X. On the distribution of intensity in broadened spectrum lines

Abstract

It is a curious fact that although our knowledge of the structure of the finest spectrum lines may now be said to rest on a secure theoretical and experimental basis, little is known of the distribution of energy in the broadened spectrum lines which are produced under certain conditions of excitation, or the exact circumstances which control their broadening. The researches of Lord Rayleigh, Michelson, Buisson and Fabry, and others have shown that in gases at low pressures, when excited by uncondensed electric discharges, the width of the spectrum lines emitted can be accounted for completely and satisfactorily by the translatory motion of the radiating particles, in accordance with Doppler’s principle. Measurements of the width of such lines are carried out with the interferometer, the measurement consisting of a determination of the limiting order of interference at which fringes can he seen. This limiting order of interference is given by the equation N = K (M/T) ½ where N is the limiting order of interference, M the mass of the luminous particle in terms of the hydrogen atom, T the absolute temperature and K a constant. This equation is derived from a consideration of the Doppler effect produced by a distribution of the velocities of the radiating particles in accordance with Maxwell’s law, and its experimental verification by Buisson and Fabry shows not only that under the conditions specified the widths of the lines are completely accounted for, but also that the distribution of intensity in the lines is given by the well-known probability law. Under these conditions it is further shown that the limiting order of interference is constant for all lines and all series of the same element. Thus the same value of N is found for the helium and the parhelium series, and in the same manner for the Rainier series and lines of the secondary spectrum of hydrogen. With any departure from the specified conditions of low pressure and excitation by uncondensed electric discharge the law breaks down, and the lines broaden in an apparently anomalous manner. The characteristics which lead Rydberg to adopt the terms diffuse and sharp series appear, the higher members of a series undergoing the greater degree of broadening. Matters are complicated by the fact that the broadening is in many cases unsymmetrical, and in addition we must take into account the fact pointed out by Royds, that different members of the same series may be unsymmetrically broadened in opposite directions. Thus in the case of the first subordinate “triplet” series of barium, the members consisting of triplet and satellites at λλ 5819-5424 are all unsymmetrically broadened towards the red, whilst the members of the succeeding triplet (and satellites) and λλ 4493-4264 are unsym­metrically broadened towards the violet. Royds shows that similar phenomena occur in the spectra of calcium and strontium, and points out the importance of the phenomena in relation to the pressure shifts of the lines in question. There can be no doubt of the intimate relation between the direction of the asymmetry and the pressure shift, since it has been shown by St. John and Ware, Fabry and Buisson, and by Gale and Adams that iron lines which broaden unsymmetrically towards the red are displaced by pressure towards the red, whilst lines which are unsym­metrically broadened towards the violet are displaced by pressure towards the violet. It is well known that broadening of spectrum lines can be produced either by an increase of the pressure of the luminous gas or by the use of highly condensed discharges as a means of excitation, and although the two conditions are different he phenomena of broadening which result appear to be similar. In a previous investigation it has been pointed out by one of the authors that from a consideration of the general characteristics of the broadening it appears difficult to refer the phenomena to the movements of the luminous particles as a whole, but rather that effects more intimately connected with the problem of radiation must be concerned. A recent suggestion by Stark as to the cause of the broadening appears to be in harmony with the experimental results at present available.