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.
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.
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) 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.
Retention of orbital alignment during near-resonant energy transfer collisions of rare-gas projectiles with excited alkaline-earth-metal atoms is explored theoretically for scattering of Xe from Rydberg states of Ca. For such collisions, conventional interpretations of alignment phenomena, which are based on potential curves for a transient molecule thought to form during the collision, are not relevant. Theoretical partial magnetic sublevel cross sections for ${\mathrm{Ca}}^{**}(4s17d{}^{1}{D}_{2}\ensuremath{\rightarrow}4s18p{}^{1}{P}_{1})$ transitions confirm the existence of alignment effects, as demonstrated experimentally by Spain et al. [J. Chem. Phys. 102, 9532 (1995)], at a mean relative velocity of 914 m/s. Theory further predicts heretofore unobserved oscillatory structures in these cross sections as a function of relative velocity and that these oscillations depend strongly on the initial magnetic quantum number of the Rydberg electron.
Aligned atomic Rydberg states of sodium can be prepared using two-step excitation from the ground state by linearly polarized pulsed lasers. Information that is normally inaccessible, e.g., sublevel partial cross sections in charge-transfer experiments, can be obtained when aligned targets are used. The calculations of orbital alignment must carefully allow for fine and hyperfine structure, laser linewidths, pulse widths and delays, sublevel coherences, and other factors. In this paper we derive the orbital alignments and time-averaged d-state sublevel populations for 3
2S1/2\ensuremath{\rightarrow}3
2PJ1\ensuremath{\rightarrow}n
2D excitations in Na using angular-momentum and density-matrix methods. We consider both quadrupole alignment
A(2) and hexadecapole alignment
A(4), with excitation through either
J1=1/2 or 3/2 intermediate states considered on the same footing. We show sublevel populations for \ensuremath{\Vert}
ML\ensuremath{\Vert}=0, 1, and 2 analytically and graphically. Finally, we formulate the experimental design problem quantitatively in order to ascertain how to optimize the choice of polarizer angles for extraction of sublevel partial cross sections. Although perhaps the commonest instance, two-step excitation of Na(nd) is but one of a large number of interesting cases, and this study is further intended to illustrate and guide the application of these methods to other light atoms.
We have performed an analysis of the effect of hyperfine structure in an experiment in which an aligned excited state is probed using linearly polarized light. The state is born with a given electronic alignment resulting from a collisional process. It is probed after a time which is short in comparison to its radiative lifetime but much longer than ω−1hfs, where ℏωhfs is the hyperfine splitting. This means that hyperfine structure has ample time to ‘‘develop.’’ It is therefore essential to take into account both the hyperfine structure of the level and the manner in which the alignment is affected by recoupling to the new basis. Ratios of fluorescent intensities for different laser polarization configurations contain information on the alignment of the system. We show how these may be calculated for a system with several isotopes, some of which have hyperfine structure, and where many components are probed with appreciable strength. A comparison is made with our experimental results for the Hg(6 3P1) level probed on the 6 3P1–7 3S1 transition. The presence of hyperfine structure has a considerable influence on the measurements. It is important to understand such effects if one is to obtain information on the nascent electronic alignment by observation of the fluorescent intensities.