## Abstract

The shapes of the extreme wings of self-broadened CO_{2} lines have been investigated in three spectral regions near 7000, 3800, and 2400 cm^{−1}. Absorption measurements have been made on the high-wavenumber sides of band heads where much of the absorption by samples at a few atm is due to the extreme wings of strong lines whose centers occur below the band heads. New information has been obtained about the shapes of self-broadened CO_{2} lines as well as CO_{2} lines broadened by N_{2}, O_{2}, Ar, He, and H_{2}. Beyond a few cm^{−1} from the line centers, all of the lines absorb less than Lorentz-shaped lines having the same half-widths. The deviation from the Lorentz shape decreases with increasing wavenumber, from one of the three spectral regions to the next. The absorption by the wings of H_{2}- and He-broadened lines is particularly low, and the absorption decreases with increasing temperature at a rate faster than predicted by existing theories.

© 1969 Optical Society of America

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### Equations (13)

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(1)
$$u(\text{atm}\hspace{0.17em}{\text{cm}}_{\text{STP}})=p(\text{atm})[1+0.005p]L(\text{cm})273/\theta (\text{K}).$$
(2)
$${T}^{\prime}(\nu )=\text{exp}[-u\kappa (\nu )],\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\text{or}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\kappa (\nu )=-(1/u)\hspace{0.17em}\text{ln}{T}^{\prime}(\nu ).$$
(3)
$$k(\nu )=Sf(\alpha ,\nu -{\nu}_{0}),$$
(4)
$${\int}_{-\infty}^{\infty}f(\alpha ,\nu -{\nu}_{0})=1,$$
(5)
$$S={\int}_{-\infty}^{\infty}k(\nu )d\nu .$$
(6)
$${f}_{L}(\alpha ,\nu -{\nu}_{0})=\frac{1}{\pi}\frac{\alpha}{{(\nu -{\nu}_{0})}^{2}+{\alpha}^{2}}.\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}(\text{Lorentz})$$
(7)
$${f}_{L}(\alpha ,\nu -{\nu}_{0})=\alpha /\pi {(\nu -{\nu}_{0})}^{2},\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}\mathrm{\hspace{0.17em}\u200a\u200a}[\text{for}\hspace{0.17em}(\nu -{\nu}_{0})\gg \alpha ].$$
(8)
$$f(\alpha ,\nu -{\nu}_{0})={f}_{L}(\alpha ,\nu -{\nu}_{0})\chi (\nu -{\nu}_{0})=[\alpha \chi (\nu -{\nu}_{0})]/\pi [{(\nu -{\nu}_{0})}^{2}+{\alpha}^{2}].$$
(9)
$${k}_{s}=\frac{S\alpha \chi}{\pi {(\nu -{\nu}_{0})}^{2}}=\frac{S{{\alpha}_{s}}^{0}p(1+0.005p)\chi}{\pi {p}^{0}{(\nu -{\nu}_{0})}^{2}},$$
(10)
$${\kappa}_{s}=\sum _{i}{k}_{s,i}=\sum _{i}\frac{{S}_{i}{\chi}_{s,i}p(1+0.005p){{\alpha}_{s,i}}^{0}}{\pi {p}^{0}{(\nu -{\nu}_{0,i})}^{2}}.$$
(11)
$$\kappa =-\frac{1}{u}\text{ln}{T}^{\prime}(\nu )=\frac{{{\kappa}_{s}}^{0}p(1+0.005p)}{{p}^{0}}+\frac{{{\kappa}_{b}}^{0}{p}_{b}}{{p}^{0}}=\sum _{i}\frac{{S}_{i}}{\pi}\frac{{{\alpha}_{s,i}}^{0}}{{p}^{0}{(\nu -{\nu}_{0,i})}^{2}}\times \left[{\chi}_{s,i}p(1+0.005p)+\left(\frac{{{\alpha}_{b}}^{0}}{{{\alpha}_{s}}^{0}}\right){\chi}_{b,i}{p}_{b}\right].$$
(12)
$${p}^{(\text{A})}={p}^{(\text{C})}+{{p}_{{\text{N}}_{2}}}^{(\text{C})}{{\alpha}_{{\text{N}}_{2}}}^{0}/{{\alpha}_{s}}^{0},$$
(13)
$${{\alpha}_{s}}^{0}({\text{cm}}^{-1})=0.050+0.12\hspace{0.17em}\text{exp}[-0.16\mid m\mid ]+0.0042\mid m\mid \text{exp}\left[-\frac{{B}^{\u2033}m\hspace{0.17em}(m-1)}{kT}\right],$$