Abstract

The absolute f-values of rotational lines in the positive and negative branches of the 2ν3 overtone band of CH4 have been derived from absorption measurements in the laboratory by two independent methods. The first method involves the use of the curve of growth and requires the observation of weak lines for which the total absorption is independent of the damping constant. In the second method the lines are broadened artificially, by the introduction of about 3 atmos of air, to half-widths that are about five times the slit width. The f-values are then determined by integration of the logarithm of the percentage absorption over the line profile. On the average, the f-values obtained by the two methods agree within 10 percent.

© 1952 Optical Society of America

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References

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  1. Robert R. McMath and Orren C. Mohler, J. Opt. Soc. Am. 39, 903 (1949).
    [CrossRef]
  2. E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
    [CrossRef]
  3. D. M. Dennison, Phys. Rev. 31, 503 (1928).
    [CrossRef]
  4. A. Unsöld, Physik der Sternatmnosphären (Verlag. Julius Springer, Berlin, 1938), p. 165.
  5. Actually, the collisional damping may be expected to increase slightly with excitation potential, since, owing to the interaction between rotation and vibration, the internuclear distance and therefore the target area for collision increases with increasing rotation. But the effect is negligibly small.
  6. G. Herzberg, Infra Red and Raman Spectra (D. van Nostrand Company, Inc., New York, 1945), p. 451.
  7. See reference 6, p. 506.
  8. W. H. J. Childs and H. A. Jahn, Proc. Roy. Soc. (London) A169, 451 (1939).
    [CrossRef]

1949 (1)

1946 (1)

E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
[CrossRef]

1939 (1)

W. H. J. Childs and H. A. Jahn, Proc. Roy. Soc. (London) A169, 451 (1939).
[CrossRef]

1928 (1)

D. M. Dennison, Phys. Rev. 31, 503 (1928).
[CrossRef]

Childs, W. H. J.

W. H. J. Childs and H. A. Jahn, Proc. Roy. Soc. (London) A169, 451 (1939).
[CrossRef]

Dennison, D. M.

D. M. Dennison, Phys. Rev. 31, 503 (1928).
[CrossRef]

Herzberg, G.

G. Herzberg, Infra Red and Raman Spectra (D. van Nostrand Company, Inc., New York, 1945), p. 451.

Jahn, H. A.

W. H. J. Childs and H. A. Jahn, Proc. Roy. Soc. (London) A169, 451 (1939).
[CrossRef]

McMath, Robert R.

Mohler, Orren C.

Unsöld, A.

A. Unsöld, Physik der Sternatmnosphären (Verlag. Julius Springer, Berlin, 1938), p. 165.

Wells, A. J.

E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
[CrossRef]

Wilson, E. B.

E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
[CrossRef]

J. Chem. Phys. (1)

E. B. Wilson and A. J. Wells, J. Chem. Phys. 14, 578 (1946).
[CrossRef]

J. Opt. Soc. Am. (1)

Phys. Rev. (1)

D. M. Dennison, Phys. Rev. 31, 503 (1928).
[CrossRef]

Proc. Roy. Soc. (London) (1)

W. H. J. Childs and H. A. Jahn, Proc. Roy. Soc. (London) A169, 451 (1939).
[CrossRef]

Other (4)

A. Unsöld, Physik der Sternatmnosphären (Verlag. Julius Springer, Berlin, 1938), p. 165.

Actually, the collisional damping may be expected to increase slightly with excitation potential, since, owing to the interaction between rotation and vibration, the internuclear distance and therefore the target area for collision increases with increasing rotation. But the effect is negligibly small.

G. Herzberg, Infra Red and Raman Spectra (D. van Nostrand Company, Inc., New York, 1945), p. 451.

See reference 6, p. 506.

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Figures (5)

Fig. 1
Fig. 1

Theoretical curves of growth for pure damping.

Fig. 2
Fig. 2

Tracings of the 4–3 line of 2ν3 of CH4 made with absorption cells (left to right) 1, 2, 4, 6, and 10 in. in length. Total pressure=25 cm of CH4. The slit width is indicated by the pair of parallel lines. The horizontal line at the bottom refers to zero intensity.

Fig. 3
Fig. 3

Profile of the 4–3 line of 2ν3 of CH4 made with a cell 7 1 4 in. in length. Total pressure=3 atmospheres; partial pressure of CH4=25 cm. The slit width is indicated by the pair of parallel lines. The horizontal line at the bottom refers to zero intensity.

Fig. 4
Fig. 4

Empirical curve of growth for lines in Positive branch of 2ν3.

Fig. 5
Fig. 5

Empirical curve of growth for lines in negative branch of 2ν3.

Tables (4)

Tables Icon

Table I Mean values of logW/λ for lines in 2ν3 band Of CH4 as a function of path length. Total pressure 25 cm CH4. The numbers in parentheses denote the number of independent observations included in each mean.

Tables Icon

Table II Experimental values of logfJJ for 2ν3 band of CH4. Values in column two by curve of growth method, total pressure=25 cm; values in column three by profile method, total pressure=3 atmos.

Tables Icon

Table III Values of logfJJ from artificially broadened profiles, derived from equivalent widths by Eq. (11) and from profiles by Eq. (5).

Tables Icon

Table IV Comparison of experimental values of logfJJ with theory.

Equations (16)

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I ν / I 0 = e - τ ν ,
τ ν = n J l α ν .
α ν = α 0 γ / 4 π 2 ( ν - ν 0 ) 2 + ( γ / 4 π ) 2 ,
α 0 = 0 α ν d ν = π 2 m c f J J ,
f J J = 1 π 2 / m c 0 α ν d ν = 1 n J l ( π 2 / m c ) 0 ln I 0 I ν d ν .
n J = n b ( T ) g J e - B h c J ( J + 1 ) / k T ,
Δ ν = 0 ( 1 - I ν I 0 ) d ν .
W = λ 2 c Δ ν .
τ 0 = 4 γ π 2 m c f J J n J l ,
δ = ( λ / 4 c ) γ .
W / λ = δ τ 0 ,
W / λ = 2 ( δ / π ) 1 2 ( δ τ 0 ) 1 2 .
log δ τ 0 - log l = log ( π 2 m c 2 λ f J J n J ) .
γ 2 π = 2 N σ 2 [ 2 R T π ( 1 μ 1 + 1 μ 2 ) ] 1 2 .
n J = p k T g J b ( T ) e ( - B 0 h c / k T ) J ( J + 1 ) ,
b ( T ) = 1.027 ( T / B 0 ) 3 2 ,