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
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.
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.
A suitable theoretical scheme able to describe, in a wide variety of astrophysical situations, the phenomenon of atomic line polarization by electron impact is developed. Starting from the general principles of quantum mechanics and assuming the Born approximation, the rate equations for the density matrix elements of a multilevel atomic system, interacting with a nonrelativistic electron beam having any kind of angular distribution, are derived in full generality. The resulting theory generalizes the previous ones by accounting for the collisional rates and the cross sections concerning both inelastic and superelastic collisions (in any geometrical situation), and, moreover, by taking into account the coherences among Zeeman sublevels split by a magnetic field. As an example of particular relevance, the general formulas derived in the first sections of the paper are subsequently particularized to the case of the electric dipole interaction.
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 theory of electron-impact excitation of atoms in which fine structure is included as a perturbation is presented in detail. Hyperfine structure is included in the target atom but neglected in the electron-atom interaction. Expressions for electron-photon angular-correlation parameters and scattering cross sections are derived in terms of products of complex scattering amplitudes, with emphasis on electron-sodium excitation. Examples are given in which zero-field quantum beats may be observed in electron-photon angular-correlation and differential-cross-section measurements. Some of the interference terms are only observable in angular-correlation experiments. Examples are also given of partial cross sections for electron-impact excitation of state-to-state hyperfine levels in terms of direct- and exchange-scattering amplitudes plus additional terms due to the inclusion of fine-structure effects. The expressions given allow a comparison between the various possible scattering experiments.
Explicit expressions for the angular distribution and frequency dependence of radiation scattered by a spatially degenerate atom undergoing collisions are derived using a previously developed formalism of the quantum theory of line broadening for an atom in its rest frame. Results valid in the impact regime for resonant scattering are presented for the cases of linear incident and scattered polarization circular incident and linear scattered polarization, and unpolarized incident radiation with no monitoring of the scattered polarization. These results relate to scattering involving a j - j + or - 1 - j atomic transition, with lower-state interactions neglected; the expressions obtained take a relatively simple form involving atomic multipolar relaxation rates of the order of k = 0 and k = 2. The angular distributions for each case are combined with the frequency dependences to yield a three-component frequency redistribution function for an s-p-s transition, the components being a coherent term, a frequency-redistributed term with the same angular dependence as the coherent term, and an isotropic frequency-redistributed term.