Abstract

The sensitivity of the resonance-fluorescence method for the measurement of very-low sodium-vapor densities (<1010 atoms/cm3) has been studied. Light from a sodium spectral lamp is sent through a sodium-containing vessel, whose temperature can be varied. The vapor density has been measured in the region of 47–146 °C. At 47 °C, the vapor density is about 107 atoms/cm3. The measurements were performed with both a photon-counting device and a lock-in amplifier. The experimental results have been normalized to absolute density data given in the literature. Fitting our points to the equation logN = a + b/T yields the values a = 23.715 and b = −5257.7 K.

© 1974 Optical Society of America

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References

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  1. L. C. J. Baghuis and H. L. Hagedoorn, Physica (Utr.) 65, 163 (1973).
    [Crossref]
  2. L. C. J. Baghuis, H. L. Hagedoorn, and J. A. van der Heide, in Proceedings of the Eleventh International Conference on Phenomena in Ionized Gases, 1973 (Czechoslovak Academy of Sciences, Prague, 1973), pp. 478 and 479.
  3. S. M. Jarrett and P. A. Franken, J. Opt. Soc. Am. 55, 1603 (1965).
    [Crossref]
  4. N. Ioli and F. Strumia, J. Opt. Soc. Am. 61, 1251 (1971).
    [Crossref]
  5. J. W. Chamberlain, D. M. Hunten, and J. E. Mack, J. Atm. Terr. Phys. 12, 153 (1958).
    [Crossref]
  6. T. M. Donahue, R. Resnick, and V. R. Stull, Phys. Rev. 104, 873 (1956).
    [Crossref]
  7. J. Kuhl and G. Marowsky, Opt. Commun. 4, 125 (1971).
    [Crossref]
  8. D. A. Jennings and R. A. Keller, J. Am. Chem. Soc. 94, 9249 (1972).
    [Crossref]
  9. A. Mitchell and M. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. P., New York, 1971), pp. 92–106.
  10. G. Schulz and W. Stopp, Z. Phys. 210, 223 (1968).
    [Crossref]
  11. A. N. Nesmeyanov, Vapor Pressure of the Chemical Elements (Elsevier, Amsterdam, 1963), pp. 128–137.

1973 (1)

L. C. J. Baghuis and H. L. Hagedoorn, Physica (Utr.) 65, 163 (1973).
[Crossref]

1972 (1)

D. A. Jennings and R. A. Keller, J. Am. Chem. Soc. 94, 9249 (1972).
[Crossref]

1971 (2)

J. Kuhl and G. Marowsky, Opt. Commun. 4, 125 (1971).
[Crossref]

N. Ioli and F. Strumia, J. Opt. Soc. Am. 61, 1251 (1971).
[Crossref]

1968 (1)

G. Schulz and W. Stopp, Z. Phys. 210, 223 (1968).
[Crossref]

1965 (1)

1958 (1)

J. W. Chamberlain, D. M. Hunten, and J. E. Mack, J. Atm. Terr. Phys. 12, 153 (1958).
[Crossref]

1956 (1)

T. M. Donahue, R. Resnick, and V. R. Stull, Phys. Rev. 104, 873 (1956).
[Crossref]

Baghuis, L. C. J.

L. C. J. Baghuis and H. L. Hagedoorn, Physica (Utr.) 65, 163 (1973).
[Crossref]

L. C. J. Baghuis, H. L. Hagedoorn, and J. A. van der Heide, in Proceedings of the Eleventh International Conference on Phenomena in Ionized Gases, 1973 (Czechoslovak Academy of Sciences, Prague, 1973), pp. 478 and 479.

Chamberlain, J. W.

J. W. Chamberlain, D. M. Hunten, and J. E. Mack, J. Atm. Terr. Phys. 12, 153 (1958).
[Crossref]

Donahue, T. M.

T. M. Donahue, R. Resnick, and V. R. Stull, Phys. Rev. 104, 873 (1956).
[Crossref]

Franken, P. A.

Hagedoorn, H. L.

L. C. J. Baghuis and H. L. Hagedoorn, Physica (Utr.) 65, 163 (1973).
[Crossref]

L. C. J. Baghuis, H. L. Hagedoorn, and J. A. van der Heide, in Proceedings of the Eleventh International Conference on Phenomena in Ionized Gases, 1973 (Czechoslovak Academy of Sciences, Prague, 1973), pp. 478 and 479.

Hunten, D. M.

J. W. Chamberlain, D. M. Hunten, and J. E. Mack, J. Atm. Terr. Phys. 12, 153 (1958).
[Crossref]

Ioli, N.

Jarrett, S. M.

Jennings, D. A.

D. A. Jennings and R. A. Keller, J. Am. Chem. Soc. 94, 9249 (1972).
[Crossref]

Keller, R. A.

D. A. Jennings and R. A. Keller, J. Am. Chem. Soc. 94, 9249 (1972).
[Crossref]

Kuhl, J.

J. Kuhl and G. Marowsky, Opt. Commun. 4, 125 (1971).
[Crossref]

Mack, J. E.

J. W. Chamberlain, D. M. Hunten, and J. E. Mack, J. Atm. Terr. Phys. 12, 153 (1958).
[Crossref]

Marowsky, G.

J. Kuhl and G. Marowsky, Opt. Commun. 4, 125 (1971).
[Crossref]

Mitchell, A.

A. Mitchell and M. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. P., New York, 1971), pp. 92–106.

Nesmeyanov, A. N.

A. N. Nesmeyanov, Vapor Pressure of the Chemical Elements (Elsevier, Amsterdam, 1963), pp. 128–137.

Resnick, R.

T. M. Donahue, R. Resnick, and V. R. Stull, Phys. Rev. 104, 873 (1956).
[Crossref]

Schulz, G.

G. Schulz and W. Stopp, Z. Phys. 210, 223 (1968).
[Crossref]

Stopp, W.

G. Schulz and W. Stopp, Z. Phys. 210, 223 (1968).
[Crossref]

Strumia, F.

Stull, V. R.

T. M. Donahue, R. Resnick, and V. R. Stull, Phys. Rev. 104, 873 (1956).
[Crossref]

van der Heide, J. A.

L. C. J. Baghuis, H. L. Hagedoorn, and J. A. van der Heide, in Proceedings of the Eleventh International Conference on Phenomena in Ionized Gases, 1973 (Czechoslovak Academy of Sciences, Prague, 1973), pp. 478 and 479.

Zemansky, M.

A. Mitchell and M. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. P., New York, 1971), pp. 92–106.

J. Am. Chem. Soc. (1)

D. A. Jennings and R. A. Keller, J. Am. Chem. Soc. 94, 9249 (1972).
[Crossref]

J. Atm. Terr. Phys. (1)

J. W. Chamberlain, D. M. Hunten, and J. E. Mack, J. Atm. Terr. Phys. 12, 153 (1958).
[Crossref]

J. Opt. Soc. Am. (2)

Opt. Commun. (1)

J. Kuhl and G. Marowsky, Opt. Commun. 4, 125 (1971).
[Crossref]

Phys. Rev. (1)

T. M. Donahue, R. Resnick, and V. R. Stull, Phys. Rev. 104, 873 (1956).
[Crossref]

Physica (Utr.) (1)

L. C. J. Baghuis and H. L. Hagedoorn, Physica (Utr.) 65, 163 (1973).
[Crossref]

Z. Phys. (1)

G. Schulz and W. Stopp, Z. Phys. 210, 223 (1968).
[Crossref]

Other (3)

A. N. Nesmeyanov, Vapor Pressure of the Chemical Elements (Elsevier, Amsterdam, 1963), pp. 128–137.

L. C. J. Baghuis, H. L. Hagedoorn, and J. A. van der Heide, in Proceedings of the Eleventh International Conference on Phenomena in Ionized Gases, 1973 (Czechoslovak Academy of Sciences, Prague, 1973), pp. 478 and 479.

A. Mitchell and M. Zemansky, Resonance Radiation and Excited Atoms (Cambridge U. P., New York, 1971), pp. 92–106.

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Figures (3)

Fig. 1
Fig. 1

Experimental apparatus: L, Na spectral lamp; D, diaphragms; C, chopper; TH, trapping horns; SC, scaler; LIA, lock-in amplifier; PM, photomultiplier; CR, cryostat; L, lenses; SVC, sodium-vapor cell.

Fig. 2
Fig. 2

Profiles of the D1 absorption line of 23Na at temperatures of 50, 100, and 150°C. The dotted line represents the gaussian approximation of the emission line in arbitrary units as used in this experiment.

Fig. 3
Fig. 3

Experimental values of the sodium concentration (filled circles with lines), adapted at absolute density measurements of Ioli et al. Line 1 is the curve given by Ioli and has been extrapolated from 100°C. Line 2 is a least-squares fitting of our experimental values, and line 3 is the extrapolated curve given by Nesmeyanov.

Equations (9)

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ϕ = i ( x ) k ( x ) d x = N i ( x ) σ ( x ) d x ;
i ( x ) = î Δ x e 2 ( ln 2 π ) 1 2 exp [ - ( x - x 0 ) 2 4 ln 2 Δ x e 2 ] ,
σ ( x ) = σ 0 exp [ - ( x - x 0 - δ ) 2 4 ln 2 Δ x a 2 ] ,
σ 0 = 1 Δ x a ( ln 2 π ) 1 2 λ 2 g 2 4 π c g 1 1 τ
Δ x a = 7.16 × 10 - 7 λ ( T M ) 1 2 .
ϕ = N î σ 0 Δ x a exp ( - δ 2 4 ln 2 Δ x a 2 + Δ x e 2 ) / ( Δ x a 2 + Δ x e 2 ) 1 2 ,
ϕ = N î σ ¯ ,
N = ϕ î σ ¯ ,
ϕ = N i ( x ) [ 0.625 σ 1 ( x ) + 0.375 σ 2 ( x ) ] d x = N î σ ¯ ,