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Physical Review

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

Bertrand J. Miller

Published Aug 1, 1940• 0 citations
Publisher

Abstract

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.

DOI
10.1103/physrev.58.258

Related papers

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

Polarization of Resonance Radiation in Mercury

Harry F. Olson

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

Physical Review•Sep 1, 1928•14 citations

Hyperfine Structure and the Polarization of Mercury Resonance Radiation

Allan C. G. Mitchell

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.

Physical Review•Jun 15, 1932•4 citations

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

The polarization of atomic line radiation excited by electron impact

Ian Colin Percival, M. J. Seaton

Abstract The dipole radiation emitted by an atom excited by a unidirectional electron beam has a nonuniform angular distribution which is simply related to the percentage polarization P of the radiation emitted perpendicular to the beam. P was first calculated using the OppenheimerPenney (O.-P.) theory. In this theory the probability of excitation of an upper quantum state and the probability of subsequent emission of a polarized photon from such a state are considered independently. P is finally expressed in terms of the cross-sections QM for excitation of states of definite component of angular momentum along the direction of the electron beam. In general, P is dependent on detailed numerical calculations of QM j, but the selection rule A = 0 removes this dependence at threshold. In the O.-P. theory allowance may be made for fine structure and hyperfine structure, but the theory is ambiguous when the f.s. or h.f.s. separations are comparable with the line width. A theory is therefore developed which is based on the calculation of the probability of a polarized photon being emitted by the complete system of atom + electron. The ambiguity of the O.-P. theory is removed by integration over line profiles, but the expressions reduce to O.-P. expressions when the f.s. or h.f.s. separations are much smaller or much larger than the line width. The Lyot line of hydrogen is an intermediate case for which the line widths and the h.f.s. separations are comparable. Assuming the validity of the Born approximation, a simple expression is obtained which allows the QM to be calculated from the angular distribution of the scattered electrons. Theoretical predictions are compared with experimental results. For the Na£) lines the predicted polarization is small enough to escape experimental detection. Polarizations observed by - Skinner & Appleyard in 1927 for various Hg lines rise to maxima with decreasing electron energy, and then tend to values close to zero at threshold. These experimental results at low energies appear to be inexplicable in terms of the reactions considered, but if the polarization curve above the maximum is extrapolated to threshold, the theory and experiment are found to be in reasonable agreement. Further experimental work is thought to be desirable

Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences•Nov 6, 1958•573 citations

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
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 1S0\ensuremath−1P1^{1}S_{0}\ensuremath{-}^{1}P_{1}1S0​\ensuremath−1P1​ 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 \ensuremathτ\ensuremath{\tau}\ensuremathτ established which agrees well with that calculated from optical dispersion data.
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.
$1^{1}S_{0}\ensuremath{-}2^{3}P_{1}$ 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 ${\mathrm{sec}}^{\ensuremath{-}1}$.
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.
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.
Abstract The dipole radiation emitted by an atom excited by a unidirectional electron beam has a nonuniform angular distribution which is simply related to the percentage polarization P of the radiation emitted perpendicular to the beam. P was first calculated using the OppenheimerPenney (O.-P.) theory. In this theory the probability of excitation of an upper quantum state and the probability of subsequent emission of a polarized photon from such a state are considered independently. P is finally expressed in terms of the cross-sections QM for excitation of states of definite component of angular momentum along the direction of the electron beam. In general, P is dependent on detailed numerical calculations of QM j, but the selection rule A = 0 removes this dependence at threshold. In the O.-P. theory allowance may be made for fine structure and hyperfine structure, but the theory is ambiguous when the f.s. or h.f.s. separations are comparable with the line width. A theory is therefore developed which is based on the calculation of the probability of a polarized photon being emitted by the complete system of atom + electron. The ambiguity of the O.-P. theory is removed by integration over line profiles, but the expressions reduce to O.-P. expressions when the f.s. or h.f.s. separations are much smaller or much larger than the line width. The Lyot line of hydrogen is an intermediate case for which the line widths and the h.f.s. separations are comparable. Assuming the validity of the Born approximation, a simple expression is obtained which allows the QM to be calculated from the angular distribution of the scattered electrons. Theoretical predictions are compared with experimental results. For the Na£) lines the predicted polarization is small enough to escape experimental detection. Polarizations observed by - Skinner & Appleyard in 1927 for various Hg lines rise to maxima with decreasing electron energy, and then tend to values close to zero at threshold. These experimental results at low energies appear to be inexplicable in terms of the reactions considered, but if the polarization curve above the maximum is extrapolated to threshold, the theory and experiment are found to be in reasonable agreement. Further experimental work is thought to be desirable
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.