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Physical Review

Polarization of Resonance Radiation in Mercury

Harry F. Olson

Published Sep 1, 1928• 14 citations
Publisher

Abstract

$1^{1}S_{0}\ensuremath{-}2^{3}P_{1}$ 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 $\frac{\mathrm{geH}}{2mc}$ 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) ${10}^{7}$ ${\mathrm{sec}}^{\ensuremath{-}1}$.

DOI
10.1103/physrev.32.443

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Hyperfine Structure and Polarization of 1S01−2P13 of Mercury in Resonance Radiation

A. Ellett, Walter A. MacNair

The incomplete polarization of $\ensuremath{\lambda}2537\mathrm{A}$ of mercury in resonance radiation is due to the peculiar behavior of the outer two hyperfine structure lines. The three remaining hyperfine structure lines behave in accordance with the predictions of the theory of the anomalous Zeeman effect for a ${1}^{1}$${\mathrm{S}}_{0}$-${2}^{3}$${\mathrm{P}}_{1}$ line. Von Keussler's observation of complete polarization in 7900 gausses is explained, in part at least, by the observed shift of the -25.6 hyperfine structure line, and complete polarization is obtained with a field only 2000 gausses using a resonance radiation source.

Physical Review•Feb 1, 1928•15 citations

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

Allan C. G. Mitchell

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.

Physical Review•Jun 1, 1933•1 citation

Depolarization of Resonance Radiation

Paul D. Foote

Depolarization and quenching of mercury resonance radiation are phenomena of quite different type. Depolarization is produced by two effects. With gases which quench by effecting the transition $^{3}P_{1}\ensuremath{\rightarrow}^{3}P_{0}$ upon collision with Hg\ensuremath{'} atoms, there exists a pronounced reverse transition $^{3}P_{0}\ensuremath{\rightarrow}^{3}P_{1}$ produced by collision with high speed molecules. Atoms which radiate without any collision emit polarized light under the conditions of the experiment. Those which become $^{3}P_{1}$ atoms after having existed as $^{3}P_{0}$ atoms have experienced a large number of collisions and have lost their orientation relative to the incident electric vector; accordingly they emit radiation polarized in random directions. The second depolarizing influence arises in collisions at distances exceeding the ordinary kinetic theory collision such as is described above, at which the distance is too great for a collision of the first or second type, but still small enough for the field of the gas atom to exert a perturbing influence on the orientation of the Hg\ensuremath{'} atom. Depolarization by ${\mathrm{H}}_{2}$ is an excellent example of the second influence while the first effect is sufficient to interpret the experimental data with the rare gases, the atomic fields of which decrease with a high power of the radial distance.

Physical Review•Sep 1, 1927•1 citation

Polarized Resonance Radiation in Weak Magnetic Fields

Robert Williams Wood, A. Ellett

Effect of a magnetic field on the polarization of resonance radiation of mercury and of sodium.---(1) Mercury $\ensuremath{\lambda}2536$. A beam of plane polarized monochromatic light was focussed on the bulb containing the vapor at low pressure (0\ifmmode^\circ\else\textdegree\fi{}C), and the polarization of the resonance radiation was determined photographically with the aid of a quartz wedge and a double image quartz prism. If the exciting beam is going east with the electric vector vertical, when the earth's field is carefully neutralized the polarization is 90 per cent in any horizontal direction and zero vertically; a field of only 2 gauss directed north reduces the polarization in its direction to nearly zero (the decrease with increasing field being exponential), changes the polarization east and also up to 60 percent, and increases the intensity directed upwards threefold. Similar effects are produced by fields in other directions. The polarization with zero field does not approach 100 per cent at low pressures, since 90 per cent was found also with the vapor at -50\ifmmode^\circ\else\textdegree\fi{}C, when the radiation first appeared. It was thought that the high value might be due to an orientation of the resonating atom by the field of the exciting light, but a beam of concentrated sunlight produced no effect. As found by Malinowski, a strong field of 10,000 gauss merely increased the intensity of the radiation about 10 per cent. This added light was found to be unpolarized. (2) Sodium $D$ line. In the case of sodium vapor the tube was heated to 185\ifmmode^\circ\else\textdegree\fi{}C, the observations were visual, and as a source of unreversed light, the glow on the surface of a sodium glass vacuum tube carrying a discharge, was used. The effects observed are similar to those for mercury, but differ for some directions; fields forty times stronger were required, and the polarization in zero field was only 6 per cent, probably due to traces of hydrogen. This was increased by the field in some directions to 30 per cent.Effect of magnetic field on fluorescent light of iodine vapor and on white scattered light from mercury and ether vapors.---The polarization was found not to be affected.

Physical Review•Sep 1, 1924•74 citations

Polarization of Radiation Excited by Electron Impact

A. Ellett, Paul D. Foote, Fred L. Mohler

Polarized radiation following electron impact.---If a unidirectional beam of electrons, of velocity slightly in excess of the resonance potential, is projected through a vapor at a very low pressure so that effects due to atomic collision and resonance radiation are negligible, and in the absence of an applied field and resulting Larmor precession, there is reason to suspect that the radiation emitted perpendicular to the electron beam should be partially polarized, especially for lines corresponding to $\ensuremath{\Delta}j=1$.Polarization in mercury and sodium vapor.---Experiment showed a polarization of about 30 percent for $\ensuremath{\lambda}2537$ with the greatest intensity of the electrical vibration having a direction perpendicular to the electron beam. No polarization was detected for the unresolved sodium D-lines, confirming the recent observation of Kossel and Gerthsen.Polarization in mercury with field of 3 gauss.---A field parallel to the electron beam produced no effect. With the field perpendicular to the beam the radiation along the field was unpolarized while that perpendicular to the field was reduced in polarization to 13 percent. These results suggest that the atom radiates with the same distribution of polarization and intensity as in zero field but with the atom rotated through an angle determined by the time of excitation and the precessional velocity.

Physical Review•Jan 1, 1926•19 citations

Effect of Hyperfine Structure upon the Magnetic Rotation of the Plane of Maximum Polarization of Resonance Radiation

Bertrand J. Miller

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 $A$ 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.

Physical Review•Aug 1, 1940•0 citations
11S0\ensuremath−23P11^{1}S_{0}\ensuremath{-}2^{3}P_{1}11S0​\ensuremath−23P1​ 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 \ensuremathα\ensuremath{\alpha}\ensuremathα, the damping constant, has been found to be 1.02 (\ifmmode\pm\else\textpm\fi{}0.02) 107{10}^{7}107 sec\ensuremath−1{\mathrm{sec}}^{\ensuremath{-}1}sec\ensuremath−1.
The incomplete polarization of $\ensuremath{\lambda}2537\mathrm{A}$ of mercury in resonance radiation is due to the peculiar behavior of the outer two hyperfine structure lines. The three remaining hyperfine structure lines behave in accordance with the predictions of the theory of the anomalous Zeeman effect for a 11{1}^{1}11S0{\mathrm{S}}_{0}S0​-23{2}^{3}23P1{\mathrm{P}}_{1}P1​ line. Von Keussler's observation of complete polarization in 7900 gausses is explained, in part at least, by the observed shift of the -25.6 hyperfine structure line, and complete polarization is obtained with a field only 2000 gausses using a resonance radiation source.
Breit has derived formulae giving the polarization P(H)P(H)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. 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 $\ensuremath{\tau}$ 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.
Depolarization and quenching of mercury resonance radiation are phenomena of quite different type. Depolarization is produced by two effects. With gases which quench by effecting the transition $^{3}P_{1}\ensuremath{\rightarrow}^{3}P_{0}$ upon collision with Hg\ensuremath{'} atoms, there exists a pronounced reverse transition $^{3}P_{0}\ensuremath{\rightarrow}^{3}P_{1}$ produced by collision with high speed molecules. Atoms which radiate without any collision emit polarized light under the conditions of the experiment. Those which become 3P1^{3}P_{1}3P1​ atoms after having existed as 3P0^{3}P_{0}3P0​ atoms have experienced a large number of collisions and have lost their orientation relative to the incident electric vector; accordingly they emit radiation polarized in random directions. The second depolarizing influence arises in collisions at distances exceeding the ordinary kinetic theory collision such as is described above, at which the distance is too great for a collision of the first or second type, but still small enough for the field of the gas atom to exert a perturbing influence on the orientation of the Hg\ensuremath{'} atom. Depolarization by H2{\mathrm{H}}_{2}H2​ is an excellent example of the second influence while the first effect is sufficient to interpret the experimental data with the rare gases, the atomic fields of which decrease with a high power of the radial distance.
Effect of a magnetic field on the polarization of resonance radiation of mercury and of sodium.---(1) Mercury $\ensuremath{\lambda}2536$. A beam of plane polarized monochromatic light was focussed on the bulb containing the vapor at low pressure (0\ifmmode^\circ\else\textdegree\fi{}C), and the polarization of the resonance radiation was determined photographically with the aid of a quartz wedge and a double image quartz prism. If the exciting beam is going east with the electric vector vertical, when the earth's field is carefully neutralized the polarization is 90 per cent in any horizontal direction and zero vertically; a field of only 2 gauss directed north reduces the polarization in its direction to nearly zero (the decrease with increasing field being exponential), changes the polarization east and also up to 60 percent, and increases the intensity directed upwards threefold. Similar effects are produced by fields in other directions. The polarization with zero field does not approach 100 per cent at low pressures, since 90 per cent was found also with the vapor at -50\ifmmode^\circ\else\textdegree\fi{}C, when the radiation first appeared. It was thought that the high value might be due to an orientation of the resonating atom by the field of the exciting light, but a beam of concentrated sunlight produced no effect. As found by Malinowski, a strong field of 10,000 gauss merely increased the intensity of the radiation about 10 per cent. This added light was found to be unpolarized. (2) Sodium DDD line. In the case of sodium vapor the tube was heated to 185\ifmmode^\circ\else\textdegree\fi{}C, the observations were visual, and as a source of unreversed light, the glow on the surface of a sodium glass vacuum tube carrying a discharge, was used. The effects observed are similar to those for mercury, but differ for some directions; fields forty times stronger were required, and the polarization in zero field was only 6 per cent, probably due to traces of hydrogen. This was increased by the field in some directions to 30 per cent.Effect of magnetic field on fluorescent light of iodine vapor and on white scattered light from mercury and ether vapors.---The polarization was found not to be affected.
Polarized radiation following electron impact.---If a unidirectional beam of electrons, of velocity slightly in excess of the resonance potential, is projected through a vapor at a very low pressure so that effects due to atomic collision and resonance radiation are negligible, and in the absence of an applied field and resulting Larmor precession, there is reason to suspect that the radiation emitted perpendicular to the electron beam should be partially polarized, especially for lines corresponding to $\ensuremath{\Delta}j=1$.Polarization in mercury and sodium vapor.---Experiment showed a polarization of about 30 percent for $\ensuremath{\lambda}2537$ with the greatest intensity of the electrical vibration having a direction perpendicular to the electron beam. No polarization was detected for the unresolved sodium D-lines, confirming the recent observation of Kossel and Gerthsen.Polarization in mercury with field of 3 gauss.---A field parallel to the electron beam produced no effect. With the field perpendicular to the beam the radiation along the field was unpolarized while that perpendicular to the field was reduced in polarization to 13 percent. These results suggest that the atom radiates with the same distribution of polarization and intensity as in zero field but with the atom rotated through an angle determined by the time of excitation and the precessional velocity.
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.