Electron-impact excitation of the 3D state of sodium from the optically prepared 3P state
Journal of Physics B: Atomic, Molecular and Optical Physics
An experimental investigation of electron-impact excitation of the 3 2 D-state from the laser-excited 3 2 P state of atomic sodium is reported for 30 eV incident electron energy. A detailed consideration of the measurement technique is presented, based on the density matrix description of electron-impact-induced atomic transitions for target atoms in which the spin of the target electron is unchanged. It is shown that some inference about excitation probabilities between individual magnetic
... tates of the P-to D-state transition can be made from measurements of the four pseudo-Stokes parameters. A description of the inelastic scattering experiment and an analysis of the experimental measurements in terms of both the standard atomic collision parameters and magnetic substate excitation probabilities are presented. Convergent close-coupling theoretical calculations are compared with the experimental results and show good agreement. † M Shurgalin et al sections (DCSs), atomic-collision parameters (ACPs) can be measured (Andersen et al 1988, Andersen and Bartschat 1997) which are related to individual scattering amplitudes and thus provide finer details about the scattering process. The combination of both DCS and ACP measurements provides for more comprehensive tests of different theoretical models. However, characterization of ACPs for transitions between excited atomic states with higher angular momenta has not been developed to the same extent as for S-to P-state transitions. This can be explained by the fact that increasing the angular momentum of the states involved in electron-impact-induced transitions leads to a substantial increase in the number of individual scattering amplitudes required to fully characterize the scattering process. Accordingly, defining the experimentally measurable quantities and the techniques for measuring these quantities becomes more complex and difficult. As an example, for electron-impact-induced transitions between P-and D-states of sodium where the total spin is conserved, the number of scattering amplitudes in each total spin channel increases to eight, in comparison with only two scattering amplitudes for an S-to P-state transition (Andersen and Bartschat 1996) . One of the first experiments to measure ACPs for electron-impact-induced transitions between excited P-and D-states was performed by Hermann (1979) for sodium atoms at 5 eV incident electron energy. These data were not published until the review of Andersen et al (1988) made the results available. The experiment involved the preparation of the 3P excited state of sodium with polarized laser radiation and the measurement of pseudo-Stokes parameters, which are the relative differences in differential cross sections for different laser polarizations, for the 3P-to 3D-state transition. No analysis was made of the electronimpact-excited 3D-state. Such an experiment is equivalent to one in which the 'isotropic' D-state is de-excited to the P-state following superelastic electron scattering. The isotropic D-state has all magnetic substates equally populated with no coherences between them. 'Standard' ACPs for the electron-impact-excited P-state were obtained and a discussion in the framework of these ACPs was presented (Andersen et al 1988) . A theoretical calculation, using the convergent close-coupling method (CCC) was presented by Bray et al (1994). The CCC calculations proved to be in good agreement with the experimental data. Recently, similar work has been performed for barium atoms at 20 eV incident electron energy Zetner 1995, 1996). A number of ACPs were measured and a comparison was made with theoretical calculations utilizing the unitarized distorted-wave approximation. Also the relationship between ACPs and the partial differential cross sections (PDCS) (Hummer and Burns 1986 , Csanak et al 1992 , Li et al 1994 and the practical significance of the latter quantities were discussed. In the work presented in this paper, a general description of electron-impact-induced transitions between states of different angular momenta is developed, based on the density matrix formalism. Atomic species are considered where the total spin is conserved during the collision. The incident electrons are spin-unpolarized and no spin analysis is carried out for the final states. Measurement techniques are considered for studying electron-impact excitation of a D-state from a P-state together with a discussion of the information that can be obtained. An experiment is described in which inelastic scattering from the laserexcited 3 2 P 3/2 state of a sodium atom occurs. The experimental data are presented and analysed for excitation to the 3 2 D-state using 30 eV incident electron energy. Certain sums of magnetic substate excitation probabilities are obtained and discussed. Standard ACPs are also deduced from the measurements for the corresponding 'time-inverse' deexcitation process from the 3D isotropic state for the corresponding 28.4 eV incident electron energy.