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.
New experimental results have been obtained in collisions of singly charged ions with Na Rydberg atoms. (a) The distribution of final n states populated by electron capture shows non-monotonic variations of width with incident energy over the range 60-2100 eV. (b) The total capture cross section for alkali ions on Rydberg targets shows peaks and dips over the same energy range, correlated with particular reduced velocities v and the polarization of the exciting laser. (c) {ell}-Changing collision of Na{sup +} on Na(nd) targets, n=26 and 28, at low v preferentially transfer multiple units {h_bar} of orbital angular momentum under single-collision conditions, despite very large impact parameters. (d) Inelastic impacts of Na{sup f+} on Na 36s and 30p states, perturbed by electric fields, populate a strongly field-dependent mixture of nearby Stark levels. A synopsis of recent progress will be given.
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.
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.
Abstract. The cross sections for the Na.4D/! Na.4F / excitation energy transfer induced by collisions with He, Ar and Na ground-state atoms have been measured. The sodium atoms in the 4D state have been produced by two-photon excitation using cw laser radiation at 578.89 nm. Within a model which takes into account collisional population and depopulation of the 4F level as well as radiative relaxation (direct or cascade) of the 3D, 4P, 4D and 4F states ending in the 3P level, the rate for the Na.4D / ! Na.4F / collisional transfer turns out to be related to the ratio of the steady-state populations created in 3D and 4D states. They have been determined by measuring the fluorescence intensities of the 3D! 3P and 4D! 3P transitions. The measurements yield the following cross section values for those
In studying ionization reactions in a single dense effusive beam of laser-excited Na(3p) atoms, we observe production of both Na{sub 2}{sup +} and Na{sup +} ions. The Na{sup +} results from the familiar associative ionization reaction of two Na(3p) atoms and the Na{sup +} ions under our conditions result mostly from the collisional dissociation of the Na{sub 2}{sup +} by reaction with a third excited Na(3p) atom, rather than from photo- dissociation or photoionization. A CW, single-frequency dye laser tuned to 589 nm resonantly excites the Na(3s) atoms to the 3p state. The atomic beam Na(3s) density is determined from low-intensity 589 absorption measurements. Na{sup +} ion yield depends on the cube of the Na beam density, suggesting successive collisions of three Na(3p) atoms: we believe the Na{sub 2}{sup +} ions polarize the third Na(3p) atom, resulting in a R{sup -4} orbiting collision interaction. A large collisional dissociation cross-section of approximately (4{plus_minus}2)x10{sup -13} cm{sup 2} results, for oven temperatures in the 500-600K range.