opt. Soc. Am. 65, 979–987 (1975).

    Article  ADS  Google Scholar 

  21. K. T. Lu, Spectroscopy and collision theory. The Xe absorption spectrum, Phys. Rev. A 4, 579–596 (1971).

    Article  ADS  Google Scholar 

  22. M. Lee, Spectroscopy and collision theory III. Atomic eigenchannel calculation by a Hartree-Fock-Roothaan method, Phys. Rev. A 10, 584–600 (1974).

    Article  ADS  Google Scholar 

  23. J. Geiger, Energy loss spectra of xenon and krypton and their analysis by energy-dependent multichannel quantum defect theory, Z. Phys. A 282, 129–141 (1977).

    Article  ADS  Google Scholar 

  24. J. A. Armstrong, P. Esherick, and J. J. Wynne, Bound even-parityJ = 0 and 2 spectra of Ca: A multichannel quantum defect theory analysis, Phys. Rev. A 15, 180–196 (1977).

    Article  ADS  Google Scholar 

  25. C. W. Clark and K. T. Taylor, Eigenchannel analysis of neon negative ion resonances, J. Phys. B 15, L213-L219 (1982).

    Article  ADS  Google Scholar 

  26. G. Herzberg and Ch. Jungen, The absorption spectra of the molecules H2, HD, and D2. Part IV, J. Mol. Spectrosc. 41, 425–486 (1972).

    Article  ADS  Google Scholar 

  27. O. Atabek, D. Dill, and Ch. Jungen, Quantum defect theory of excited 1IIu -levels of H2, Phys. Rev. Lett. 33, 123–126 (1974).

    Article  ADS  Google Scholar 

  28. O. Atabek and Ch. Jungen, Quantum defect theory of excited 1∑u +levels of H2, in Electron and Photon Interactions with Atoms, H. Kleinpoppen and M. R. C. Mowell, Eds., Plenum, New York, 1976, pp. 613–620.

    Google Scholar 

  29. Ch. Jugen and O. Atabek, Rovibrational interactions in the photoabsorption spectrum of molecular hydrogen and deuterium: An application of multichannel quantum defect methods, J. Chem. Phys. 66, 5584–5609 (1977).

    Article  ADS  Google Scholar 

  30. C. M. Lee, Multichannel dissociative recombination theory, Phys. Rev. A 16, 109–122 (1977).

    Article  ADS  Google Scholar 

  31. A. Giusti, A multichannel quantum defect approach to dissociative recombination, J. Phys. B 13, 3867–3894 (1980).

    Article  ADS  Google Scholar 

  32. Ch. Jungen and D. Dill, Calculation of rotational-vibrational preionization in H2 by multichannel quantum defect theory, J. Chem. Phys. 73, 3338–3345 (1980).

    Article  ADS  Google Scholar 

  33. A. Giusti and Ch. Jungen, “A Multichannel Quantum Defect Treatment of the Competition Between Preionization and Predissociation in the NO Molecule,” in Abstracts of Contributed Papers, XII International Conference on the Physics of Electronic and Atomic Collisions, Gatlinburg, 1981, S. Datz, Ed., pp. 71–72 (1981).

    Google Scholar 

  34. W. R. Johnson and K. T. Cheng, Quantum defects for highly stripped ions, J. Phys. B 12, 863–879 (1979).

    Article  ADS  Google Scholar 

  35. C. M. Lee and W. R. Johnson, Scattering and spectroscopy: Relativistic multichannel quantum defect theory, Phys. Rev. A 22, 979–988 (1980).

    Article  MathSciNet  ADS  Google Scholar 

  36. W. R. Johnson, K. T. Cheng, K.-N. Huang, and M. Le Dourneuf, Analysis of Beutler-Fano autoionizing resonances in the rare-gas atoms using the relativistic multichannel quantum defect theory, Phys. Rev. A 22, 989–997 (1980).

    Article  ADS  Google Scholar 

  37. D. R. Bates and A. Damgaard, The calcualtion of the absolute strengths of spectral lines, Phil Trans. R. Soc. Lond. Ser. A 242, 101–122 (1949).

    Article  ADS  MATH  Google Scholar 

  38. H. E. Saraph, O IV: Bound states, oscillator strengths, and photoionization cross sections, J. Phys. B 13, 3129–3148 (1980).

    Article  ADS  Google Scholar 

  39. R. P. Machran and M. Cohen, Theoretical oscillator strengths for the boron isoelectronic sequence, J. Quant. Spectrosc. Radiat. Transfer 11, 1819–1826 (1971).

    Article  ADS  Google Scholar 

  40. D. Burgess and M. J. Seaton, A general formula for the calculation of atomic photoionization cross sections, Mon. Not. R. Astron. Soc. 120, 121–151 (1960).

    MathSciNet  ADS  MATH  Google Scholar 

  41. G. Peach, A general formula for the calculation of absorption cross sections for free-free transitions in the field of positive ions, Mon. Not. R. Astron. Soc. 130, 361–377 (1965).

    ADS  Google Scholar 

  42. G. Peach, A revised general formula for the calculation of atomic photoionization cross sections, Mem. R. Astron. Soc. 71, 13–27 (1967).

    ADS  Google Scholar 

  43. G. Peach, Continuous absorption coefficients for nonhydrogenic atoms, Mem. R. Astron. Soc.73, 1–123 (1970).

    ADS  Google Scholar 

  44. H. van Regemorter, D. Hoang-Binh, and M. Prud’homme, Radial transition integrals involving low or high effective quantum numbers in the Coulomb approximation, J. Phys. B12, 1053–1061 (1979).

    Article  ADS  Google Scholar 

  45. D. Hoang-Binh and H. van Regemorter, The calculation of radial integrals for bound-free and free-free transitions, J. Phys. B 14, L329-L335 (1981).

    Article  Google Scholar 

  46. D. Hoang-Binh and H. van Regemorter, Photoionisation from low or high excited states, Phys. B 12, L715-L718 (1979).

    Article  Google Scholar 

  47. H. E. Saraph and M. J. Seaton, The calculation of energy levels for atoms in configurations 1s 22s 22p q nl, Phil. Trans. R. Soc. Lond. Ser. A 271, 1–39 (1971).

    Article  ADS  Google Scholar 

  48. M. J. Seaton, A variational principle for the scattering phase matrix, Proc. Phys. Soc. 89, 469–470 (1966).

    Article  ADS  Google Scholar 

  49. H. Van Regemorter, Rate of collisional excitation in stellar atmospheres, Astrophys. J. 136, 906–915 (1962).

    Article  ADS  Google Scholar 

  50. C. D. H. Chisholm and U. Öpik, A simplified Hartree-Fock procedure for atoms with two electrons outside closed shells, Proc. Phys. Soc. 83, 541–547 (1964); and corrigendum in Proc. Phys. Soc. 84, 1041 (1964).

    Article  ADS  Google Scholar 

  51. W. R. S. Garton and K. Codling, Ultraviolet extensions of the arc spectra of the alkaline earths: the absorption spectrum of calcium vapour, Proc. Phys. Soc. 86, 1067–1075 (1965).

    Article  ADS  Google Scholar 

  52. L. N. Shabanova, Oscillator strengths of the spectral lines of Ca I, Opt. Spectrosc. 15, 450–451 (1963).

    Google Scholar 

  53. P. W. Ditchburn and R. D. Hudson, The absorption of light by calcium vapour (2100 to 1080Å), Proc. R. Soc. Lond. Ser. A 256, 53–61 (1960).

    Article  ADS  Google Scholar 

  54. G. H. Newsom, The absorption spectrum of calcium vapour: 1660–2028Å, Proc. Phys. Soc. 87, 975–982 (1966).

    Article  ADS  Google Scholar 

  55. T.J. Mlrath and R. J. Sandeman, Revised absolute absorption cross sections of Ca I at 1886.5 and 1765.1A, J. Phys. B 5, L217-L219 (1972).

    Article  ADS  Google Scholar 

  56. V. L. Carter, R. D. Hudson, and E. L. Breig, Autoionization in the uv photoabsorption of atomic calcium, Phys. Rev. A 4, 821–825 (1971).

    Article  ADS  Google Scholar 

  57. C. Froese-Fischer and J. E. Hansen, Comparison of multichannel quantum defect theory and multiconfiguration-Hartree-Fock wave functions for alkaline earth atoms, Phys. Rev. A 24, 631–634 (1981).

    Article  ADS  Google Scholar 

  58. H. E. Saraph, M. J. Seaton, and J. Shemming, Excitation of forbidden lines in gaseous nebulae I. Formulation and calculations for 2p qions, Phil. Trans. R. Soc. Lond. Ser. A 264, 77–105 (1969).

    Article  ADS  Google Scholar 

  59. H. E. Saraph, Fine structure cross sections from reactance matrices, Comput. Phys. Commun. 3, 256–268 (1972).

    Article  ADS  Google Scholar 

  60. E. S. Chang and U. Fano, Theory of electron-molecule collisions by frame transformations, Phys. Rev. A 6, 173–185 (1972).

    Article  ADS  Google Scholar 

  61. A. Monfils, The absorption spectra of the molecules H2, HD, and D2; Part VII, J. Mol. Spectrosc. 25, 513–517 (1968).

    Article  ADS  Google Scholar 

  62. D. L. Moores, to be submitted.

    Google Scholar 

  63. D. M. Dehmer and W. A. Chupka, Very high resolution study of photoabsorption, photoionization, and predissociation in H2, J. Chem. Phys. 65, 2243–2273 (1976).

    Article  ADS  Google Scholar 

  64. A. Pradhan, Collision strengths for [O II] and [S II], Mon. Not. R. Astron. Soc. 177, 31–38 (1976).

    ADS  Google Scholar 

  65. K. Giles, Collision strengths for [Ne v], Mon. Not. R. Astron. Soc. 187, 49p-51p (1979).

    MathSciNet  ADS  Google Scholar 

  66. C. Mendoza, Compilation of transition probabilities, electron excitation rate coefficients, and photoionization cross sections, in Proceedings of IAU Symposium No. 103: Planetary nebulae, D. R. Flower, Ed., D. Reidel, Dordrecht, Holland (1983).

    Google Scholar 

  67. T. M. Luke, Autoionization states in the photoionization of neon, J. Phys. B 6, 30–41 (1973).

    Article  ADS  Google Scholar 

  68. H. E. Saraph, Photoionization cross sections from solutions of the close-coupling equations, Comput. Phys. Commun., to be published.

    Google Scholar 

  69. U. Fano, Effects of configuration interaction on intensities and phase shifts, Phys. Rev. 124, 1866–1878 (1961).

    Article  ADS  MATH  Google Scholar 

  70. H. Jakubowicz and D. L. Moores, Electron impact ionization of Li-like and Be-like ions, J. Phys. B 14, 3733–3760 (1981).

    Article  ADS  Google Scholar 

  71. M. A. Crees, M. J. Seaton, and P. M. H. Wilson, IMPACT, a program for the solution of the coupled integro-differential equations of electron-atom collision theory, Comput. Phys. Commun. 15, 23–83 (1978).

    Article  ADS  Google Scholar 

  72. H. Jakubowicz, Theoretical studies of the electron impact ionization of positive ions, Ph.D. thesis, University of London, 1980.

    Google Scholar 

  73. M. H. Ross and G. L. Shaw, Multichannel effective range theory, Ann. Phys. 13, 147–186 (1961).

    Article  ADS  MATH  Google Scholar 

  74. C. Greene, U. Fano, and G. Strinati, General form of the quantum defect theory, Phys. Rev. A 19, 1485–1509 (1979).

    Article  ADS  Google Scholar 

  75. R. Damburg and R. Peterkop, Application of the multichannel effective range theory to electron-hydrogen scattering, Proc. Phys. Soc. 80, 1073–1077 (1962).

    Article  ADS  Google Scholar 

  76. D. L. Moores and D. W. Norcross, Alkali-metal negative ions. I. Photodetachment of Li-, Na-and K-, Phys. Rev. A 10, 1598–1604 (1974).

    Article  Google Scholar 

  77. C. M. Lee, Spin polarization and angular distribution of photoelectrons in the Jacobi-Wick helicity formalism. Application to autoionization resonances, Phys. Rev. A 10, 1598–1604 (1974).

    Article  ADS  Google Scholar 

  78. D. W. Norcross and K. Taylor, private communication (1974).

    Google Scholar 

  79. S. Watanabe and C. Greene, Atomic polarizability in negative-ion photo-detachment, Phys. Rev. A 22, 158–169 (1980).

    Article  ADS  Google Scholar 

  80. C. Greene, Dependence of the photoabsorption spectra on long range fields, Phys. Rev. A 22, 149–157 (1980).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. University College London, Gower Street, WC1 E6BT, London, England

    David L. Moores & Hannelore E. Saraph

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  1. David L. Moores
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  2. Hannelore E. Saraph
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Editor information

Editors and Affiliations

  1. The Queen’s University of Belfast, Belfast, Northern Ireland

    P. G. Burke

  2. Science and Engineering Research Council, Daresbury, England

    W. B. Eissner

  3. Joint Institute for Laboratory Astrophysics, University of Colorado, Boulder, Colorado, USA

    D. G. Hummer

  4. University of London, London, England

    I. C. Percival

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© 1983 Plenum Press, New York

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Moores, D.L., Saraph, H.E. (1983). Application of Quantam Defect Theory. In: Burke, P.G., Eissner, W.B., Hummer, D.G., Percival, I.C. (eds) Atoms in Astrophysics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3536-8_6

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  • DOI: https://doi.org/10.1007/978-1-4613-3536-8_6

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