Analytical formula for radiation trapping with partial frequency redistribution

A highly realistic Monte Carlo code is used to simulate radiation trapping including effects due to partial frequency redistribution and with a spectral line profile dominated by natural (radiative) broadening resonance collisional broadening and Doppler broadening. Results from 294 simulations are used to determine the fundamental mode trapped decay rate in cylindrical geometry over a very wide range of parameter space including a factor of in gas density, a factor of 1000 in column radius, and a factor of 1000 in Doppler width. The fundamental mode decay rates are fitted to an analytical formula expressed in terms of three dimensionless parameters which can conveniently be applied to a variety of gases, column radii and Doppler widths.