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Journal of Physics B Atomic and Molecular Physics

On the coherence of the excitation of the 32P state in sodium by 100 eV electrons

P. J. O. Teubner, J L Riley, J. E. Furst, Stephen J. Buckman

Published Jan 28, 1985• 11 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/18/2/021

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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.
Components of the Stokes vector have been measured using an electron-photon coincidence technique for radiation emitted normal to the scattering plane in the electron excitation of the 3 2 P state in sodium at several energies from 5.1 to 30 eV. The coherence of the excitation process is probed through the concept of the reduced polarisation. The data are compared with those derived from optical pumping experiments, which are the time-reversed equivalent of the present experiments. In general, very good agreement is found with the data from the two techniques. Scattering amplitudes derived from the components of the Stokes vector are compared with theoretical predictions. It is observed that there is only moderate agreement between theory and experiment.
This thesis presents the results of experimental investigation of coherence in the excitation of the 2p states of atomic hydrogen through a collision with an unpolarised electron. The polarisation correlation variation of the delayed coincidence method has been employed to simultaneously measure the reduced Stokes parameters P1,P2 and P3, which are needed to fully characterise the state of the atom immediately after the collision. This has also allowed the excitation coherence parameter P+ to be determined directly. In the case of the excitation of 2p states of hydrogen, a deviation of P+ from unity is indicative of the importance of spin exchange during the collision. A new Lyman- polarisation analyser, that permits independent rotation of a retarder and a linear polariser, was developed for this work. A novel approach to the analysis of data from electron-photon coincidence measurements has been implemented to improve the quality of the final results. The reduced Stokes parameters P1,P2 and P3 were measured at 54.4 eV electron energy, and in the 4-40 range of electron scattering angles. The P1 and P2 results are consistent with the earlier measurements, and recent theoretical predictions. The new P3 results, however, deviate significantly from the predictions of all modern theories, and also differ from previous experimental results. The newly measured values of P+ also suggest less coherent excitation than predicted by the theory, even at a relatively low scattering angle of 30. Several possible sources of systematic error including resonance radiation trapping, Stark mixing and erroneous phase-shift of the retarder have been considered, but are insufficient to explain the observed deviations from theory. Therefore, we are forced to conclude that spin exchange may play a more significant role during the collision than current theoretical methods predict.
The linear and circular polarisation of the K(4 2 P to 4 2 S) photons detected in delayed coincidence with the inelastically scattered K atoms are presented for K-He collisions at 93 eV as a function of the scattering angle. Data are analysed in terms of the Stokes parameters, and the coherence properties of the excitation process are examined. It is concluded that spin dependent forces do not play an important role in the excitation process. The lambda and chi parameters are also derived. Simple models for the excitation process are discussed in order to explain the impact parameter dependence of chi .
The atomic collision parameters ?, ?, ?, ?, P, |P| and |�| were determined from measurements of the pseudo Stokes parameters for superelastic scattering of 20 eV incident electrons at angles of 10� and 15� from the 32P312 excited state of sodium. Two depolarising factors K and K' for the pseudo Stokes parameters are defined for it and a laser excitation respectively to account for the depolarising influence due to optical pumping in the hyperfine structure of the 32P3t2 excited state. A theoretical model of the laser excitation of the sodium transition is developed to determine K and K'. The theory developed is a quantum -electrodynamic description of the resonant interaction of monochromatic light with the 32S in(F'=2) <-> 32P3a(F=3,2,1) hyperfine transitions of the sodium D2 line formualated in terms of the Heisenberg atomic operator. Off diagonal state coherences and all relaxation terms are included. It is found that the equations for the populations, optical coherences and certain state coherences form a closed subset of the total system of equations. This subset is sufficiently small to enable numerical computation. As well as K and K', the model is used to calculate the probability of occupation of the various atomic states and the polarisation of the sideways scattered fluorescence from the laser excited atoms. The results of this model are compared with the predictions of four other models, a rate equation model which includes only the F=3 excited state, a semiclassical model based on the density operator, a low light intensity approximation to the semiclassical model and a high intensity model which uses a transformed basis for the states. For both it and a laser excitation it is shown that the QED calculated values converge to the values predicted by the high and low intensity approximations in the appropriate limits.
We present experimental values of the electron impact coherence parameters (EICP) and reduced Stokes parameters for excitation of 51P1 state of cadmium atoms. The results have been obtained using electron–photon coincidence technique for incident electron energies 80 eV and 60 eV and electron scattering angles in the range of 5° to 50°. We also present an additional set of data for electron energy 100 eV and scattering angle 50° which complements our previous results. All the experimental values are compared with theoretical relativistic distorted-wave approximation (RDWA) calculations. The first Born approximation (FBA) predictions of the alignment angle are also presented. The theoretical results are in good qualitative agreement with the experimental data.
In an electron-polarized photon coincidence experiment the Stokes' parameters P 1 , P 2 , P 3 and P 4 have been determined for four Ne * (3p) to Ne * (3s) transitions at a fixed electron energy of 50 eV and in the electron angular scattering range 30 degrees -70 degrees . The results indicate a tendency towards positive values for P 3 at the lowest scattering angles studied and a strong tendency towards zero and even negative values for P 4 . In all cases a drop in the total polarization degree between 30 degrees and 50 degrees electron scattering angle is observed, indicating that there is a decrease of coherence at these scattering angles.