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Physical Review

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

Allan C. G. Mitchell

Published Jun 1, 1933• 1 citation
Publisher

Abstract

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. $\frac{P(H)}{{P}_{0}}$ 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 $\ensuremath{\tau}$ 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.

DOI
10.1103/physrev.43.887

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Fluorescence of the visible triplet lines of mercury (4047, 4358, 5461) was obtained by exciting a mixture of mercury vapor and a small amount of nitrogen by radiation from a quartz mercury arc. The fluorescence was observed at right angles to the exciting light beam and the polarization of each line, isolated by suitable filters, was measured by the method of crossed Wollaston prisms. Measurements in zero magnetic field (polarized excitation) gave 88.2 percent for 4047, -65.5 for 4358, and 14.55 for 5461, compared to theoretical values (broad line excitation) of 84.7, -67.0, and 8.7 percent, respectively. Measurements were then made of the polarization as a function of a magnetic field applied in the observation direction and the mean life of the $7^{3}S_{1}$ state calculated from the data. The mean life of this state as measured by 4047 and 4358 was 0.8\ifmmode\pm\else\textpm\fi{}0.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec. at about 3.0 mm nitrogen pressure. The mean life as measured by the line 5461 was about 0.6\ifmmode\pm\else\textpm\fi{}0.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec. The collision cross section for the $7^{3}S_{1}$ state against nitrogen was measured by measuring the polarization of 4358 at a field of 3 gauss and varying nitrogen pressures, giving the result ${{\ensuremath{\sigma}}_{q}}^{2}=1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$.

Physical Review•Jul 1, 1934•12 citations
Breit has derived formulae giving the polarization P(H)P(H)P(H) and the angle of maximum polarization \ensuremathθ\ensuremath{\theta}\ensuremathθ 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 \ensuremathτ\ensuremath{\tau}\ensuremathτ 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 Cd(\ensuremathλ3261)\mathrm{Cd}(\ensuremath{\lambda}3261)Cd(\ensuremathλ3261) and that of Hg(\ensuremathλ2537)\mathrm{Hg}(\ensuremath{\lambda}2537)Hg(\ensuremathλ2537), and it is found that the differences between the value of \ensuremathτ\ensuremath{\tau}\ensuremathτ calculated from hyperfine structure data and that calculated from tan2\ensuremathθtan2\ensuremath{\theta}tan2\ensuremathθ by the usual non-hyperfine structure method lie well within the experimental error. P(H)P0\frac{P(H)}{{P}_{0}}P0​P(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 ggg-value for the upper state of these isotopes is larger than any other upper hyperfine structure state involved. The mean lives of the 73S17^{3}S_{1}73S1​ state of mercury have been recalculated from Richter's data on the polarization of stepwise radiation. The values of \ensuremathτ\ensuremath{\tau}\ensuremathτ obtained by this method of calculation are 7.2\ifmmode\times\else\texttimes\fi{}10\ensuremath−9{10}^{\ensuremath{-}9}10\ensuremath−9 for \ensuremathλ4047\ensuremath{\lambda}4047\ensuremathλ4047, 1.69\ifmmode\times\else\texttimes\fi{}10\ensuremath−8{10}^{\ensuremath{-}8}10\ensuremath−8 for \ensuremathλ4358\ensuremath{\lambda}4358\ensuremathλ4358 and 1.53\ifmmode\times\else\texttimes\fi{}10\ensuremath−8{10}^{\ensuremath{-}8}10\ensuremath−8 for \ensuremathλ5461\ensuremath{\lambda}5461\ensuremathλ5461. 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 equation has been developed for the polarization, and the angle of maximum polarization of resonance radiation as observed along a magnetic field perpendicular to the electric vector and the direction of propagation of the incident beam. Explicit application has been made to the polarization and the angle for the line $^{1}S_{0}\ensuremath{-}^{1}P_{1}$ for various values of the ratio of the hyperfine separation constant to the natural breadth of the levels, for a nuclear moment of \textonehalf{}. It was noted here that the form of the curves might differ widely from that to be expected from classical considerations. The polarization, and the angle of maximum polarization for the sodium D lines, for several values of the same ratio, were computed and compared with experimental observations. Thus a range of possible values of AAA was determined, which is not in disagreement with previous figures, and a value for $\ensuremath{\tau}$ established which agrees well with that calculated from optical dispersion data.
Excitation of atoms in a vapor by polarized light produces unequal population of the magnetic sublevels of the excited state. The emitted optical resonance radiation is therefore partly polarized. The application of radiofrequency or microwave fields at a magnetic resonance frequency will induce transitions between sublevels of the excited state. The degree of polarization of the emitted optical resonance radiation is altered when the magnetic resonance condition is fulfilled. As suggested by Brossel and Kastler, this effect may be used to reveal the structure of the energy level. A detailed theory applicable to, and experiments on the 3P1^{3}P_{1}3P1​ state of all the isotopes of mercury are reported. The results obtained indicate that double resonance phenomena constitute a valuable new tool for investigating the structure of atomic energy levels. The mean life of the 3P1^{3}P_{1}3P1​ state is shown by observations on the resonance line widths to be 1.55\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}7}$ sec for all the isotopes. The ggg-factor of the 3P1^{3}P_{1}3P1​ state for isotopes with zero spin, measured in terms of the proton ggg-factor, is 1.4838\ifmmode\pm\else\textpm\fi{}0.0004.
$1^{1}S_{0}\ensuremath{-}2^{3}P_{1}$ of mercury excited by plane polarized light shows incomplete polarization both in the absence and in the presence of a weak field parallel to the electric vector. The amount of initial polarization depends upon the relative intensities of the hyperfine structure lines in the exciting light. The polarization with various relative orientations of field and light vector and the variation of polarization with field intensity in weak fields may be interpreted successfully by means of a semi-classical model, with proper relative intensities parallel and prependicular to the light vector, rotating after excitation with an angular velocity geH2mc\frac{\mathrm{geH}}{2mc}2mcgeH​ and emitting a damped wave. From curves connecting depolarization, rotation of maximum of polarization, etc., with field intensity $\ensuremath{\alpha}$, the damping constant, has been found to be 1.02 (\ifmmode\pm\else\textpm\fi{}0.02) 107{10}^{7}107 ${\mathrm{sec}}^{\ensuremath{-}1}$.
We have performed an analysis of the effect of hyperfine structure in an experiment in which an aligned excited state is probed using linearly polarized light. The state is born with a given electronic alignment resulting from a collisional process. It is probed after a time which is short in comparison to its radiative lifetime but much longer than ω−1hfs, where ℏωhfs is the hyperfine splitting. This means that hyperfine structure has ample time to ‘‘develop.’’ It is therefore essential to take into account both the hyperfine structure of the level and the manner in which the alignment is affected by recoupling to the new basis. Ratios of fluorescent intensities for different laser polarization configurations contain information on the alignment of the system. We show how these may be calculated for a system with several isotopes, some of which have hyperfine structure, and where many components are probed with appreciable strength. A comparison is made with our experimental results for the Hg(6 3P1) level probed on the 6 3P1–7 3S1 transition. The presence of hyperfine structure has a considerable influence on the measurements. It is important to understand such effects if one is to obtain information on the nascent electronic alignment by observation of the fluorescent intensities.
Fluorescence of the visible triplet lines of mercury (4047, 4358, 5461) was obtained by exciting a mixture of mercury vapor and a small amount of nitrogen by radiation from a quartz mercury arc. The fluorescence was observed at right angles to the exciting light beam and the polarization of each line, isolated by suitable filters, was measured by the method of crossed Wollaston prisms. Measurements in zero magnetic field (polarized excitation) gave 88.2 percent for 4047, -65.5 for 4358, and 14.55 for 5461, compared to theoretical values (broad line excitation) of 84.7, -67.0, and 8.7 percent, respectively. Measurements were then made of the polarization as a function of a magnetic field applied in the observation direction and the mean life of the 73S17^{3}S_{1}73S1​ state calculated from the data. The mean life of this state as measured by 4047 and 4358 was 0.8\ifmmode\pm\else\textpm\fi{}0.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec. at about 3.0 mm nitrogen pressure. The mean life as measured by the line 5461 was about 0.6\ifmmode\pm\else\textpm\fi{}0.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}8}$ sec. The collision cross section for the 73S17^{3}S_{1}73S1​ state against nitrogen was measured by measuring the polarization of 4358 at a field of 3 gauss and varying nitrogen pressures, giving the result ${{\ensuremath{\sigma}}_{q}}^{2}=1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}$ cm2{\mathrm{cm}}^{2}cm2.