Analytic formula for radiation trapping with partial frequency redistribution and foreign gas broadening

A recently developed analytic formula for radiation trapping in cylindrical geometry with partial frequency redistribution and with a spectral lineshape dominated by almost any combination of natural (radiative) broadening, resonance collisional broadening, and Doppler broadening is generalized to include foreign or buffer gas broadening. The effect of foreign gas broadening is incorporated by rescaling the radius and absorbing gas density. In some cases rescaling results in an unphysically small radius. The analytic formula reported here, which is accurate to zero radius, is an improved version of the earlier formula. The accuracy of the improved formula is verified with 198 new simulations, in addition to the original 294 simulations, all using a highly realistic Monte Carlo code.