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Canadian Journal of Physics

Collisional depolarization of light alkali atoms excited to their lowest 2P levels

M. Elbel

Published Dec 15, 1970• 10 citations
Publisher

Abstract

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.

DOI
10.1139/p70-378

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•Jan 1, 1967•0 citations
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.
An account of recent work is given by the author and co-workers on the experimental determination of cross sections for excitation transfer between the (2)P((1/2)) and (2)P(3/2)resonance levels in potassium, rubidium and cesium, induced by inelastic collisions with alkali atoms and inert gas atoms in their ground states. Forty values of cross sections were obtained in a series of sensitized fluorescence experiments, in which alkali vapors and vapor-gas mixtures were irradiated with one component of the appropriate alkali resonance doublet, and the relative intensities of both components appearing in the fluorescent light were measured. The experiments indicate that the collisional interaction between an alkali atom in a (2)P state and a ground state inert gas atom probably occurs between the inert gas atom and the (2)P alkali valence electron which behaves like a quasi-free particle.
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 2P^{2}P2P potassium atoms with ground-state He, Ne, and Ar atoms.
The effect of the hyperfine interaction on collisional relaxation among Zeeman sublevels is evaluated for a J=32J=\frac{3}{2}J=23​ state coupled to nuclear spins of 32\frac{3}{2}23​, 52\frac{5}{2}25​, and 72\frac{7}{2}27​. Standard depolarization experiments, performed on atoms with hyperfine structure, are discussed in terms of relaxation-probability matrices parametrized in terms of the relative collisional-transition probabilities for a nuclear-spin-zero atom. Experimental results involving D2{D}_{2}D2​ optical pumping of 85Rb^{85}\mathrm{Rb}85Rb and 87Rb^{87}\mathrm{Rb}87Rb are shown to support the approximation of nuclear decoupling in collisional relaxation. The cross sections for electronic collisional relaxation, assuming a van der Waals model for the collisional interaction, are, in units of ${10}^{\ensuremath{-}14}$ cm2{\mathrm{cm}}^{2}cm2, 1.19 (85Rb^{85}\mathrm{Rb}85Rb-He), 1.09 (85Rb^{85}\mathrm{Rb}85Rb-Ne), 2.44 (85Rb^{85}\mathrm{Rb}85Rb-Ar), 1.13 (87Rb^{87}\mathrm{Rb}87Rb-He), 1.03 (87Rb^{87}\mathrm{Rb}87Rb-Ne), and 2.26 (87Rb^{87}\mathrm{Rb}87Rb-Ar).
The polarization properties of excited alkali atoms having suffered half collisions with noble gas atoms following excitation by nonresonant photon absorption during a strong collision, are investigated. On the basis of a semiclassical perturbation treatment of the density matrix up to second order in the driving field a general expression for the polarization dependent intensity of the emitted alkali fluorescence is derived. Assuming quasistatic excitation of the collision complex and considering reorientation of the orbital and spin electronic angular momenta within a cut off radius, explicit results for the polarization degrees are presented and discussed, depending on the initial molecular excited state and coupling case.
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.
The mj mixing cross section for disorientation of magnetically 2 oriented potassium atoms in the 4 ^2/2 state» induced by collisions with ground state helium atoms, was measured using a modified Zeeman scanning technique.The mj substates of potassium atoms, situated in a strong magnetic field, were selectively excited and the collisionally induced mixing manifested itself by the depolarization of the potassium resonance fluorescence.The depolarization measurements yielded mixing cross -14 2 -14 2 sections ranging from 0.77 x 10 cm to 1.4 x 10 cm .It is felt that this discrepancy may be due to a selection rule for transitions between the fine structure states such that £nij = 0 is preferred.