Theory of Pressure Effects of Foreign Gases on Spectral Lines

Abstract

The chief aim of the considerations presented is to contribute to the understanding of the effects of high pressures of foreign gases upon the shape and the position of a spectral line. A formal distinction is made between statistical and impact distributions, and the former is calculated in closed form for an interaction law of the type $\ensuremath{\Delta}\ensuremath{\nu}=\ensuremath{-}\frac{\ensuremath{\alpha}}{{r}^{6}}$. The distribution (Eq. (7a)) is a special case of Pearson's curves. Next the relation between the statistical and the true distribution is examined from a fundamental point of view which illuminates the character of the approximations made in the various theories of pressure broadening. Finally, by the use of a simplified procedure, approximative expressions are developed for the entire intensity distribution within the line, probably valid for pressures around 20 atoms. An expression (Eq. (18)) capable of graphical integration, is given which represents the true distribution for lower pressures. The theoretical results are compared with experimental data. Some concrete conclusions: the shift of the maximum is nearly proportional to the pressure of the perturbing gas at low pressure, proportional to its square at high pressures. The transition occurs at a pressure for which the impact half-width $\ensuremath{\approx}$ the shift of the statistical maximum. (About 20 atmos. for K --- ${\mathrm{N}}_{2}$, 50 atmos. for Hg --- ${\mathrm{N}}_{2}$.) At pressures up to $\ensuremath{\approx}20$ atmos. the impact width determines the shift of the intensity maximum, the latter being at low pressures far greater than the shift of the statistical maximum. Half-widths are also proportional to approximately the first power of the pressure at low, to the second power at high pressures. At pressures up to $\ensuremath{\approx}10$ atmos., the half-width is about twice the shift of the maximum. The shift is a function of the temperature as well as the pressure.