Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Four-vector correlation experiment on Ne(3p)+He collisions: Measurements on intramultiplet mixing

S. S. Op de Beek, Jan P. J. Driessen, K. H. J. M. Robben, Herman C. W. Beijerinck, BOUDEWIJN J. VERHAAR

Published Oct 1, 1997• 4 citations
Publisher

Abstract

Intramultiplet mixing collisions have been investigated using polarized $\mathrm{Ne}(3p)$ 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 $E=70\mathrm{meV},$ 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 $\mathrm{Ne}{(3s,}^{3}{P}_{0})$ state. Inelastic collisions have been investigated for the ${\ensuremath{\alpha}}_{9}$ state, that forms a closed level system with the metastable $\mathrm{Ne}{(3s,}^{3}{P}_{2})$ 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.

DOI
10.1103/physreva.56.2833

Related papers

Initial- and final-state alignment and orientation effects in Ca energy pooling

Harold Parks, Stephen R. Leone

An experimental investigation is performed to determine the initial- and final-state alignment effects in the energy-pooling process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ This paper represents a type of four-vector correlation experiment, where two aligned atoms collide and the alignment of the final excited state is observed. The initial $\mathrm{Ca}(4s4p{}^{3}{P}_{1})$ state polarization is controlled with polarized lasers and magnetic fields, and the final-state alignment is partially resolved by observing the polarization of the fluorescence from the $\mathrm{Ca}(4s4p{}^{1}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}{(4s}^{2})$ emission. The mathematics are developed in this paper to provide a full quantitative description of the four-vector alignment cross sections observed here. Relative values that describe 18 of the 39 total independent parameters are obtained, thus defining the results of this collision process at an unprecedented level of detail. The final-state Ca polarization is found to be only weakly dependent on the initial-state alignment, with final-state fluorescence predominately polarized along the relative velocity vector of the collision.

Physical Review A•Oct 1, 1999•5 citations

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

‘‘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 Journal of Chemical Physics•Feb 1, 1993•16 citations

Laser preparation and probing of initial and final orbital alignment in collision-induced energy transfer Ca(4s5p, 1P1) +He→Ca(4s5p, 3P2)+He

Christopher J. M. Smith, Jan P. J. Driessen, Larry Eno +1 more

In a crossed beam atomic energy transfer experiment, relative cross sections are measured between initial and final magnetic substates of atomic orbitals in a three vector correlation experiment. A pulsed laser beam prepares Ca(4s5p 1P1) in a single magnetic sublevel ‖j1mi〉 with respect to the laser polarization vector. Subsequent collision with He at a well-defined relative velocity yields Ca(4s5p 3P2). The near-resonant Ca(4s5p 3P2) is probed by a second polarized pulsed laser, revealing its magnetic sublevel ‖j2mf〉 distribution with respect to the probe laser polarization vector. The experiment is analyzed in the collision frame where the direction of the initial relative velocity vector serves as the quantization axis. In this frame, the initial and final Ca states are characterized by substates ‖j1m1〉 and ‖j2m2〉, respectively. Fourteen collision frame cross sections are needed to describe the energy transfer completely. Eight of these cross sections are real and positive (conventional type—describing population transfer) and six are complex (coherence type—containing phase information). By symmetry, only 15 unique parameters for the real and imaginary parts of the cross sections are required, nine of which are obtained here using linear polarizations and collinear laser beams. Possible cases for circularly polarized light are also tabulated; measurement of these cases would provide several more parameters. For initial parallel preparation of the 1P1 p orbital with respect to the relative velocity (m1=0), the final 3P2 state is highly aligned in the m2=±1 and m2=±2 sublevels. Initial preparation of the p orbital perpendicular to the relative velocity vector (m1=±1) produces an aligned 3P2 state with greater population in the m2=0 and m2=±1 sublevels compared to the m2=±2 sublevels. Using the coherence information and symmetry, orientation cross sections are obtained into the m2=±1 sublevels (i.e., m preserving 1→1 and m-changing 1→−1) and are nearly identical. Preparation of the Ca p orbital perpendicular to the initial relative velocity enhances the state-specific collisional transfer of 1P1→3P2 by a factor of 2.2±0.2 over initial parallel preparation.

The Journal of Chemical Physics•Jun 1, 1992•34 citations

Polarization spectra of excited-state-Mg(3p)–rare-gas-atom optical collisions

Rosemary A. Lasell, D. A. Olsgaard, Mark D. Havey +1 more

Experimental, polarization-dependent excitation spectra for excited-state-Mg--rare-gas-atom optical collisions are reported. In these first studies of the process, polarized Mg atoms in the 3p $^{1}$${\mathit{P}}_{1}$ level are produced by absorption of linearly polarized light tuned to the 3s $^{1}$${\mathit{S}}_{0}$\ensuremath{\rightarrow}3p $^{1}$${\mathit{P}}_{1}$ resonance transition at 285.2 nm. Detuning-dependent, collision-induced polarization spectra are measured in a \ifmmode\pm\else\textpm\fi{}200-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range around the Mg 3p $^{1}$${\mathit{P}}_{1}$\ensuremath{\rightarrow}5s $^{1}$${\mathit{S}}_{0}$ transition at 571.2 nm. The spectra correspond to probing transient Mg-Ne and Mg-Ar molecules on 3p $^{1}\mathrm{\ensuremath{\Pi}}_{1}$\ensuremath{\rightarrow}5s $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$ and 3p $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$\ensuremath{\rightarrow}5s $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$ electronic transitions. Measurements of these excited-state polarization spectra for Mg-Ne optical collisions reveal that for detunings to the red of the atomic Mg 3p $^{1}$${\mathit{P}}_{1}$\ensuremath{\rightarrow}5s $^{1}$${\mathit{S}}_{0}$ transition, electronic linear polarization greater than 50% survives far into the molecular regime. This represents a direct measure of the polarization important to alignment-dependent inelastic processes in alkaline-earth-metal--rare-gas-atom collisions. The polarization spectra are discussed in terms of existing information on the interatomic potentials and through an axial recoil limit for the polarization degree for parallel and perpendicular molecular transitions. Rate coefficients k for disalignment of Mg 3p $^{1}$${\mathit{P}}_{1}$ atoms by collisions with Ar [k=9.4(5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/s] and with Ne [k=6.5(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{3}$/s] are also extracted from the data.

Physical Review A•Jul 1, 1994•9 citations

Spin exchange in the excitation of spin-polarized Na atoms by Ne+ -ion impact

Wolfgang Jitschin, S. Osimitsch, H Reihl +3 more

The 3s-3p excitation of spin-polarized Na atoms by ${\mathrm{Ne}}^{+}$ ions has been studied for impact energies ${E}_{\mathrm{lab}=200}$ eV to 6 keV, i.e., in the adiabatic regime. The total excitation cross section and the three Stokes polarization parameters of the fluorescence light have been measured. The linear polarization of the light shows a preferential excitation of the \ensuremath{\Vert}${m}_{l}$\ensuremath{\Vert}=1 magnetic substates. The circular polarization probes the spin orientation of the excited 3p state. At the highest impact energies investigated the experimental data are compatible with conservation of spin orientation during the collision. With decreasing impact energy, the spin polarization of the final 3p state becomes smaller than the spin polarization of the initial 3s state. This apparent spin depolarization is attributed to the exchange interaction between the Na valence electron and the unfilled ${\mathrm{Ne}}^{+}$ 2${p}^{5}$ core in the quasimolecule formed during the collision.

Physical Review A•Nov 1, 1986•19 citations

Resonant degenerate four-wave mixing spectroscopy of transitions with degenerate energy levels: Saturation and polarization effects

Thomas A. Reichardt, Robert P. Lucht

The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.

The Journal of Chemical Physics•Dec 8, 1999•22 citations
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 \ensuremathα7{\ensuremath{\alpha}}_{7}\ensuremathα7​ and \ensuremathα9{\ensuremath{\alpha}}_{9}\ensuremathα9​ (Paschen numbering) initial states. For the elastic \ensuremathα7\ensuremath→\ensuremathα7{\ensuremath{\alpha}}_{7}\ensuremath{\rightarrow}{\ensuremath{\alpha}}_{7}\ensuremathα7​\ensuremath→\ensuremathα7​ 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 \ensuremathα9{\ensuremath{\alpha}}_{9}\ensuremathα9​ 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 \ensuremathα9\ensuremath→\ensuremathα8{\ensuremath{\alpha}}_{9}\ensuremath{\rightarrow}{\ensuremath{\alpha}}_{8}\ensuremathα9​\ensuremath→\ensuremathα8​ 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 (\ensuremathσ+,\ensuremathσ+)({\ensuremath{\sigma}}^{+},{\ensuremath{\sigma}}^{+})(\ensuremathσ+,\ensuremathσ+) and (\ensuremathσ+,\ensuremathσ\ensuremath−)({\ensuremath{\sigma}}^{+},{\ensuremath{\sigma}}^{\ensuremath{-}})(\ensuremathσ+,\ensuremathσ\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.
An experimental investigation is performed to determine the initial- and final-state alignment effects in the energy-pooling process $\mathrm{Ca}(4s4p{}^{3}{P}_{1})+\mathrm{Ca}(4s4p{}^{3}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}(4s4p{}^{1}{P}_{1})+\mathrm{Ca}{(4s}^{2}).$ This paper represents a type of four-vector correlation experiment, where two aligned atoms collide and the alignment of the final excited state is observed. The initial Ca(4s4p3P1)\mathrm{Ca}(4s4p{}^{3}{P}_{1})Ca(4s4p3P1​) state polarization is controlled with polarized lasers and magnetic fields, and the final-state alignment is partially resolved by observing the polarization of the fluorescence from the $\mathrm{Ca}(4s4p{}^{1}{P}_{1})\ensuremath{\rightarrow}\mathrm{Ca}{(4s}^{2})$ emission. The mathematics are developed in this paper to provide a full quantitative description of the four-vector alignment cross sections observed here. Relative values that describe 18 of the 39 total independent parameters are obtained, thus defining the results of this collision process at an unprecedented level of detail. The final-state Ca polarization is found to be only weakly dependent on the initial-state alignment, with final-state fluorescence predominately polarized along the relative velocity vector of the collision.
‘‘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.
In a crossed beam atomic energy transfer experiment, relative cross sections are measured between initial and final magnetic substates of atomic orbitals in a three vector correlation experiment. A pulsed laser beam prepares Ca(4s5p 1P1) in a single magnetic sublevel ‖j1mi〉 with respect to the laser polarization vector. Subsequent collision with He at a well-defined relative velocity yields Ca(4s5p 3P2). The near-resonant Ca(4s5p 3P2) is probed by a second polarized pulsed laser, revealing its magnetic sublevel ‖j2mf〉 distribution with respect to the probe laser polarization vector. The experiment is analyzed in the collision frame where the direction of the initial relative velocity vector serves as the quantization axis. In this frame, the initial and final Ca states are characterized by substates ‖j1m1〉 and ‖j2m2〉, respectively. Fourteen collision frame cross sections are needed to describe the energy transfer completely. Eight of these cross sections are real and positive (conventional type—describing population transfer) and six are complex (coherence type—containing phase information). By symmetry, only 15 unique parameters for the real and imaginary parts of the cross sections are required, nine of which are obtained here using linear polarizations and collinear laser beams. Possible cases for circularly polarized light are also tabulated; measurement of these cases would provide several more parameters. For initial parallel preparation of the 1P1 p orbital with respect to the relative velocity (m1=0), the final 3P2 state is highly aligned in the m2=±1 and m2=±2 sublevels. Initial preparation of the p orbital perpendicular to the relative velocity vector (m1=±1) produces an aligned 3P2 state with greater population in the m2=0 and m2=±1 sublevels compared to the m2=±2 sublevels. Using the coherence information and symmetry, orientation cross sections are obtained into the m2=±1 sublevels (i.e., m preserving 1→1 and m-changing 1→−1) and are nearly identical. Preparation of the Ca p orbital perpendicular to the initial relative velocity enhances the state-specific collisional transfer of 1P1→3P2 by a factor of 2.2±0.2 over initial parallel preparation.
Experimental, polarization-dependent excitation spectra for excited-state-Mg--rare-gas-atom optical collisions are reported. In these first studies of the process, polarized Mg atoms in the 3p 1^{1}1P1{\mathit{P}}_{1}P1​ level are produced by absorption of linearly polarized light tuned to the 3s 1^{1}1S0{\mathit{S}}_{0}S0​\ensuremath{\rightarrow}3p 1^{1}1P1{\mathit{P}}_{1}P1​ resonance transition at 285.2 nm. Detuning-dependent, collision-induced polarization spectra are measured in a \ifmmode\pm\else\textpm\fi{}200-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ range around the Mg 3p 1^{1}1P1{\mathit{P}}_{1}P1​\ensuremath{\rightarrow}5s 1^{1}1S0{\mathit{S}}_{0}S0​ transition at 571.2 nm. The spectra correspond to probing transient Mg-Ne and Mg-Ar molecules on 3p $^{1}\mathrm{\ensuremath{\Pi}}_{1}$\ensuremath{\rightarrow}5s $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$ and 3p $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$\ensuremath{\rightarrow}5s $^{1}\mathrm{\ensuremath{\Sigma}}_{0}^{+}$ electronic transitions. Measurements of these excited-state polarization spectra for Mg-Ne optical collisions reveal that for detunings to the red of the atomic Mg 3p 1^{1}1P1{\mathit{P}}_{1}P1​\ensuremath{\rightarrow}5s 1^{1}1S0{\mathit{S}}_{0}S0​ transition, electronic linear polarization greater than 50% survives far into the molecular regime. This represents a direct measure of the polarization important to alignment-dependent inelastic processes in alkaline-earth-metal--rare-gas-atom collisions. The polarization spectra are discussed in terms of existing information on the interatomic potentials and through an axial recoil limit for the polarization degree for parallel and perpendicular molecular transitions. Rate coefficients k for disalignment of Mg 3p 1^{1}1P1{\mathit{P}}_{1}P1​ atoms by collisions with Ar [k=9.4(5)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ cm3{\mathrm{cm}}^{3}cm3/s] and with Ne [k=6.5(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}10}$ cm3{\mathrm{cm}}^{3}cm3/s] are also extracted from the data.
The 3s-3p excitation of spin-polarized Na atoms by Ne+{\mathrm{Ne}}^{+}Ne+ ions has been studied for impact energies Elab=200{E}_{\mathrm{lab}=200}Elab=200​ eV to 6 keV, i.e., in the adiabatic regime. The total excitation cross section and the three Stokes polarization parameters of the fluorescence light have been measured. The linear polarization of the light shows a preferential excitation of the \ensuremath{\Vert}ml{m}_{l}ml​\ensuremath{\Vert}=1 magnetic substates. The circular polarization probes the spin orientation of the excited 3p state. At the highest impact energies investigated the experimental data are compatible with conservation of spin orientation during the collision. With decreasing impact energy, the spin polarization of the final 3p state becomes smaller than the spin polarization of the initial 3s state. This apparent spin depolarization is attributed to the exchange interaction between the Na valence electron and the unfilled Ne+{\mathrm{Ne}}^{+}Ne+ 2p5{p}^{5}p5 core in the quasimolecule formed during the collision.
The physics of the degenerate four-wave mixing process for resonant transitions between two degenerate energy levels is investigated by direct numerical integration of the time-dependent density matrix equations. The Zeeman structure of the upper and lower energy levels is included in a multistate formulation of the density matrix equations. The inclusion of the Zeeman structure enables the investigation of the degenerate four-wave mixing process for different polarization configurations of the forward pump, backward pump, and probe beams. Saturation curves and lineshapes are calculated for different polarization configurations and for numerous low-J transitions. At low laser intensity, the results of our calculations are in excellent agreement with perturbation theory in terms of the relative intensities of the degenerate four-wave mixing signal for linear polarization configurations. As the laser intensity increases and the resonance starts to saturate, we find in general that the relative degenerate four-wave mixing reflectivity increases for the crossed polarization configurations compared to the parallel polarization configuration because the saturation intensity is higher. However, for some resonance transitions, some of the crossed polarization configurations saturate at lower laser intensities than the parallel polarization configuration, even though the reflectivity for these crossed polarization configurations is much lower than for the parallel polarization configuration in the perturbative intensity limit. This result is explained in terms of the coupling of the various Zeeman states during the degenerate four-wave mixing interaction for specific polarization configurations. The effect of saturation on the resonance line shapes for the different polarization configurations is also investigated. Finally, a limited number of calculations are performed for resonances that are Doppler broadened as well as collision broadened. The effect of saturation on the reflectivity of the crossed polarization configurations compared to the parallel polarization configuration is even more significant for resonances with comparable Doppler and collisional broadening.