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The Journal of Chemical Physics

Three-vector correlation study of orientation and coherence effects in Na(3p,2P1/2←2P3/2)+He: Semiclassical and quantum calculations

Regina de Vivie‐Riedle, Jan P. J. Driessen, Stephen R. Leone

Published Feb 1, 1993• 16 citations
Publisher

Abstract

‘‘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.

DOI
10.1063/1.465053

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‘‘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.
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.
Intramultiplet mixing collisions have been investigated using polarized Ne(3p)\mathrm{Ne}(3p)Ne(3p) atoms with a well-defined initial relative velocity, i.e., two initial-state vectors. By analyzing the final-state center-of-mass velocity with a (Doppler-detuned) probe laser with a well-defined polarization and detecting the laser-induced fluorescence we measure the differential cross section and the polarization of the final state, i.e., two final-state vectors. Measurements have been done at a collision energy E=70meV,E=70\mathrm{meV},E=70meV, for both the ${\ensuremath{\alpha}}_{7}$ and ${\ensuremath{\alpha}}_{9}$ (Paschen numbering) initial states. For the elastic ${\ensuremath{\alpha}}_{7}\ensuremath{\rightarrow}{\ensuremath{\alpha}}_{7}$ collisions the experimental results are strongly hindered by the undesired response on elastic scattering of the metastable Ne(3s,3P0)\mathrm{Ne}{(3s,}^{3}{P}_{0})Ne(3s,3P0​) state. Inelastic collisions have been investigated for the ${\ensuremath{\alpha}}_{9}$ state, that forms a closed level system with the metastable Ne(3s,3P2)\mathrm{Ne}{(3s,}^{3}{P}_{2})Ne(3s,3P2​) state. For the ${\ensuremath{\alpha}}_{9}\ensuremath{\rightarrow}{\ensuremath{\alpha}}_{8}$ transition experimental results are presented for both parallel and perpendicular orientations of the polarizations of the pump and probe laser, respectively, as well as for circular polarized $({\ensuremath{\sigma}}^{+},{\ensuremath{\sigma}}^{+})$ and $({\ensuremath{\sigma}}^{+},{\ensuremath{\sigma}}^{\ensuremath{-}})$ configurations. The experiments are compared to a full quantum-mechanical coupled channels calculation of the scattering process, using the model potentials of Hennecart and Masnou-Seeuws as input. The output of this calculation is combined with a density matrix description of the initial- and final-state polarization. Both shape of the differential cross sections and their relative scaling for different laser polarizarion configurations agree well with experiment. This gives strong support for the quality of the model potentials used.
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.
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 of the Na atoms is in the 5s or 4d state and the other in the ground state. The polarization of the Na*(3p) atoms can be varied by changing the laser polarization. By using two counterpropagating Na beams and intersecting them twice by a laser beam (directly and indirectly after reflection against a mirror) the polarization of the two collision partners can be varied independently. Since the laser beam intersects the Na beams at an angle of 87.6 degrees , the relative velocity of the atoms can furthermore be selected by exploiting the Doppler effect. In the authors' experiment the relevant cross sections and coherences, specified according to the various magnetic substate combinations of the colliding Na*(3p) atoms, can be determined.
A laser pump–probe experiment is used to study the orbital alignment effects, orientation effects and vector correlations of collisional transfer of the Ca (4s)1(4p)1, 3P1 state to the Ca (4s)1(4p)1, 3P2, 0 levels. The experiment is configured in a single-collision crossed-beam arrangement between Ca and He, and multi-structure cross-sections are determined using appropriate combinations of linear and circular laser light for the pump/probe steps. Real and imaginary parts of coherence cross-sections are obtained along with the conventional population cross-sections for the m1→m2 magnetic sublevel transitions into the 3P2 level. The total relative cross-section ratio for the perpendicular (m1=±1) to parallel (m1= 0) polarization preparation of 3P1 transferring to 3P2 is 1.46 ± 0.15. For initial 3P1 preparation with laser light linearly polarized perpendicular to the initial relative velocity vector, the transfer into the m2-sublevels of the 3P2 state show a distinct preference for the sign-changing m1=+ 1 →m2=–1 transition. Preparation of Ca 3P1 with laser light linearly polarized parallel to the initial relative velocity vector produces population transfer into the 3P2 level that is completely aligned in the ±1 and ±2 sublevels, consistent with symmetry considerations. The magnitudes of the coherence cross-sections range from a few percent to greater than 100% of some of the population transfer conventional cross-sections. Study of the alignment effect into the final 3P0 state found a very large observed effect (σ|m|= 1/σ|m|= 0) of 23 ± 0.9. Interpretation of the energy transfer results indicates that the energy transfer obeys symmetry rules and follows predictions of curve crossings between the Σ and Π potentials, where for the transfer into 3P2 only indirect coupling can occur.
Coherence transfer accompanying 32P1/2 → 32P3/2 excitation transfer in sodium, induced in collisions with noble gas atoms, has been investigated using methods of sensitized fluorescence. Oriented 32P1/2 sodium atoms were produced by irradiating a mixture of sodium vapor and a noble gas with D1σ+ resonance radiation, and their subsequent collisions with the buffer gas atoms resulted in the simultaneous transfer of coherence and excitation from the 2P1/2 state to the 2P3/2 state. Measurements of the ratio of circular polarizations of the D2 sensitized fluorescence and D1 resonance fluorescence resulted in the following cross sections for coherence transfer. Na–He : 7.1 ± 0.7 Å2; Na–Ne : 6.2 ± 0.6 Å2; Na–Ar : 12.0 ± 1.2 Å2; Na–Kr : 6.8 ± 0.7 Å2; Na–Xe : 6.9 ± 0.7 Å2.