the v=0, J=0 energy level of the ground electronic state, X', and the minimum of the potential energy curve of the excited electronic state. Te is obtained by adding the zero-point energy of the X 1Σ+ state to Teo. Traditionally, spectroscopic constants would be determined from the empirical fit of all the observed data to the above expressions. The coefficients obtained would be the Dunham coefficients and the equilibrium constants Be, we, etc. would be obtained by applying the Dunham corrections to these coefficients. Since the Dunham corrections for a molecule like CO are very small, one would normally set the first few Dunham coefficients approximately equal to the equilibrium constants (for example, B, Yo1). e We have not followed the traditional procedure here for the a', e, and I states in CO for reasons discussed now. For these states the observed data extend over such a large portion of the potential energy curve that relatively high order expressions are required to fit the observed data. The coefficients of the high order expressions, however, vary considerably as a function of both the order of the expression used and the number of data points included in the fit. Therefore, the first few coefficients of a particular high order least squares fit including all the observed data do not necessarily represent the best values for the equilibrium constants. The best equilibrium constants can be determined by fitting the observed data for the lower vibrational levels to relatively low order expressions. The disadvantage of quoting only these values for the spectroscopic constants is that they do not accurately reproduce the observed data for the higher vibrational levels. We have, therefore, chosen to report here two sets of constants for the states mentioned above. (1) A high order set of coefficients, which taken as a set reproduce the data over the entire observed range and which further: (a) predict rather accurately any missing data points within the range of observed data, even at high vibrational levels, and (b) give a smoothed polynomial for all the observed data from which potential curves and subsequently Franck-Condon factors can be calculated. (2) A set of low order coefficients which are individually meaningful within stated error limits and which best correspond to the traditional equilibrium spectroscopic constants. The set of equilibrium constants were determined in the following way. First, the coefficients were ob tained for two or more low orders as a function of the number of data points included in the fit. For example. the B-values of the e 3Σ- state were fit to expressions of first and second orders. For each order the least squares fit is performed repeatedly, successively excluding the highest-v B,-value of the previous fit until the number of B-values included is just greater than the number of coefficients in the expression. Then the values of a particular coefficient, for example, You. are plotted against the number of vibrational levels included in the fits for the two orders. Such a graph is illustrated in figure 1. The error bars indicated on the plotted values represent one standard deviation as given by the least squares subroutine ORTHO. The quoted value for the equilibrium constant is then determined visually from the graph and the size of the error limits chosen to enclose most of the values in the stable range of the coefficient. Therefore, the value quoted is relatively independent of the order of the expression and the number of data points included in the fits. The set of high order coefficients is that obtained from a single least squares fit of the observed data to expressions of the particular order indicated by the superscript on the coefficients. The limits given in the tables for these coefficients are one standard devia tion. The values of an individual coefficient, particularly those of the higher terms, are very much dependent on the order of the expression and the number of data points included in the fit. For this reason the individual coefficients are rather meaningless, but the set taken as a whole is significant to the extent that it gives a smoothed polynomial that accurately represents the data over the entire observed range. These polynomials are very useful for interpolation, but it would be very 1 1 dangerous to extrapolate them outside the range of observed data. We are greatly indebted to G. Herzberg, A. M. Bass, and F. Alberti for their help in obtaining the plates at the National Research Council of Canada and to R. Naber for his help with the experimental work at the U.S. Naval Research Laboratory. 7. References [1] Herzberg, G., and Hugo, T. J., Can. J. Phys. 33, 157 (1955). [2] Krupenie, P. H., The Band Spectrum of Carbon Monoxide, Nat. Stand. Ref. Data Ser., Nat. Bur. Stand. (U.S.), 5, 92 pages (July 1966). [3] Stepanov, B. I., J. Phys. U.R.S.S. 2, 205 (1940). [4] Herzberg, G., Simmons, J. D., Bass, A. M., and Tilford, S. G., Can. J. Phys. 44, 3039 (1966). [5] Simmons, J. D., and Tilford, S. G., J. Chem. Phys. 45, 2965 (1966). [6] Douglas, A. E., and Potter, J. G., Appl. Opt. 1, 727 (1962). [7] Brix, P., and Herzberg, G., Can. J. Phys. 32, 110 (1954). [8] Wilkinson, P. G., and Byram, E. T., Appl. Opt. 5, 581 (1965). [9] Simmons, J. D., Bass, A. M., and Tilford, S. G., Astrophys. J. 155, 345 (1969). [10] Herzberg, G., Hugo, T. J., Tilford, S. G., and Simmons, J. D., Can. J. Phys. 48, 3004 (1970). [11] Slanger, T. G., and Black, G., in press. [12] Gero, L. Z. Physik 109, 216 (1938). [13] Garg, S. N., Indian J. Phys. 23, 161 (1949). [14] Gaydon, A. G., Dissociation Energies and Spectra of Diatomic Molecules, Third Edition (Chapman and Hall, London, 1968), p. 211. JOURNAL OF RESEARCH of the National Bureau of Standards - A. Physics and Chemistry Vol. 75A, No. 5, September-October 1971 A Study of Line Shape of CO Infrared Emission Lines* es A. Dowling,** Shirleigh Silverman, William S. Benedict,*** and Jarus W. Quinn**** Office of the Associate Director, National Bureau of Standards, Washington, D.C. 20234 (March 2, 1971) 2 The shape of several vibration-rotation lines of CO emitted by a C2H.-O. flame was investigated. An equivalent width measurement was made using an absorption cell of room temperature CO as an analyzer. Analysis of the data showed that line shapes could be fitted to a Voigt function with shape parameters a between 1.0 and 1.5. The collision widths of the flame lines, as determined by the shape parameters, are in essential agreement with earlier room temperature measurements. The extrapolation of the widths measured at room temperature to high temperature has been shown to be reliable within the uncertainty of this experiment (±15%). Key words: Carbon monoxide; collision parameters; equivalent width; flame spectra; line shapes. 1. Introduction he purpose of this work was to measure the linedening parameters in the fundamental band of as emitted in a CH2-O flame. The two necessary meters are the line strength and line shape. The strength may be calculated for any temperature a measurement of the lifetime or transition bability. At low pressures the line shape is detered by the Doppler effect and is a known factor of perature and molecular mass. At high pressures line shape is Lorentzian and is determined by the rmolecular forces as expressed by a collisiondening diameter. Most measurements of this ntity have been made in a narrow temperature ge near room temperature and the extrapolation to her temperature is quite uncertain. For gases in the perature range 1500 to 3500 K and the pressure ge 0-1 atm the shape results from both Doppler Lorentz broadening and is described by the Voigt ction [1]. The spectral absorption coefficient for a line of onant wavenumber v with a Voigt profile is: This work was supported by the Air Force Cambridge Research Laboratories and is ed on a thesis submitted (by J. A. Dowling) to the Physics Dept., Catholic University artial fulfillment of the requirements for the degree of Doctor of philosophy. A prelimi account of this work was presented at the meeting of the Optical Society of America, shington, D.C., March 1968. Present address: Naval Research Laboratory, Washington, D.C. 20390. Present address: Institute for Molecular Physics, The University of Maryland, ege Park, Maryland 20740. ***Present address: Optical Society of America, 2100 Pennsylvania Ave., NW., Washon, D.C. 20037. where σ1, σ2, and M1, M2 are the colliding molecular diameters in A, and molecular weights in grams per mol, respectively, and P is pressure in atmospheres. For self broadening [2] σ1 =σ = 3.12 Å, ye for CO is 5.63 x 10-2 cm-1 at 273 K and is 1.57 × 10-2 cm-1 at 3500 K and 1 atm. On this basis, referring to eq (2), the emission lines of CO in the vicinity of 2200 cm-1 should be described by Voigt profiles with 1 < a <2, for a pressure of 1 atm and temperature of 3500 K. The effect of the finite bandpass of an observing instrument on the apparent shape and width of an observed spectral line has been treated elsewhere [3–6]. Kostkowski and Bass [5] give results of errors made in measured peak absorptions and line-widths. Their results show that accurate corrections may be applied to observed shapes for slit functions having widths a maximum of 1/2 to 1 times the half-width of the line under investigation. However, such a procedure for determining the actual line shape from the observed profile is not applicable in the present experiment. The grating instrument used in the present experiment has a theoretical resolution of 0.04 to 0.05 cm 1 which is about three times greater than the anticipated line half-width. Therefore, one may resort to the curveof-growth method which is implemented by changing the physical path length in order to change the optical path, maintaining a constant gas pressure, and thus, a constant value of Ye. However, such a procedure is not readily adaptable to flame studies. Although the optical density can be varied by changing the pressure of the gas surrounding the flame, this would not allow observation of the lines at constant pressure, i.e., constant collision width. An alternative is to study several flames of various thicknesses. The method described here employs an equivalent width measurement, but unlike a curve-of-growth procedure, the conditions in the flame remain fixed for a series of observations. An absorption cell containing CO is introduced between the flame source and the detector. The equivalent width in emission of a single line in the flame is measured with the cell evacuated. where VE(P, ) is the Voigt function describing the emission line. A similar relation holds for the Voi function for the absorption line V1(v, a1). However. measurement of R* does not determine the line shap parameter a uniquely in VE(v, E) since P. and are both undetermined. However, one can make unique determination by plotting R* as a function o absorber pressure. This is done by fitting data to curve calculated for various combinations of PVɛ(v, a and X. E It should be noted here that the parameters, P and V1(v, a1) are known either from measurement this experiment, i.e., by measuring X, or from C absorption measurements reported by other worker [7]. The Voigt function is given in terms of an integr whose solution is obtained by various approximation methods, each one effective for a limited range o values of a (see chap. 4 of reference [1]). Therefore. attempt has been made to derive a general relationshi between the measured quantity R* and the line shap parameter of interest a such as exists between the equivalent width, and ye in the case of the Lader burg-Reiche curve of growth formulation. Since the absorber pressure is varied over a wide range (0-60 torr) in this experiment, the value of a is changed with |