Imprisonment of Resonance Radiation in a Gaseous Discharge

Abstract

Following the theory of Holstein, the density, $N_r$, and the imprisonment lifetime of resonance radiation, $T$, has been investigated for a gaseous discharge between parallel plates. A general solution is given. Two approximate solutions occur according as the number of electronic de-excitations of the resonance state during the imprisonment time of a photon is much less than or much greater than unity. When this number is much less than unity, $N_r$ can be given by a simple relation which compares well with computations based on the exact solution in the case of Doppler broadening. $T$ is then essentially equal to the decay time as calculated by Holstein for the decay of resonance radiation following optical excitation. For large numbers of de-excitations $T$ falls somewhat below the decay value and, as expected, $N_r$ is given by its thermodynamic equilibrium value at the temperature of the electrons.