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The Journal of Chemical Physics

Mechanism of collisionally induced transitions among fine-structure levels: Semiclassical calculations of alignment effects in the Na–He system

Laurie J. Kovalenko, Stephen R. Leone, J. B. Delos

Published Dec 1, 1989• 47 citations
Publisher

Abstract

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.

DOI
10.1063/1.457312

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3 2P1/2 ↔ 3 2P3/2 excitation transfer in sodium, induced in inelastic collisions with ground-state N2, H2, HD, and D2 molecules, has been investigated in a series of sensitized fluorescence experiments. Mixtures of sodium vapor at a pressure of 5 × 10−7 Torr, and the gases, were irradiated with each NaD component in turn, and the fluorescence which contained both D components was monitored at right angles to the direction of the exciting beam. Measurements of the relative intensities of the NaD fluorescent components yielded the following collision cross sections for excitation transfer. For Na–N2 collisions: Q12(2P1/2 → P3/2) = 144 Å2, Q21(2P1,2 ← 2P3/2) = 76 Å2 for Na–H2 collisions: Q12 = 80 Å2, Q21 = 42 Å2. For Na–HD collisions: Q12 = 84 Å2, Q21 = 44 Å2. For Na–D2 collisions: Q12 = 98 Å2, Q21 = 52 Å2. The cross sections Q21 exhibit a slight resonance effect between the atomic and molecular rotational transitions.

Canadian Journal of Physics•Oct 1, 1968•23 citations
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.
‘‘Multistructure’’ cross sections, of both conventional and coherence types, are calculated for the fine structure transition Na(2P1/2←2P3/2)+He in an energy range of 10–200 meV. The cross sections are related to conditions of a crossed beams experiment in which the three controlled vectors are the initial relative velocity and the two polarization directions of excitation and probe laser beams. Both semiclassical and quantum mechanical calculations are performed. The semiclassical method is employed to interpret and visualize the collision mechanism leading to the multistructure cross sections. In addition, the validity of the approximations used in the semiclassical model is investigated. For the conventional cross sections, the semiclassical and quantum-mechanical results are in good agreement. We find that both initial sodium states 3 2P3/2,3/2 and 3 2P3/2,1/2 preferentially populate the 3 2P1/2,−1/2 final state, i.e., a final state in which the sign of the magnetic quantum number has changed. Vector evolution diagrams are introduced to interpret the conventional cross sections and the pattern of the Stückelberg-like oscillations. The semiclassical model gives the correct order of magnitude for the coherence cross sections, but in this case, is inadequate in the quantitative description; thus the coherence cross sections are mainly studied with full quantum calculations. The coherence cross section is especially sensitive to small variations in the energy difference and shape of the potential curves. The value of the coherence cross section is strongly correlated to the position and well depth of the potential minimum of the 2Π state.
The cross sections for the excitation energy transfer in the collisional processes Na*(3P 1 2/)+M(nS 1 2/) to or from Na*(3p 3 2/)+m(Ns 3 2/), m being ground-state Rb (n=5) or Cs (n=6) atom, have been measured by laser fluorescence method. With either of the two sodium 3P fine-structure states optically excited, the intensity ratio of the sensitized to direct fluorescence was measured. The polarization effects due to partially polarized and anisotropic direct fluorescence were investigated. The measured cross sections (T=530 K) for the sodium 3P fine-structure excitation transfer induced by collisions with Rb are: sigma ( 1 / 2 to 3 / 2 )=170 AA 2 , with an overall accuracy of 20%. The corresponding values in the Cs case are: sigma ( 1 / 2 to 3 / 2 )=140 AA 2 , sigma ( 3 / 2 to 1 / 2 )=83 AA 2 . The theoretical calculations reveal the decisive role of the dipole-quadrupole interaction. The obtained values are in satisfactory agreement with the experiment only if both the dipole-dipole and dipole-quadrupole interactions are taken into account, while the calculations involving the dipole-dipole term alone yield the cross section values which are as much as one order of magnitude lower than the experimentally observed ones.
We have studied the effect of reactant Na(3p) polarization on the rotational angular momentum alignment of product Na2{\mathrm{Na}}_{2}Na2​+{\mathrm{}}^{+}+ ions arising from associative-ionization (AI) collisions. Our results show that sensitivity of the AI rate constant to initial atomic polarization persists even when all hyperfine states are populated with broadband (3 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) pulsed laser excitation of Na(2{(\mathrm{}}^{2}(2P3/2{P}_{3/2}P3/2​) and that the spatial distribution of product rotational angular momentum vectors is anisotropic. We discuss a qualitative description of the collision process consistent with our measurements which indicates that \ensuremath{\sigma}-orbital symmetry is preferred to \ensuremath{\pi}-orbital symmetry as the colliding partners approach.
We present a detailed study of the mechanism of spin–changing transitions between 1P and 3P electronic states corresponding to the nsn′p Rydberg state of an alkaline earth atom in collision with a structureless, spherical partner. This type of process takes place on four potential curves and involves collisional coupling between the electronic angular momentum L of the electronically excited atom, the spin S of the atom in the final 3P state, and the orbital angular momentum l associated with the relative motion of the collision partners. We review the use of Hund’s case coupling schemes in describing the collision and present a careful analysis of the initial state preparation under conditions of laser excitation in a crossed beam experiment. This underlies the development of a new statistical model for the dependence of the spin–changing cross section on the alignment of the pump laser. Finally, we describe a new technique to follow the redistribution of flux onto locally adiabatic states as the initially excited atom is approached by the closed-shell partner. This is used to show that dynamical corrections to our simple statistical model are small.
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.
3 2P1/2 ↔ 3 2P3/2 excitation transfer in sodium, induced in inelastic collisions with ground-state N2, H2, HD, and D2 molecules, has been investigated in a series of sensitized fluorescence experiments. Mixtures of sodium vapor at a pressure of 5 × 10−7 Torr, and the gases, were irradiated with each NaD component in turn, and the fluorescence which contained both D components was monitored at right angles to the direction of the exciting beam. Measurements of the relative intensities of the NaD fluorescent components yielded the following collision cross sections for excitation transfer. For Na–N2 collisions: Q12(2P1/2 → P3/2) = 144 Å2, Q21(2P1,2 ← 2P3/2) = 76 Å2 for Na–H2 collisions: Q12 = 80 Å2, Q21 = 42 Å2. For Na–HD collisions: Q12 = 84 Å2, Q21 = 44 Å2. For Na–D2 collisions: Q12 = 98 Å2, Q21 = 52 Å2. The cross sections Q21 exhibit a slight resonance effect between the atomic and molecular rotational transitions.