Imprisonment of Resonance Radiation in Gases

TLDR

Resonance quanta are highly absorbable by gas atoms, so escaping a gas‑filled enclosure requires many repeated absorptions and emissions. The study applies the developed theory to various problems involving excited atoms. The authors model radiative transport using the transmission probability T(ρ) and solve a Boltzmann‑type integro‑differential equation via a variational method. Applying the theory to an infinite slab, they compute the excitation decay rate and find good agreement with Zemansky’s mercury‑vapor measurements.

Abstract

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, $T(\ensuremath{\rho})$, that a quantum traverses a layer of gas of thickness, $\ensuremath{\rho}$, without being absorbed; the dependence of $T(\ensuremath{\rho})$ 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 $T(\ensuremath{\rho})$; 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.