Imprisonment of Resonance Radiation in Gases

It is known that resonance quanta are highly absorbable by normal atoms of the emitting gas; hence, under suitable conditions of gas density the eventual escape of these quanta from a gas-filled enclosure may require a large number of repeated absorptions and emissions. This "radiative" transport of excitation is determined essentially by the probability, $T\left(\rho \right)$, that a quantum traverses a layer of gas of thickness, $\rho$, without being absorbed; the dependence of $T\left(\rho \right)$ on the frequency distribution of the resonance line is investigated, and explicit expressions are derived for the cases of Doppler and dispersion broadening. The general transport problem is formulated in terms of a Boltzmann-type integro-differential equation involving $T\left(\rho \right)$; the variational method of obtaining steady-state solutions of this equation is discussed. The theory is then applied to the evaluation of the rate of decay of excitation in an infinite slab; the results are compared with Zemansky's measurements of the decay of radiation from an enclosure of mercury vapor. Finally, the application of the theory to a number of problems concerning excited atoms is discussed briefly.