Abstract

Phase-shifted-channel, multichannel quantum-defect theory parameters and complex quantum defects are shown to be convenient for comparisons of theoretical studies (which lead to a set of eigen quantum defects μ¯α and a transformation matrix U) with experimental determinations of resonance energies and linewidths, using the autoionizing Rydberg series of Xe as a specific example.

© 1987 Optical Society of America

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References

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  1. See, for example, J. Berkowitz, Photoabsorption, Photoionization, and Photoelectron Spectroscopy (Academic, New York, 1979), and references therein.
  2. R. E. Huffman, Y. Tanaka, and J. C. Larrabee, “Absorption coefficients of xenon and argon in the 600–1025 Å wavelength regions,” J. Chem. Phys. 39, 902 (1963).
    [CrossRef]
  3. K. Yoshino and D. E. Freeman, “Absorption spectrum of xenon in the vacuum-ultraviolet region,” J. Opt. Soc. Am. B 2, 1268 (1985).
    [CrossRef]
  4. K. D. Bonin, T. J. McIlrath, and K. Yoshino, “High-resolution laser and classical spectroscopy of xenon autoionization,” J. Opt. Soc. Am. B 2, 1275 (1985).
    [CrossRef]
  5. L. G. Wang and R. D. Knight, “Two-photon laser spectroscopy of the ns′ and nd′ autoionizing Rydberg series of xenon,” Phys. Rev. A 34, 3902 (1986).
    [CrossRef] [PubMed]
  6. M. J. Seaton, “Quantum defect theory,” Rep. Prog. Phys. 46, 167 (1983).
    [CrossRef]
  7. K. T. Lu, “Spectroscopy and collisiontheory. The Xe absorption spectrum,” Phys. Rev. A 4, 579 (1971).
    [CrossRef]
  8. J. Geiger, “Energy loss spectra of xenon and krypton and their analysis by energy dependent multichannel quantum defect theory,” Z. Phys. A 282, 129 (1977).
    [CrossRef]
  9. 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 (1980).
    [CrossRef]
  10. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961); U. Fano and J. W. Cooper, “Line profiles in the far-UV absorption spectra of the rare gases,” Phys. Rev. 137, A1364 (1965).
    [CrossRef]
  11. A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of two-channel coupling,” J. Phys. B 17, 215 (1984).
    [CrossRef]
  12. W. E. Cooke and C. L. Cromer, “Multichannel quantum defect theory and an equivalent N-level system,” Phys. Rev. A 32, 2725 (1985); C. L. Cromer, National Bureau of Standards, Gaithersburg, Maryland 02899 (personal communication).
    [CrossRef] [PubMed]
  13. K. Ueda, “Spectral line shapes of autoionizing Rydberg series,” Phys. Rev. A (to be published).
  14. J. Dubau and M. J. Seaton, “Quantum defect theory XIII. Radiative transitions,” J. Phys. B 17, 381 (1984). See also Ref. 6.
    [CrossRef]
  15. B. W. Shore, “Parametrization of absorption-line profiles,” Phys. Rev. 171, 43 (1968).
    [CrossRef]
  16. J. P. Connerade, “On Rydberg series of autoionizing resonances,” J. Phys. B 16, L329 (1983); “Autoionizing line shapes,” J. Phys. B 18, L367 (1985).
    [CrossRef]

1986 (1)

L. G. Wang and R. D. Knight, “Two-photon laser spectroscopy of the ns′ and nd′ autoionizing Rydberg series of xenon,” Phys. Rev. A 34, 3902 (1986).
[CrossRef] [PubMed]

1985 (3)

K. Yoshino and D. E. Freeman, “Absorption spectrum of xenon in the vacuum-ultraviolet region,” J. Opt. Soc. Am. B 2, 1268 (1985).
[CrossRef]

K. D. Bonin, T. J. McIlrath, and K. Yoshino, “High-resolution laser and classical spectroscopy of xenon autoionization,” J. Opt. Soc. Am. B 2, 1275 (1985).
[CrossRef]

W. E. Cooke and C. L. Cromer, “Multichannel quantum defect theory and an equivalent N-level system,” Phys. Rev. A 32, 2725 (1985); C. L. Cromer, National Bureau of Standards, Gaithersburg, Maryland 02899 (personal communication).
[CrossRef] [PubMed]

1984 (2)

J. Dubau and M. J. Seaton, “Quantum defect theory XIII. Radiative transitions,” J. Phys. B 17, 381 (1984). See also Ref. 6.
[CrossRef]

A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of two-channel coupling,” J. Phys. B 17, 215 (1984).
[CrossRef]

1983 (2)

J. P. Connerade, “On Rydberg series of autoionizing resonances,” J. Phys. B 16, L329 (1983); “Autoionizing line shapes,” J. Phys. B 18, L367 (1985).
[CrossRef]

M. J. Seaton, “Quantum defect theory,” Rep. Prog. Phys. 46, 167 (1983).
[CrossRef]

1980 (1)

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 (1980).
[CrossRef]

1977 (1)

J. Geiger, “Energy loss spectra of xenon and krypton and their analysis by energy dependent multichannel quantum defect theory,” Z. Phys. A 282, 129 (1977).
[CrossRef]

1971 (1)

K. T. Lu, “Spectroscopy and collisiontheory. The Xe absorption spectrum,” Phys. Rev. A 4, 579 (1971).
[CrossRef]

1968 (1)

B. W. Shore, “Parametrization of absorption-line profiles,” Phys. Rev. 171, 43 (1968).
[CrossRef]

1963 (1)

R. E. Huffman, Y. Tanaka, and J. C. Larrabee, “Absorption coefficients of xenon and argon in the 600–1025 Å wavelength regions,” J. Chem. Phys. 39, 902 (1963).
[CrossRef]

1961 (1)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961); U. Fano and J. W. Cooper, “Line profiles in the far-UV absorption spectra of the rare gases,” Phys. Rev. 137, A1364 (1965).
[CrossRef]

Berkowitz, J.

See, for example, J. Berkowitz, Photoabsorption, Photoionization, and Photoelectron Spectroscopy (Academic, New York, 1979), and references therein.

Bonin, K. D.

Cheng, K. T.

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 (1980).
[CrossRef]

Connerade, J. P.

J. P. Connerade, “On Rydberg series of autoionizing resonances,” J. Phys. B 16, L329 (1983); “Autoionizing line shapes,” J. Phys. B 18, L367 (1985).
[CrossRef]

Cooke, W. E.

W. E. Cooke and C. L. Cromer, “Multichannel quantum defect theory and an equivalent N-level system,” Phys. Rev. A 32, 2725 (1985); C. L. Cromer, National Bureau of Standards, Gaithersburg, Maryland 02899 (personal communication).
[CrossRef] [PubMed]

Cromer, C. L.

W. E. Cooke and C. L. Cromer, “Multichannel quantum defect theory and an equivalent N-level system,” Phys. Rev. A 32, 2725 (1985); C. L. Cromer, National Bureau of Standards, Gaithersburg, Maryland 02899 (personal communication).
[CrossRef] [PubMed]

Dubau, J.

J. Dubau and M. J. Seaton, “Quantum defect theory XIII. Radiative transitions,” J. Phys. B 17, 381 (1984). See also Ref. 6.
[CrossRef]

Fano, U.

A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of two-channel coupling,” J. Phys. B 17, 215 (1984).
[CrossRef]

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961); U. Fano and J. W. Cooper, “Line profiles in the far-UV absorption spectra of the rare gases,” Phys. Rev. 137, A1364 (1965).
[CrossRef]

Freeman, D. E.

Geiger, J.

J. Geiger, “Energy loss spectra of xenon and krypton and their analysis by energy dependent multichannel quantum defect theory,” Z. Phys. A 282, 129 (1977).
[CrossRef]

Giusti-Suzor, A.

A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of two-channel coupling,” J. Phys. B 17, 215 (1984).
[CrossRef]

Huang, K.-N.

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 (1980).
[CrossRef]

Huffman, R. E.

R. E. Huffman, Y. Tanaka, and J. C. Larrabee, “Absorption coefficients of xenon and argon in the 600–1025 Å wavelength regions,” J. Chem. Phys. 39, 902 (1963).
[CrossRef]

Johnson, W. R.

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 (1980).
[CrossRef]

Knight, R. D.

L. G. Wang and R. D. Knight, “Two-photon laser spectroscopy of the ns′ and nd′ autoionizing Rydberg series of xenon,” Phys. Rev. A 34, 3902 (1986).
[CrossRef] [PubMed]

Larrabee, J. C.

R. E. Huffman, Y. Tanaka, and J. C. Larrabee, “Absorption coefficients of xenon and argon in the 600–1025 Å wavelength regions,” J. Chem. Phys. 39, 902 (1963).
[CrossRef]

Le Dourneuf, M.

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 (1980).
[CrossRef]

Lu, K. T.

K. T. Lu, “Spectroscopy and collisiontheory. The Xe absorption spectrum,” Phys. Rev. A 4, 579 (1971).
[CrossRef]

McIlrath, T. J.

Seaton, M. J.

J. Dubau and M. J. Seaton, “Quantum defect theory XIII. Radiative transitions,” J. Phys. B 17, 381 (1984). See also Ref. 6.
[CrossRef]

M. J. Seaton, “Quantum defect theory,” Rep. Prog. Phys. 46, 167 (1983).
[CrossRef]

Shore, B. W.

B. W. Shore, “Parametrization of absorption-line profiles,” Phys. Rev. 171, 43 (1968).
[CrossRef]

Tanaka, Y.

R. E. Huffman, Y. Tanaka, and J. C. Larrabee, “Absorption coefficients of xenon and argon in the 600–1025 Å wavelength regions,” J. Chem. Phys. 39, 902 (1963).
[CrossRef]

Ueda, K.

K. Ueda, “Spectral line shapes of autoionizing Rydberg series,” Phys. Rev. A (to be published).

Wang, L. G.

L. G. Wang and R. D. Knight, “Two-photon laser spectroscopy of the ns′ and nd′ autoionizing Rydberg series of xenon,” Phys. Rev. A 34, 3902 (1986).
[CrossRef] [PubMed]

Yoshino, K.

J. Chem. Phys. (1)

R. E. Huffman, Y. Tanaka, and J. C. Larrabee, “Absorption coefficients of xenon and argon in the 600–1025 Å wavelength regions,” J. Chem. Phys. 39, 902 (1963).
[CrossRef]

J. Opt. Soc. Am. B (2)

J. Phys. B (3)

A. Giusti-Suzor and U. Fano, “Alternative parameters of channel interactions: I. Symmetry analysis of two-channel coupling,” J. Phys. B 17, 215 (1984).
[CrossRef]

J. Dubau and M. J. Seaton, “Quantum defect theory XIII. Radiative transitions,” J. Phys. B 17, 381 (1984). See also Ref. 6.
[CrossRef]

J. P. Connerade, “On Rydberg series of autoionizing resonances,” J. Phys. B 16, L329 (1983); “Autoionizing line shapes,” J. Phys. B 18, L367 (1985).
[CrossRef]

Phys. Rev. (2)

U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. 124, 1866 (1961); U. Fano and J. W. Cooper, “Line profiles in the far-UV absorption spectra of the rare gases,” Phys. Rev. 137, A1364 (1965).
[CrossRef]

B. W. Shore, “Parametrization of absorption-line profiles,” Phys. Rev. 171, 43 (1968).
[CrossRef]

Phys. Rev. A (4)

W. E. Cooke and C. L. Cromer, “Multichannel quantum defect theory and an equivalent N-level system,” Phys. Rev. A 32, 2725 (1985); C. L. Cromer, National Bureau of Standards, Gaithersburg, Maryland 02899 (personal communication).
[CrossRef] [PubMed]

L. G. Wang and R. D. Knight, “Two-photon laser spectroscopy of the ns′ and nd′ autoionizing Rydberg series of xenon,” Phys. Rev. A 34, 3902 (1986).
[CrossRef] [PubMed]

K. T. Lu, “Spectroscopy and collisiontheory. The Xe absorption spectrum,” Phys. Rev. A 4, 579 (1971).
[CrossRef]

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 (1980).
[CrossRef]

Rep. Prog. Phys. (1)

M. J. Seaton, “Quantum defect theory,” Rep. Prog. Phys. 46, 167 (1983).
[CrossRef]

Z. Phys. A (1)

J. Geiger, “Energy loss spectra of xenon and krypton and their analysis by energy dependent multichannel quantum defect theory,” Z. Phys. A 282, 129 (1977).
[CrossRef]

Other (2)

See, for example, J. Berkowitz, Photoabsorption, Photoionization, and Photoelectron Spectroscopy (Academic, New York, 1979), and references therein.

K. Ueda, “Spectral line shapes of autoionizing Rydberg series,” Phys. Rev. A (to be published).

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Figures (1)

Fig. 1
Fig. 1

The photoionization cross section of Xe calculated (solid curve) using ab initio MQDT parameters by Johnson et al.9 and calculated (filled circles) from Eqs. (6a) and (6b) using the parameters listed in text. (a) One periodic cycle of the Rydberg spectrum. (b) A portion of (a) that features a sharp s′ line. Both (a) and (b) were calculated at the energy of the second ionization limit I1/2.

Tables (2)

Tables Icon

Table 1 Coupling-Matrix Elements and Phase Shiftsa for J = 1° Channels of Xe

Tables Icon

Table 2 Values of μk and Wk for the s′ and d′ Channels of Xe

Equations (17)

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s = sV cos π μ + cV sin π μ
c = cV cos π μ - sV sin π μ ,
R = ( cos π μ + V T R V sin π μ ) - 1 ( V T R V cos π μ - sin π μ ) .
R = [ 0 0 0 R 14 R 15 0 0 0 R 24 R 25 0 0 0 R 34 R 35 R 14 R 24 R 34 0 0 R 15 R 25 R 35 0 0 ] .
R = U tan π μ ¯ U T .
D = ( cos π μ - sin π μ R ) T V T U cos π μ ¯ - 1 D ¯ ,
σ = k = 4 5 σ a k ( k + q k ) 2 / ( k 2 + 1 ) + σ b ,
k = tan π ( ν 1 / 2 + μ k ) / W k
ω k n + E 0 = I 1 / 2 - Ry / ( n - μ k ) 2
Γ k n / 2 = 2 Ry W k / π ( n - μ k ) 3 ,
W k = i = 1 3 R i k 2 .
μ c k = α k + i β k
μ k = μ k = α k
W k = i = 1 3 R i k 2 = tan π β k .
χ c c X = X exp ( 2 π i μ c ) ,
χ U = U exp ( 2 π i μ ¯ ) .
χ k k = α = 1 5 U k α exp ( 2 π i μ ¯ α ) U k α ,

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