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Annalen der Physik

Zur Theorie depolarisierender Stöße von angeregten Alkaliatomen mit Edelgasatomen

M. Elbel

Published Jan 1, 1969• 3 citations
Publisher

Abstract

Abstract A recently proposed model providing an easy calculation of the branching ratios of collision‐induced transitions among the ZEEMAN sublevels of exited alkali atoms is criticized. It proves valid if no coupling takes place between the angular momentum of the motion of the colliding atoms and the projection of the electronic orbital momentum upon the internuclear axis. This coupling would arise if the molecular σ‐ and π‐states of the incoming wave would be strongly dephased during the collision. As a consequence, the transitions 2P1/2, m = 1/2 ↔ 1P1/2, m = −1/2 and 2P3/2, m = − 1/2 would occur which would be forbidden in the case of only slight dephasing of the σ‐ and the π‐states.

DOI
10.1002/andp.19694770508

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Depolarisation in Na-Ar optical collisions

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The depolarisation of the redistributed Na D1and D2line fluorescence caused by Na-Ar collisions after far-wing excitation was investigated. In the limit of zero Ar density the J=1/2orientation and J=3/2alignment reflect the distribution among Zeeman sublevels of Na 32PJproduced after absorption of a photon into one or several excited Na-Ar molecular states at small internuclear separation, followed by a mixing between these states during dissociation. Measurements of these quantities as functions of the detuning up to Delta omegaJ=50 cm-1in the red wings are compared with quantum-mechanical coupled-channel (CC) calculations using realistic molecular potentials and thermal averaging, and with predictions from the factorisation approximation (FA) of the theory of redistribution. Fair agreement with CC calculations and FA predictions was obtained within the impact region, proving the validity of the factorisation assumption there. Outside this region the overall depolarisation is primarily due to reorientation of the Na 3P electronic angular momentum and is reproduced qualitatively by the CC calculations but not by the FA theory. Additional depolarisation connected with the fine-structure coupling was observed.

Journal of Physics B Atomic and Molecular Physics•Jul 14, 1985•19 citations
Abstract A recently proposed model providing an easy calculation of the branching ratios of collision‐induced transitions among the ZEEMAN sublevels of exited alkali atoms is criticized. It proves valid if no coupling takes place between the angular momentum of the motion of the colliding atoms and the projection of the electronic orbital momentum upon the internuclear axis. This coupling would arise if the molecular σ‐ and π‐states of the incoming wave would be strongly dephased during the collision. As a consequence, the transitions 2P1/2, m = 1/2 ↔ 1P1/2, m = −1/2 and 2P3/2, m = − 1/2 would occur which would be forbidden in the case of only slight dephasing of the σ‐ and the π‐states.
Transition matrix elements connecting the Zeeman sublevels of the lowest p doublets in light alkali atoms have been derived using methods of steady-state collision theory. The matrix elements generally consist of two parts which, under rotations of the quantization axis with respect to the scattering plane, behave like components of a first rank and a second rank tensor, respectively. Only the second rank tensor components lead to the selection rule j, mJ↔j, −mj, whereas the first rank tensor components do not. The latter can be ascribed to a formal interaction term which is proportional to the inner product of the orbital angular momenta of the valence electron and the colliding atoms, respectively, thus accounting for molecular coupling phenomena during the collision. Finally, the transition matrix elements are used to calculate the depolarizing cross sections from the van der Waals potential.
To gain insight into the mechanism of Na(3p)2P3/2→2P1/2 fine-structure transitions induced by collision with He, we monitor the expectation values of the orbital- and spin-angular momentum vectors, l and s, as a function of time along the trajectory, using a semiclassical formalism. In a typical collision, 〈s〉 remains nearly space-fixed while 〈l〉 precesses about the rotating internuclear axis. Thus, in the interaction region, the projection of 〈l〉 onto the internuclear axis, 〈λ〉, remains nearly constant, and the molecular alignment of the orbital is preserved. We show how equations of motion for the classical analogues of these expectation values agree qualitatively with the quantum equations of motion. A qualitative comparison is also made with the Cs–He system for which the spin–orbit coupling is much stronger. We calculate cross sections for Na(2P3/2)+He→Na(2P1/2)+He as a function of the alignment of the excitation laser polarization with respect to the asymptotic relative velocity vector. For stationary pumping of the excited F=3 hyperfine level, this calculation predicts that the perpendicular alignment gives a cross section which is larger by a factor of 1.8 than that obtained by parallel alignment.
The nonadiabatic mechanism of the quenching of the alkali atoms' Rydberg states in collisions with atoms of the same type, is described. The diabatic energy curves depend on the internuclear distance due to internuclear axis rotation and transitions are produced by the polarisation interaction of the atom with the Rydberg electron. It is shown that the cross sections of the processes may be large enough: sigma approximately 103-104 au and the principal role of classically forbidden nuclear configurations is exposed. The results are shown to be dependent on the type of Rydberg atom.
Transitions between states with the same principal quantum number n in the collision of a Rydberg atom with an ion are described within the classical approximation for the Rydberg electron. The quantum electron state is represented by an ensemble of classical trajectories. Within the dipole approximation for the interaction the final value of the orbital momentum l is calculated analytically for each initial trajectory in the ensemble. Averaging over the ensemble gives the distribution function over l. For the initial s state of the Rydberg atom the distribution functions are found also for the pairs of variables, namely: {the angular momentum; its projection on the collision velocity}; {projections of the angular momentum and the Runge - Lenz vector on the collision velocity} and {projections of the angular momentum and the Runge - Lenz vector on the plane perpendicular to the collision velocity}. The l-distributions for the orbitally polarized initial p and d Rydberg states with definite projections of the initial angular momentum on the velocity axis are also obtained. The influence of the non-Coulomb core is taken into account by an approximation. The final l-distributions (calculated for the initial s-state) are shifted towards the large-l values as the relative collision velocity vn decreases. Good agreement is achieved with the recent experimental data for Na(28d) and Na(26d) Rydberg atoms.
The dependence of the circular polarization of the fluorescence of alkali atoms on the intensity and spectral composition of the σ+-polarized exciting D1 line has been investigated by considering the stationary solutions of rate equations for populations of the Zeeman sublevels. The calculations were performed for pumping-light intensities corresponding to those of classical light sources, e.g., radio frequency or microwave discharge lamps, and commonly accepted values of cross sections for collisional relaxation of ground-state and excited atoms. The systematic errors of cross sections for collisional disorientation of 2P1/2 alkali atoms due to the neglect of intensity and spectral composition of the exciting light are estimated.
The depolarisation of the redistributed Na D1and D2line fluorescence caused by Na-Ar collisions after far-wing excitation was investigated. In the limit of zero Ar density the J=1/2orientation and J=3/2alignment reflect the distribution among Zeeman sublevels of Na 32PJproduced after absorption of a photon into one or several excited Na-Ar molecular states at small internuclear separation, followed by a mixing between these states during dissociation. Measurements of these quantities as functions of the detuning up to Delta omegaJ=50 cm-1in the red wings are compared with quantum-mechanical coupled-channel (CC) calculations using realistic molecular potentials and thermal averaging, and with predictions from the factorisation approximation (FA) of the theory of redistribution. Fair agreement with CC calculations and FA predictions was obtained within the impact region, proving the validity of the factorisation assumption there. Outside this region the overall depolarisation is primarily due to reorientation of the Na 3P electronic angular momentum and is reproduced qualitatively by the CC calculations but not by the FA theory. Additional depolarisation connected with the fine-structure coupling was observed.