Following the theory of Holstein, the density,
Nr, 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,
Nr 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,
Nr is given by its thermodynamic equilibrium value at the temperature of the electrons.
The predictions of the incoherent scattering theory of the transport of resonance radiation developed by Holstein and by Biberman are shown to agree with laboratory measurements of the decay constants for the intensity of the mercury 2537 A resonance radiation following a period of optical excitation. Also, the relative importance of the diffusion of resonance atoms and the escape of resonance radiation as mechanisms for the destruction of mercury atoms in the
3P1 or resonance state are determined from measurements of decay constants as a function of mercury density and cell radius. The experimental results show that diffusion of the resonance atoms is negligible and that the predictions of imprisonment theory are confirmed to within 15%. The experiment sets an upper limit to the diffusion coefficient at unit gas density for atoms in the
3P1 state of 5\ifmmode\times\else\texttimes\fi{}
1017 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ at 340\ifmmode^\circ\else\textdegree\fi{}K, which is consistent with a value of 4\ifmmode\times\else\texttimes\fi{}
1016 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ predicted using the frequency of excitation transfer collisions calculated by Holstein. The success of the theories based on completely incoherent scattering of resonance radiation points to the desirability of including this feature in the treatment of those astrophysical problems in which the spectral line shape is determined by Doppler broadening or by collision broadening.
Breit has derived formulae giving the polarization
P(H) and the angle of maximum polarization $\ensuremath{\theta}$ of a resonance line showing hyperfine structure, as a function of a weak magnetic field applied in the direction of observation of the resonance radiation. The formulae give a means of estimating the effect of hyperfine structure on the calculation of the mean life $\ensuremath{\tau}$ of an excited atom from experiments on the magnetic depolarization and rotation of the plane of polarization of resonance radiation. The calculation has been carried through for the case of the resonance line of $\mathrm{Cd}(\ensuremath{\lambda}3261)$ and that of $\mathrm{Hg}(\ensuremath{\lambda}2537)$, and it is found that the differences between the value of $\ensuremath{\tau}$ calculated from hyperfine structure data and that calculated from $tan2\ensuremath{\theta}$ by the usual non-hyperfine structure method lie well within the experimental error.
P0P(H) is found to be practically the same whether hyperfine structure is taken into account or neglected. This is due to the fact that the greatest contribution of the polarization in these cases comes from the isotopes having no nuclear spin and the
g-value for the upper state of these isotopes is larger than any other upper hyperfine structure state involved. The mean lives of the
73S1 state of mercury have been recalculated from Richter's data on the polarization of stepwise radiation. The values of $\ensuremath{\tau}$ obtained by this method of calculation are 7.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}9}$ for $\ensuremath{\lambda}4047$, 1.69\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ for $\ensuremath{\lambda}4358$ and 1.53\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ for $\ensuremath{\lambda}5461$. A discussion of Richter's results is given.
The general theory of the calculation of the polarization of resonance radiation is discussed for the case when hyperfine structure has to be considered. The polarization of mercury resonance radiation is computed for various orientations of electric vector and magnetic field, use being made of the hyperfine structure data of Sch\"uler and his collaborators. The polarization of the stepwise radiation of mercury is also calculated and the results compared with the experiments of Richter. Fair agreement between theory and experiment is found. von Keussler's method of calculating the polarization is discussed and it is shown that his method leads to incorrect results.
An eigenvalue problem for decay modes of resonance radiation proposed by Holstein is solved by a variational method and some higher decay modes are obtained by rigorous calculations of matrix elements when enclosure geometry is an infinite slab and the line-shape is due to Doppler broadening. Holstein's intergo-differential equation is extended to include the effect of external radiation and the contributions of higher modes to output radiation are calculated after stationary external radiation irradiated perpendicularly to one of the surfaces of the slab is abruptly cut off. This result is not consistent with the strange experimental results for mercury 2537 Å radiation obtained by Mochizuki and Fowler–advancement of the relative phase of the output radiation when the intensity of external radiation is modulated sinusoidally–and it is concluded that the reason for their results should be found in some unknown mechanisms.
Inclusion of collisional destruction mechanisms as sink terms in the theory of imprisonment of resonance radiation appears to have been neglected in the case of the 2537-Å mercury line. In this paper, the Holstein photon transport equation is employed to determine the effect of destructive or self-quenching collisions between resonance state and ground state atoms, processes in which the resonance state is converted to another excited state with the release of kinetic energy. These mechanisms seem to explain experimental work in which the decay constant of the 2537-Å mercury line reaches a minimum and then increases with density. Comparison of theory with experimental data yields a cross section between 3.0 and 10.0 × 10−18 for the conversion of Hg(3P1) to metastable Hg(3P0) by two-body collisions with Hg(1S0). The sharp increase at high density of the decay constant of the 2537-Å mercury line has not been predicted by previous theories but is a general consequence of the inclusion of collisional destruction mechanisms.