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Journal of Physics B Atomic and Molecular Physics

Polarisation of the 63P1from S61S0line of mercury

R. A. Bonham

Published May 28, 1982• 12 citations
Publisher

Abstract

The theory of the polarisation of the 6 3 P 1 from 6 1 S 0 line of Hg after excitation by forward scattered electrons is reviewed. Certain problems encountered in previous studies are pointed out and it is shown that the Ochkur approximation fails to give adequate agreement with the experiment. It is also pointed out that in the case where hyperfine splitting is not resolved experimentally that a different means of averaging over the nuclear hyperfine contribution must be employed. A discussion is presented on why an Ochkur-type approximation might improve on the Born approximation near an excitation threshold.

DOI
10.1088/0022-3700/15/10/005

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An isotope cell was used to eliminate the effect of hyperfine structure on the polarisation of radiation, near threshold, for the 6 3 P 1 -6 1 S 0 line of mercury (253.7 nm) excited by electron impact. These results are compared with the polarisation of the radiation when hyperfine structure is present.

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On the excitation of polarised light by electron impact. II.—Mercury

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Abstract In a number of recent papers descriptions have been given of how the light from atoms excited by a directed stream of electrons is polarised, in the absence of any external field of force. In particular we may refer to the paper by one of the present writers (Paper I), where some of the characteristics of the effect in mercury were discussed. It was found that the different lines of the spectrum were differently polarised, both in magnitude and direction. The behaviour of the polarisation when a magnetic field is applied to the mercury atoms was found to be identical with the effect produced by a similar field on the polarisa­tion when the light is excited by the absorption of plane polarised light, the electric vector of which is parallel to the direction of the stream of electrons. In this way, the polarisation of the light excited by electron impact was shown to be closely related to the polarisation of resonance radiation, which had been investigated by Wood and Ellett and others. In the paper referred to, the measurement of the polarisation of the spectral lines was, except in an individual instance, only qualitative. Since its appearance two papers have appeared in which polarisation measurements of the mercury lines excited by electron impact have appeared. Eldridge and Olsen gave qualitative results, and these confirmed those which we had given. Quarder gives quantitative measure­ments which are also for the most part in general accord. The aim of the present paper is to describe quantitative results, and, as will be seen, these are not in all cases in detailed agreement with those given by Quarder. The second aim is to determine the variation of the polarisation with the velocity of the electron stream, a point which has not been previously attempted. In Paper I it was shown that the magnitude of the polarisation is intimately connected with the dynamics of the collision process. By the electron impact, the atom is raised from its normal state into an upper quantum state, and by its return into the normal state, or into another state, light is emitted. The magnitude of the polarisation depends on both of these processes, but the second process, the actual emission of the light, is well understood. Polarisation measurements therefore give a powerful means of investigating the collision of an electron with an atom in the case when excitation of the atom takes place, and it is in this that their main interest lies.

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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

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
The theory of the polarisation of the 6 3 P 1 from 6 1 S 0 line of Hg after excitation by forward scattered electrons is reviewed. Certain problems encountered in previous studies are pointed out and it is shown that the Ochkur approximation fails to give adequate agreement with the experiment. It is also pointed out that in the case where hyperfine splitting is not resolved experimentally that a different means of averaging over the nuclear hyperfine contribution must be employed. A discussion is presented on why an Ochkur-type approximation might improve on the Born approximation near an excitation threshold.
The polarisation of 2154 nm photons emitted from Hg atoms which are excited by electrons scattered in the forward direction has been measured for collision energies between 5.5 and 15 eV. From the results the relative contribution of exchange excitation could be determined. Exchange is found to be the dominant excitation mechanism from threshold up to 8 eV collision energy. The results are also expressed by the alignment parameter lambda and good agreement is found with a previous measurement using incident polarised electrons. The results are explained in terms of intermediate coupling.
Abstract In a number of recent papers descriptions have been given of how the light from atoms excited by a directed stream of electrons is polarised, in the absence of any external field of force. In particular we may refer to the paper by one of the present writers (Paper I), where some of the characteristics of the effect in mercury were discussed. It was found that the different lines of the spectrum were differently polarised, both in magnitude and direction. The behaviour of the polarisation when a magnetic field is applied to the mercury atoms was found to be identical with the effect produced by a similar field on the polarisa­tion when the light is excited by the absorption of plane polarised light, the electric vector of which is parallel to the direction of the stream of electrons. In this way, the polarisation of the light excited by electron impact was shown to be closely related to the polarisation of resonance radiation, which had been investigated by Wood and Ellett and others. In the paper referred to, the measurement of the polarisation of the spectral lines was, except in an individual instance, only qualitative. Since its appearance two papers have appeared in which polarisation measurements of the mercury lines excited by electron impact have appeared. Eldridge and Olsen gave qualitative results, and these confirmed those which we had given. Quarder gives quantitative measure­ments which are also for the most part in general accord. The aim of the present paper is to describe quantitative results, and, as will be seen, these are not in all cases in detailed agreement with those given by Quarder. The second aim is to determine the variation of the polarisation with the velocity of the electron stream, a point which has not been previously attempted. In Paper I it was shown that the magnitude of the polarisation is intimately connected with the dynamics of the collision process. By the electron impact, the atom is raised from its normal state into an upper quantum state, and by its return into the normal state, or into another state, light is emitted. The magnitude of the polarisation depends on both of these processes, but the second process, the actual emission of the light, is well understood. Polarisation measurements therefore give a powerful means of investigating the collision of an electron with an atom in the case when excitation of the atom takes place, and it is in this that their main interest lies.
For the mercury 6s6p 1 P 1 and 6s6p 3 P 1 states excited by electron impact, the linear polarization of the light emitted in the transition to the ground state has been measured from threshold to intermediate energy for the decay photons of 254 and 185 nm wavelength, respectively. The results for both lines are in surprisingly good agreement with a calculation based on the Born-Ochkur approximation, neglecting spin-orbit terms for the continuum electron but allowing for electron exchange effects and intermediate coupling.
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
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.