We consider collisions between (quasi-) one- or two-electron atoms, each of which has been prepared in a fixed distribution of hyperfine magnetic substates. The resulting ``polarization-dependent'' reaction rates are functions of (1) the (experimentally adjustable) orientation of the quantization axis associated with the hyperfine substates, (2) the hyperfine terms of the colliding atoms, and (3) the detailed reaction dynamics as characterized by preparation- and fine-structure-independent cross sections. These effects are deconvoluted and analyzed, and their use in elucidating reaction mechanisms is discussed. Particular emphasis is placed on the associative ionization of two Na(3p) atoms, each prepared by adsorption of resonant laser photons. The quasimolecular states of Na...Na that might react in this case are limited by selection rules. More information on the reaction mechanism is then obtained by using experimental data, in combination with the formal analysis, to draw further conclusions about the active quasimolecular states.
For the first time, associative ionization has been observed in an atomic beam of excited sodium atoms in both the and the state. Relative values for the partial cross sections were obtained specified according to the different magnetic substate combinations of the two fine-structure states. These were found to be comparable to those for associative ionization between two atoms. However, the effect of the excitation on the ion production rate was found to be considerable and to depend strongly on the relative polarizations of the laser beams producing the two populations due to the redistribution of the involved magnetic sublevels. The results indicate that the initial orientation of the electron spin S does not significantly influence the associative ionization reaction at the mean collision energy of 25 meV.
We analyze the dependence of the rate of associative ionization of two radiatively excited atoms on the polarization properties of the exciting light. This provides a direct relation between the observed ion-production rate as a function of the polarization and the ionization rates for various combinations of the magnetic substates. We consider an atomic beam irradiated by a single laser beam, as well as an atomic vapor. The description applies to a recent experimental observation of a strong polarization dependence of the ionization rate in an atomic beam, and at the same time we suggest alternate experimental methods of analyzing the total cross sections of any inelastic or reactive binary collision of excited atoms as a function of the magnetic quantum numbers.
The associative ionization ${\mathrm{Na}}^{*}+{\mathrm{Na}}^{*}\ensuremath{\rightarrow}{{\mathrm{Na}}_{2}}^{+}+e$, when Na atoms in a single thermal beam are excited by linearly polarized light, was observed. The ion yield increases by a factor of 1.7 when the light polarization vector is rotated from a perpendicular to a parallel direction with respect to the beam. A theoretical analysis shows that the ionization rates
K obey the relations
K(21,23)=0 and
K(21,21)=1.4K(23,23), where the arguments indicate the initial magnetic substates
∣MJ∣ of the two colliding atoms.
The authors have studied in a beam experiment the energy pooling reaction between two laser-excited Na* (3p) atoms, where in the final state one Na atom is in the 5s or 4d state and the other in the ground state. They have found that this reaction is strongly dependent on the polarization of the laser light used to prepare the Na*(3p) atoms. An analysis of theoretical potential curves suggests that the reaction mainly proceeds via the input channel where one of the atoms is in the M=0 and the other in the M=1 substate. Their experimental results are in qualitative agreement with that suggestion.
The rate coefficient for the laser-induced associative-ionization reaction of ultracold Na in an optical trap is calculated as a function of the trap laser detuning from the Na
(2S1/2,F=2)\ensuremath{\rightarrow}Na
(2P3/2,F=3) resonance. Aided by a knowledge of the excited-state potential-energy curves and of the nature of the free-atom optical-pumping process, we propose the following mechanism, which we call photoassociative ionization (PAI): 2Na
(3${\mathrm{\ensuremath{\Sigma}}}_{\mathit{u}}^{+}$)${\ensuremath{\rightarrow}}^{\mathrm{\ensuremath{\Elzxh}}\mathrm{\ensuremath{\omega}}}$
Na2∗(${0}_{\mathit{g}}^{\mathrm{\ensuremath{-}}}$ and
1g)${\ensuremath{\rightarrow}}^{\mathrm{\ensuremath{\Elzxh}}\mathrm{\ensuremath{\omega}}}$
Na2∗∗(
1u)\ensuremath{\rightarrow}
Na2++${\mathit{e}}^{\mathrm{\ensuremath{-}}}$. Maxima in the calculated PAI rate coefficient occur at detunings that are simultaneously one-photon resonant with bound levels of the long-range ${0}_{\mathit{g}}^{\mathrm{\ensuremath{-}}}$ state and two-photon resonant with the lower rotational levels of a vibrational level lying 9 GHz below the dissociation threshold of the autoionizing
1u state. The calculated PAI spectrum (PAI rate coefficient versus trap-laser detuning) displays a series of broad peaks between -0.5 and -4 GHz detuning and a cutoff at -5 GHz detuning, as does the experimentally measured spectrum of Lett et al. [Phys. Rev. Lett. 67, 2139 (1991)].The broad widths of the peaks in the PAI spectrum is due in part to the orientation averaging of the collision vector with respect to the electric-field vector and to the optical pumping of the
Na2\ensuremath{\rightarrow}
Na2∗ rovibronic transition. The calculated PAI rate coefficient at -0.6 GHz detuning is a factor of 4 higher than the experimental value. Fine-structure-changing transitions play a role in the doubly excited states, because of the
1u avoided crossing, but not in the intermediate states, because they have gerade symmetry and the only states that have been shown to undergo fine-structure-changing transitions with large probability have ungerade symmetry. Several predictions based on the proposed model and suggestions for future experiments are discussed.
We have experimentally and theoretically investigated the behavior of excited Na atoms under the combined influence of resonant laser light and a weak magnetic field. The use of weak magnetic fields gives another possibility to vary the polarization of the atoms, additional to variation of the polarization of the exciting laser. We calculated in detail the influence of weak magnetic fields on the density matrix describing the excited atoms, using generalized rate equations. We checked the results of our model experimentally, at the Na(3 2 S1/2, Fl=2) →(3 2 P3/2, Fu =3) transition, excited with circularly polarized light. We determined the polarization of the excited atoms, by measuring the fluorescence light at various angles, as a function of both magnetic field strength and laser irradiance. Model and experiment agreed very well. We applied our model to the associative ionization of the excited Na atoms. We measured the ion signal as a function of magnetic field. Analyzing the results, we could determine a specific associative ionization cross section, which is not accessible in our experimental geometry without the use of magnetic fields. Thereby we showed that the application of magnetic fields in polarization dependence studies can provide us with additional information about the process.