General Theory of Pressure Broadening of Spectral Lines

Abstract

A new, more consistent, shape has been given to the theory of pressure broadening of spectral lines recently published by the author. In contradistinction to other theories, the present theory constitutes a very close analogy to the theory of intensity distribution in molecular spectra. There is no doubt that both phenomena are due to the same cause, i.e., to the relative movements of atomic nuclei. Thus, the theoretical treatment of both must be identical as far as possible. The method used by James and Coolidge for the calculations of intensity distribution in ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ continuous spectra can be adapted to the calculations of the profiles of broadened lines. In this case, presumably, it will not be possible to represent the intensity distribution in a closed form. In order to obtain a closed form, Condon's method (the quantum mechanical form of the Franck-Condon principle) is applied, and the Wentzel-Kramers-Brillouin approximate eigenfunctions are used for nuclear motions. The limitations of applicability of this approximation are discussed (the same limitations apply $a$ fortiori to the applicability of every theory based on the classical description of nuclear motions). Because of the above simplifications, the resulting intensity distribution formula must be considered as an asymptotic one only, valid in a restricted region of frequencies of the broadened line and only in the case of heavy atoms and high temperatures (it certainly fails in the case of broadening by light gases such as He and ${\mathrm{H}}_2$ or electrons), though it still constitutes a better approximation than that previously published. Apart from a correction which is in most cases insignificant, it is identical with Kuhn's intensity distribution obtained on the basis of the primitive form of the Franck-Condon principle. The present paper is drafted so as to be comprehensible to the reader without knowledge of the preceding papers of the author, the main results of which are being included here.