Pressure Shift and Broadening of Spectral Lines

The pressure shift of spectral lines, unexplained by the usual theories of pressure broadening, can be adequately treated on the basis of a theory which considers the perturbations produced by neighboring atoms on the two states between which transitions occur. The analysis presented in the paper is directly applicable only to absorption lines, but its consequences are qualitatively correct for emission lines as well. The forces acting on the unexcited atom are the usual van der Waals forces; the perturbations of the excited state are produced by interactions of the same character (dispersion forces) but of different magnitude. The energy increments for both cases can be roughly computed by means of spectroscopic data, which renders possible the evaluations of the mean energies of transitions and hence of pressure shifts. Details are worked out mainly for the shift of $\lambda 2537$ (Hg) in foreign gases, and are compared with the experimental data of Füchtbauer, Joos, and Dinkelacker. In this case, the energy increments are negative both for the excited and for the normal state of Hg, but larger for the former. Hence there results a red shift, whose magnitude agrees well with observations. The line width produced by the perturbations here considered is an appreciable portion of the total experimental half-width. It is no longer necessary, therefore, to explain the total broadening effect of foreign gases by an appeal to Lorentz collisions. Main results of the theory are: the shift is proportional to the density of the perturbing gas; it is usually to the red, but may, under conditions discussed in the paper, be to shorter wave-lengths; a dependence of the shift on the temperature exists, but is slight at ordinary temperatures; the "standard deviation" of frequencies within the broadened line is proportional to the square root of the density of the perturbing gas.