Stark-Effect Broadening of Hydrogen Lines. II. Observable Profiles

The hydrogen-line profiles previously derived for the case of single encounters are integrated over all encounters to yield the observable profiles. The encounters are assumed to be uniformly distributed over different distances of closest approach, and the ions are assumed to have a Maxwellian velocity distribution. Approximation functions allow the integration to be carried through with rigor in the two limiting cases of very fast and very slow encounters, and with a probable error not exceeding ten percent in the more general case. The resultant profiles illustrate quantitatively Margenau's effect—the transition from impact to statistical broadening with increasing line width. The effect of fast electron encounters is shown to be negligible, in general, in comparison with the effect produced by an equal density of slowly moving ions. An evaluation is made of the error produced by the neglect of the inhomogeneity of the ionic field. The final formulas have a probable error of less than 12 percent for most cases of astrophysical interest.