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The Journal of Chemical Physics

A classical ensemble model of three-body collisions in the point contact approximation and application to alignment effects in near-resonant energy transfer collisions of He atoms with Rydberg Ca atoms

Neil E. Shafer, Michael A. Morrison, Gregory A. Parker

Published Sep 8, 2000• 1 citation
Publisher

Abstract

A classical ensemble model of three-body energy transfer in the point contact approximation is presented. This model yields cross sections for transitions between initial and final states defined by energy, magnitude of angular momentum, and projection of angular momentum along an axis of spatial quantization corresponding to the quantum numbers of the initial and final stationary states, n,l,m and n′,l′,m′. Using a cross section that is differential in the final-state quantum numbers, the spatial constraints imposed by conservation of energy and angular momentum can be investigated even for comparatively small quantum numbers. When applied to the Ca(17d)+He→Ca(18p)+He energy transfer processes, the model sheds light on recently discovered alignment phenomena in collisions of rare-gas atoms with initially aligned Rydberg atoms. Materials for the implementation of this model are available from the authors via the Internet.

DOI
10.1063/1.1287325

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A classical ensemble model of three-body energy transfer in the point contact approximation is presented. This model yields cross sections for transitions between initial and final states defined by energy, magnitude of angular momentum, and projection of angular momentum along an axis of spatial quantization corresponding to the quantum numbers of the initial and final stationary states, n,l,m and n′,l′,m′. Using a cross section that is differential in the final-state quantum numbers, the spatial constraints imposed by conservation of energy and angular momentum can be investigated even for comparatively small quantum numbers. When applied to the Ca(17d)+He→Ca(18p)+He energy transfer processes, the model sheds light on recently discovered alignment phenomena in collisions of rare-gas atoms with initially aligned Rydberg atoms. Materials for the implementation of this model are available from the authors via the Internet.
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.
Recent experimental and theoretical studies of near-resonant energy transfer collisions involving rare-gas atoms and alkali or alkaline earth atoms which have been initially excited to an aligned state via one or more linearly polarized rasters have yielded a wealth of insight into orbital alignment and related effects. We have extended this inquiry to initially aligned Rydberg states, examining state-to-state and alignment-selected cross sections using quantum collision theory augmented by approximations appropriate to the special characteristics of the Rydberg state (e.g., the quasi-free-electron model and the impulse approximation).
A recent quantum mechanical study [W. Isaacs and M. A. Morrison, Phys. Rev. A 57, R9 (1998)] discovered pronounced oscillations in cross sections for near-resonant energy transfer collisions of rare-gas atoms with initially aligned Rydberg atoms. We analyze such collisions for 17d(m)-->18p(m(')) transitions in the Ca-He system semiclassically and show that the oscillations arise from a phase interference process unique to Rydberg target states. In addition to explaining the origin of these structures, this analysis explains their disappearance when the relative Ca-He velocity goes to infinity and/or the energy defect vanishes and their dependence on the initial and final magnetic quantum numbers of the transition.
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.
A classical model for l mixing of Rydberg states in atomic collisions is described. The primary assumption of the model is that l changing occurs in a single hard-sphere collision between the Rydberg electron and the perturbing atom which is represented by the zero-energy scattering length L. Predictions of the model, which are in the form of cross sections as functions of principal quantum number n, are compared with data for l mixing of Na(nd) and Rb(nf) by rare-gas atoms. Agreement is, in most cases, quite good, comparable with that of other, more sophisticated, models. It is shown that, because the calculation must be carried out in the reference frame of the ion core, the energy deficit between low angular momentum states and the nearest hydrogenic manifold can be made up in a single collision between the Rydberg electron and the perturbing atom, an effect that is analogous to the gravitational slingshot effect used to alter the orbits of a spacecraft under the influence of the Sun's gravitational field. Comparison of data for l mixing by ground-state Rb atoms with model calculations in which L is treated as a free parameter leads to an estimate of 10 a.u. for the zero-energy scattering length of Rb.
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.