Abstract

Curves of growth are calculated for autoionizing transitions having the Beutler–Fano form of absorption cross section. Both graphs and tabulated values of the curves are presented. The curve-of-growth analysis is applied to the 3s–4p transition in argon at 466 Å. The line parameters Γ, q, and ρ2 obtained by fitting the theoretical and experimental equivalent widths are in good agreement with other high-resolution values. The curve-of-growth technique thus appears to be an attractive method for determining the parameters of autoionizing features. The application of this technique to make path-length or particle-density measurements in, for example, a King furnace or a plasma is also discussed.

© 1970 Optical Society of America

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References

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  1. U. Fano, Phys. Rev. 124, 1866 (1961).
    [Crossref]
  2. U. Fano and J. W. Cooper, Phys. Rev. 137, 1364 (1965).
    [Crossref]
  3. H. Beutler, Z. Physik 93, 177 (1935).
    [Crossref]
  4. R. P. Madden and K. Codling, Astrophys. J. 141, 364 (1965).
    [Crossref]
  5. M. E. Levy and R. E. Huffman, J. Quant. Spectrosc. Radiative Transfer 9, 1349 (1969).
    [Crossref]
  6. R. P. Madden, D. L. Ederer, and K. Codling, Phys. Rev. 177, 136 (1969).
    [Crossref]
  7. See, for example, S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison–Wesley, Reading, Mass., 1959), Ch. 4.
  8. S. D. Conte, Elementary Numerical Analysis (McGraw–Hill, New York, 1965), p. 138. We are grateful to V. Tice of the USC Computing Center for making available to us his integration program.
  9. G. Balloffet, J. Romand, and B. Vodar, Compt. Rend. 252, 4139 (1961); H. Damany, J.-Y. Roncin, and N. Damany-Astoin, Appl. Opt. 5, 297 (1966).
    [Crossref] [PubMed]
  10. R. Nossal and G. H. Weiss, J. Quant. Spectrosc. Radiative Transfer 8, 763 (1968).
    [Crossref]

1969 (2)

M. E. Levy and R. E. Huffman, J. Quant. Spectrosc. Radiative Transfer 9, 1349 (1969).
[Crossref]

R. P. Madden, D. L. Ederer, and K. Codling, Phys. Rev. 177, 136 (1969).
[Crossref]

1968 (1)

R. Nossal and G. H. Weiss, J. Quant. Spectrosc. Radiative Transfer 8, 763 (1968).
[Crossref]

1965 (2)

U. Fano and J. W. Cooper, Phys. Rev. 137, 1364 (1965).
[Crossref]

R. P. Madden and K. Codling, Astrophys. J. 141, 364 (1965).
[Crossref]

1961 (2)

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

G. Balloffet, J. Romand, and B. Vodar, Compt. Rend. 252, 4139 (1961); H. Damany, J.-Y. Roncin, and N. Damany-Astoin, Appl. Opt. 5, 297 (1966).
[Crossref] [PubMed]

1935 (1)

H. Beutler, Z. Physik 93, 177 (1935).
[Crossref]

Balloffet, G.

G. Balloffet, J. Romand, and B. Vodar, Compt. Rend. 252, 4139 (1961); H. Damany, J.-Y. Roncin, and N. Damany-Astoin, Appl. Opt. 5, 297 (1966).
[Crossref] [PubMed]

Beutler, H.

H. Beutler, Z. Physik 93, 177 (1935).
[Crossref]

Codling, K.

R. P. Madden, D. L. Ederer, and K. Codling, Phys. Rev. 177, 136 (1969).
[Crossref]

R. P. Madden and K. Codling, Astrophys. J. 141, 364 (1965).
[Crossref]

Conte, S. D.

S. D. Conte, Elementary Numerical Analysis (McGraw–Hill, New York, 1965), p. 138. We are grateful to V. Tice of the USC Computing Center for making available to us his integration program.

Cooper, J. W.

U. Fano and J. W. Cooper, Phys. Rev. 137, 1364 (1965).
[Crossref]

Ederer, D. L.

R. P. Madden, D. L. Ederer, and K. Codling, Phys. Rev. 177, 136 (1969).
[Crossref]

Fano, U.

U. Fano and J. W. Cooper, Phys. Rev. 137, 1364 (1965).
[Crossref]

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

Huffman, R. E.

M. E. Levy and R. E. Huffman, J. Quant. Spectrosc. Radiative Transfer 9, 1349 (1969).
[Crossref]

Levy, M. E.

M. E. Levy and R. E. Huffman, J. Quant. Spectrosc. Radiative Transfer 9, 1349 (1969).
[Crossref]

Madden, R. P.

R. P. Madden, D. L. Ederer, and K. Codling, Phys. Rev. 177, 136 (1969).
[Crossref]

R. P. Madden and K. Codling, Astrophys. J. 141, 364 (1965).
[Crossref]

Nossal, R.

R. Nossal and G. H. Weiss, J. Quant. Spectrosc. Radiative Transfer 8, 763 (1968).
[Crossref]

Penner, S. S.

See, for example, S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison–Wesley, Reading, Mass., 1959), Ch. 4.

Romand, J.

G. Balloffet, J. Romand, and B. Vodar, Compt. Rend. 252, 4139 (1961); H. Damany, J.-Y. Roncin, and N. Damany-Astoin, Appl. Opt. 5, 297 (1966).
[Crossref] [PubMed]

Vodar, B.

G. Balloffet, J. Romand, and B. Vodar, Compt. Rend. 252, 4139 (1961); H. Damany, J.-Y. Roncin, and N. Damany-Astoin, Appl. Opt. 5, 297 (1966).
[Crossref] [PubMed]

Weiss, G. H.

R. Nossal and G. H. Weiss, J. Quant. Spectrosc. Radiative Transfer 8, 763 (1968).
[Crossref]

Astrophys. J. (1)

R. P. Madden and K. Codling, Astrophys. J. 141, 364 (1965).
[Crossref]

Compt. Rend. (1)

G. Balloffet, J. Romand, and B. Vodar, Compt. Rend. 252, 4139 (1961); H. Damany, J.-Y. Roncin, and N. Damany-Astoin, Appl. Opt. 5, 297 (1966).
[Crossref] [PubMed]

J. Quant. Spectrosc. Radiative Transfer (2)

R. Nossal and G. H. Weiss, J. Quant. Spectrosc. Radiative Transfer 8, 763 (1968).
[Crossref]

M. E. Levy and R. E. Huffman, J. Quant. Spectrosc. Radiative Transfer 9, 1349 (1969).
[Crossref]

Phys. Rev. (3)

R. P. Madden, D. L. Ederer, and K. Codling, Phys. Rev. 177, 136 (1969).
[Crossref]

U. Fano, Phys. Rev. 124, 1866 (1961).
[Crossref]

U. Fano and J. W. Cooper, Phys. Rev. 137, 1364 (1965).
[Crossref]

Z. Physik (1)

H. Beutler, Z. Physik 93, 177 (1935).
[Crossref]

Other (2)

See, for example, S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison–Wesley, Reading, Mass., 1959), Ch. 4.

S. D. Conte, Elementary Numerical Analysis (McGraw–Hill, New York, 1965), p. 138. We are grateful to V. Tice of the USC Computing Center for making available to us his integration program.

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Figures (4)

Fig. 1
Fig. 1

Recording of the 3snp Rydberg series in argon with a value of β of 6.8. The wavelength scale is approximate. The slit width here is about 2/3Γ, but we can pick out the steeper side of the 4p member. In this I/I0 spectrum the steeper side is toward lower energy, so that q is negative.

Fig. 2
Fig. 2

Curves of growth of spectral lines having the Beutler–Fano profile. The curves are computed with ρ2=1. Curves for ρ2<1 can be derived from the generating formula given in Eq. (5).

Fig. 3
Fig. 3

Plot of the experimental equivalent widths (open circles) with the best-fit curve having ρ2=0.85 (——), and with curves for ρ2=0.80 (– – – –) and 0.90 (– - – - –). The value of |q| here is 0.22.

Fig. 4
Fig. 4

Plot of the experimental equivalent widths (open circles) with the best-fit curve having |q| =0.22 (——), and with the curves for |q| =0.0 (– – – –) and 0.5 (– - – - –). The value of ρ2 here is 0.85.

Tables (1)

Tables Icon

Table I Numerical evaluation of the negative of the integral W(q,1,β)/Γ from Eq. (4) by gaussian quadratures. The relative error in the tabulated values is less than 0.035%.

Equations (5)

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σ ( ) ( cm 2 ) = σ a [ ( q + ) 2 / ( 1 + 2 ) ] + σ b .
σ ( ) = σ t [ 1 + ρ 2 ( q 2 - 1 + 2 q ) / ( 1 + 2 ) ] ,
W ( eV ) = - I 0 exp ( - σ t N l ) - I 0 exp [ - σ ( ) N l ] I 0 × d ω ( eV ) .
W ( q , ρ 2 , β ) Γ = exp [ β ( ρ 2 - 1 ) ] { exp ( - ρ 2 β ) × 0 [ 1 - exp ( - ρ 2 β q 2 - 1 1 + 2 ) cosh ( ρ 2 β 2 q 1 + 2 ) ] d } ,
W ( q , ρ 2 , β ) / Γ = exp [ β ( ρ 2 - 1 ) ] [ W ( q , 1 , ρ 2 β ) / Γ ] .