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Electron Impact Excitation of Polarised Sodium and Potassium.

Muhammad Abdul-Hakim Bukhari

Published Jan 1, 1991• 0 citations
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Abstract

A beam of unpolarised electrons is crossed at right angles with a beam of partially polarised sodium or potassium atoms (degree of polarisation PA = 21%). The resonance radiation from excited 2P3/2,1/2 states is observed in a direction perpendicular to both beams, and the Stokes parameters P1, P2 and P3, of the emitted photons are measured, \n \n[equation omitted] \n \nwhere 0 degrees, 45 degrees, 90 degrees and 135 degrees corresponds to the polariser angle measured from the electron beam direction and RHC, LHC to right and left hand circular polarisation in the spectroscopic definition. Because of reflection symmetries, only P1 is expected to be non-zero for unpolarised atoms. If polarised atoms are used with their spins parallel to the direction of the observed photons, P3 should also become non-zero (in addition to P1) while P2 remains zero. Such an experiment was originally proposed by Kleinpoppen, Phys. Rev. A3, 2015 (1971). \n \nWe report here an independent measurement on the neutral sodium NaI (32P3/2,1/2 – 32S1/2) transition (lambda = 589.0, 589.6 nm) and present new results for the neutral potassium KI (52P3/2,1/2 – 42S1/2) transition (lambda = 404.4, 404.7nm). The sodium results show close similarities to the work done by S. Osimitsch, Diplomarbeit Universitat Bielefeld (1983) and Jitschln at al J. Phys. B 17 1899 (1984) especially for P1 and P2. \nThe potassium results for P2 agree well with the theoretical prediction of zero and the results for P1 show close similarities to those of sodium results at high and intermediate energies, while at low energy especially close to threshold they differ. The threshold polarisation (P1) in the case of potassium is about 10%. Our values for sodium are somewhat higher than the results of Osimitsch (1983) and Jitschin et al (1984) and in very close agreement with the theoretical work done by Moores and Norcross, J. Phys. B5, 1482 (1972) and Kennedy et al, J. Phys. B10 3759 (1977) .The trend of P3 for potassium is similar to that of sodium in such a way that it is low at low energy and Increases in value as the energy increases, until it reaches a limit of 17% at high energy. The circular polarisation, P3, depends on the particular interaction processes which took place. At low energy, the three interaction channels, the exchange, the direct and the interference interaction are comparable and this will explain the low value of P3, at low energy due to spin flips of the electron of the atom in the exchange processes. At high energy the circular polarisation P3, is high which indicates that the exchange processes are minimal.

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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

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Extension of a basic experiment: the polarisation of the white-light-excited spectrally resolved Na D lines and its relation to electron impact excitation

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The polarisation of spectrally resolved Na D lines excited by white, linearly polarised light in a homogeneous magnetic field up to 1000 G was measured by means of the crossed-beam technique. The axis of observation, the sodium beam and the direction of the magnetic field were mutually at right angles. The incoming light beam was directed along the magnetic field and linearly polarised either parallel to the axis of observation or perpendicular to it. A Lyot filter of high transmission and a sensitive photon-counting technique made it possible to detect the small intensities of the resolved Na D doublet excited by the light of a xenon arc lamp. The measured polarisations are found to be in excellent agreement with those calculated by means of Breit's theory and the ambiguities of earlier investigations are completely removed. The importance of our results for electron impact excitation in magnetic fields parallel to the beam is discussed. It is shown that the polarisation of the electron impact excited Na D lines is no longer perturbed by hyperfine structure if a magnetic field of 500 G parallel to the beam is applied.

Journal of Physics B Atomic and Molecular Physics•Nov 14, 1980•1 citation
A beam of unpolarised electrons is crossed at right angles with a beam of partially polarised sodium or potassium atoms (degree of polarisation PA = 21%). The resonance radiation from excited 2P3/2,1/2 states is observed in a direction perpendicular to both beams, and the Stokes parameters P1, P2 and P3, of the emitted photons are measured, \n \n[equation omitted] \n \nwhere 0 degrees, 45 degrees, 90 degrees and 135 degrees corresponds to the polariser angle measured from the electron beam direction and RHC, LHC to right and left hand circular polarisation in the spectroscopic definition. Because of reflection symmetries, only P1 is expected to be non-zero for unpolarised atoms. If polarised atoms are used with their spins parallel to the direction of the observed photons, P3 should also become non-zero (in addition to P1) while P2 remains zero. Such an experiment was originally proposed by Kleinpoppen, Phys. Rev. A3, 2015 (1971). \n \nWe report here an independent measurement on the neutral sodium NaI (32P3/2,1/2 – 32S1/2) transition (lambda = 589.0, 589.6 nm) and present new results for the neutral potassium KI (52P3/2,1/2 – 42S1/2) transition (lambda = 404.4, 404.7nm). The sodium results show close similarities to the work done by S. Osimitsch, Diplomarbeit Universitat Bielefeld (1983) and Jitschln at al J. Phys. B 17 1899 (1984) especially for P1 and P2. \nThe potassium results for P2 agree well with the theoretical prediction of zero and the results for P1 show close similarities to those of sodium results at high and intermediate energies, while at low energy especially close to threshold they differ. The threshold polarisation (P1) in the case of potassium is about 10%. Our values for sodium are somewhat higher than the results of Osimitsch (1983) and Jitschin et al (1984) and in very close agreement with the theoretical work done by Moores and Norcross, J. Phys. B5, 1482 (1972) and Kennedy et al, J. Phys. B10 3759 (1977) .The trend of P3 for potassium is similar to that of sodium in such a way that it is low at low energy and Increases in value as the energy increases, until it reaches a limit of 17% at high energy. The circular polarisation, P3, depends on the particular interaction processes which took place. At low energy, the three interaction channels, the exchange, the direct and the interference interaction are comparable and this will explain the low value of P3, at low energy due to spin flips of the electron of the atom in the exchange processes. At high energy the circular polarisation P3, is high which indicates that the exchange processes are minimal.
A beam of unpolarized electrons is crossed at right angles with a beam of partially polarized sodium or potassium atoms (degree of polarization P A approximately=21%) and resonance lines from the excited 2 P 3/2, 1/2 states are observed in a direction perpendicular to both the atom and electron beams for electron energies from threshold to 200 eV. The polarization of the emitted photons is measured in the form of the Stokes parameters P 1 , P 2 and P 3 . The present measurements for sodium atoms are in better agreement with the theoretical values than the previously published experimental results. No other experimental or theoretical results are available for potassium atoms.
General expressions are presented and investigated for the degree of polarisation of electrons produced in the resonant two-photon ionisation of unpolarised atoms from the ground S state. The exciting and ionising electromagnetic fields are assumed to have arbitrary directions of propagation and arbitrary degrees of polarisation. It is shown that completely polarised electrons can be obtained when the matrix element of the P to S transition from the resonant state to the continuum is larger than the matrix element of the P to D transition. Such cases are realised in sodium and potassium atoms.
An electron-photon coincidence technique has been used to study the coherence of the excitation of the 3 2 P state in sodium. The total polarisation of the decay photons has been determined by measuring the linear and circular components of the Stokes's vector. Analysis of the reduced degree of polarisation mod P mod shows that the excitation is coherent for electrons which have been scattered through the angular range from 3 to 10 degrees . The concept of reduced polarisation assumes that the Percival-Seaton hypothesis applies to the collision. Thus the authors deduce that the nuclear spin plays no role in the excitation process at this energy and over these scattering angles. Scattering parameters have been deduced from the individual components of the Stokes's vector. These have been compared with those predicted by calculations based on the first Born and distorted-wave polarised orbital approximations. It is found that neither theory adequately describes the interaction.
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
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.
The polarisation of spectrally resolved Na D lines excited by white, linearly polarised light in a homogeneous magnetic field up to 1000 G was measured by means of the crossed-beam technique. The axis of observation, the sodium beam and the direction of the magnetic field were mutually at right angles. The incoming light beam was directed along the magnetic field and linearly polarised either parallel to the axis of observation or perpendicular to it. A Lyot filter of high transmission and a sensitive photon-counting technique made it possible to detect the small intensities of the resolved Na D doublet excited by the light of a xenon arc lamp. The measured polarisations are found to be in excellent agreement with those calculated by means of Breit's theory and the ambiguities of earlier investigations are completely removed. The importance of our results for electron impact excitation in magnetic fields parallel to the beam is discussed. It is shown that the polarisation of the electron impact excited Na D lines is no longer perturbed by hyperfine structure if a magnetic field of 500 G parallel to the beam is applied.