Hyperfine Structure and the Polarization of Resonance Radiation. II. Magnetic Depolarization and the Determination of Mean Lives

Breit has derived formulae giving the polarization $P\left(H\right)\mathrm{}$ and the angle of maximum polarization $\theta$ 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 $\tau$ 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 $\mathrm{Cd}\left(\lambda 3261\right)$ and that of $\mathrm{Hg}\left(\lambda 2537\right)$, and it is found that the differences between the value of $\tau$ calculated from hyperfine structure data and that calculated from $tan2\theta$ by the usual non-hyperfine structure method lie well within the experimental error. $\frac{P\left(H\right)\mathrm{}}{P_0}$ 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 $7{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of mercury have been recalculated from Richter's data on the polarization of stepwise radiation. The values of $\tau$ obtained by this method of calculation are 7.2×${10}^{-9\mathrm{}}$ for $\lambda 4047$, 1.69×${10}^{-8\mathrm{}}$ for $\lambda 4358$ and 1.53×${10}^{-8\mathrm{}}$ for $\lambda 5461$. A discussion of Richter's results is given.