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AIP conference proceedings

Experimental determination of orbital and spin contributions to density matrices of excited atomic states formed in transfer-excitation

O. Yenen, D. H. Jaecks, B. W. Moudry

Published Jan 1, 1997• 0 citations

Abstract

For a quantum system, the density matrix contains all the statistical information that can be obtained from measurements. For excited atomic states, the coefficients in a spherical basis expansion of the density matrix, up to rank two, are proportional to Alignment and Orientation Parameters given by Fano and Macek and are called the state multipoles or multipole moments. They can be experimentally determined from the measurements of the Stokes parameters of the emitted photon. To obtain maximum possible information, one needs to break the axial symmetry of the experiment by specifying a reflection plane determined through a coincidence measurement. For LS coupled atomic states, if one can spectroscopically resolve J-multiplets, and if the process is spin dependent, information about the contributions to the state multipoles due to orbital and spin angular momenta can be extracted. In the process, it is also possible to determine the octupole moments of the excited state due to orbital and spin angular momenta. An illustrative example from transfer-excitation reactions in He+-Ar collisions at low keV energies will be presented. For coupling schemes other than LS coupling, using a similar decoupling one can determine the contributions due to appropriate angular momenta. The method is general enough that one can apply it to ion, atom, electron or photon projectiles incident on atomic targets.

DOI: 10.1063/1.52668

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For a quantum system, the density matrix contains all the statistical information that can be obtained from measurements. For excited atomic states, the coefficients in a spherical basis expansion of the density matrix, up to rank two, are proportional to Alignment and Orientation Parameters given by Fano and Macek and are called the state multipoles or multipole moments. They can be experimentally determined from the measurements of the Stokes parameters of the emitted photon. To obtain maximum possible information, one needs to break the axial symmetry of the experiment by specifying a reflection plane determined through a coincidence measurement. For LS coupled atomic states, if one can spectroscopically resolve J-multiplets, and if the process is spin dependent, information about the contributions to the state multipoles due to orbital and spin angular momenta can be extracted. In the process, it is also possible to determine the octupole moments of the excited state due to orbital and spin angular momenta. An illustrative example from transfer-excitation reactions in He+-Ar collisions at low keV energies will be presented. For coupling schemes other than LS coupling, using a similar decoupling one can determine the contributions due to appropriate angular momenta. The method is general enough that one can apply it to ion, atom, electron or photon projectiles incident on atomic targets.

The density matrix parametrisation of collisionally excited atomic ensembles is generalised to account for projectile and target spin polarisations. The density matrix elements, containing spin-resolved alignment and orientation parameters, can be determined by measurements of the 'generalised Stokes parameters' introduced by Andersen and Bartschat (1994) to describe scattered-projectile-polarised-photon coincidence experiments. Focusing on electron impact excitation of light alkali-type targets and mercury, the present experimental status of such experiments is reviewed, in particular with regard to the 'perfect scattering experiment' whereby all independent scattering amplitudes are determined.

The description of alignment and orientation for collisional excitation of atomic states by electron and heavy-particle impact, including electron transfer processes, is reviewed. For D states, a new parametrization of the excited atomic ensemble is proposed, and the density matrices describing the excited target state and the light emitted in a subsequent optical decay are expressed in terms of the new parameter set. Recipes for performing complete experiments through scattered-particle - multiple-photon coincidence set-ups are discussed. Because of the difficulties associated with such experiments, attention is also given to the generally incomplete case of scattered-particle - one-photon coincidence arrangements. For D-state excitation, it is demonstrated how the new set of parameters allows for a systematic description of the collision process, and provides opportunities for consistency checks.

The density matrix parametrization of collisionally excited atomic ensembles is generalized to account for a projectile spin. The elements are related to the ``generalized Stokes parameters'' of Andersen and Bartschat [J. Phys. B 27, 3189 (1994)], determined in scattered-projectile--polarized-photon coincidence experiments after impact excitation by spin-polarized electrons. The well-established orientation propensity rule for unpolarized electron beam experiments is not valid for spin-resolved collisions.

A brief review is given on development of electron-photon coincidence studies from electron impact of atoms. The theory of electron-photon correlations is outlined in detail in terms of cross sections of excited atoms and excited state charge clouds. The state of a target atom is determined by the various orientation and alignment parameters and the multipole moments of the excited atom. General considerations, such as coherence effects in impact excitation, the influence of fine and hyperfine structures in correlations are taken into account. The relationship between scattering amplitudes (including their phases) and target parameters is worked out for singlet and doublet transitions.

The resonant interaction of optical radiation with atomic vapors can excite the atoms into anisotropic states with long lifetimes. The conventional description of these states uses an expansion in a basis of multipole moments, which are represented by irreducible tensor operators. We demonstrate an experimental method that permits the excitation of these atomic multipole moments in specific, experimentally controllable spatial orientations. Complementary optical methods permit the observation of multipole moments of arbitrary order and a direct measurement of their spatial orientation. We demonstrate these procedures in the ground state of atomic sodium, using optical pumping to polarize the angular-momentum substates. We show how the experimental results can be used to separate signal contributions that originate from different multipole moments.

The determination of cross sections for the relaxation of atomic multipole moments from the intensities of the components of a resolved Zeeman fluorescence spectrum may be carried out using the density-matrix formalism. However, the spherical-tensor basis is not well adapted to state-selected measurements and can allow a significant propagation of error. We can reduce the error by determining the Q(j,m\ensuremath{\rightarrow}j',m') cross sections directly from the data taken at the lowest pressures. A comparison is given between recent experimental and theoretical relaxation cross sections for collisions of 5

^{2}P

potassium atoms with ground-state He, Ne, and Ar atoms.