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Physical Review A

Theory of angular momentum mixing in Rydberg-atom-rare-gas collisions

A. P. Hickman

Published Oct 1, 1978• 65 citations
Publisher

Abstract

A coupled-channel approach based on the Arthurs and Dalgarno formalism is presented to describe the scattering of a Rydberg atom and a rare-gas atom. The method permits the calculation of cross sections for changes in the electronic orbital angular momentum of the Rydberg atom. The theory explicitly relates the scattering behavior of the Rydberg state to the electron-rare-gas scattering length. Preliminary results for ${\mathrm{Na}}^{*}(\mathrm{nd})$+He and ${\mathrm{Na}}^{*}(\mathrm{nf})$+He are in good agreement with experiment.

DOI
10.1103/physreva.18.1339

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Physical Review A•Oct 1, 1996•26 citations
A coupled-channel approach based on the Arthurs and Dalgarno formalism is presented to describe the scattering of a Rydberg atom and a rare-gas atom. The method permits the calculation of cross sections for changes in the electronic orbital angular momentum of the Rydberg atom. The theory explicitly relates the scattering behavior of the Rydberg state to the electron-rare-gas scattering length. Preliminary results for Na∗(nd){\mathrm{Na}}^{*}(\mathrm{nd})Na∗(nd)+He and Na∗(nf){\mathrm{Na}}^{*}(\mathrm{nf})Na∗(nf)+He are in good agreement with experiment.
Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the sss-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the lll-mixing cross section at a particular nnn is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on nnn. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of Na(nd)+He\mathrm{Na}(\mathrm{nd})+\mathrm{He}Na(nd)+He, Ne, and Ar are treated as specific examples.
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.
An approximate scaling formula has been determined that permits the rapid estimation of cross sections for angular-momentum-changing collisions of Rydberg atoms with a variety of targets, using information about low-energy-electron scattering from the target. The formula is obtained by fitting the results of coupled-channel and Born-approximation calculations to functions of reduced parameters. Application to Na(nd)\mathrm{Na}(\mathrm{nd})Na(nd) + He, Ne, Ar, N2{\mathrm{N}}_{2}N2​, CH4{\mathrm{H}}_{4}H4​, C3{\mathrm{C}}_{3}C3​H8{\mathrm{H}}_{8}H8​; Rb(nf)\mathrm{Rb}(\mathrm{nf})Rb(nf) + He, Ar, Xe; and Xe(nf)\mathrm{Xe}(\mathrm{nf})Xe(nf) + CO2{\mathrm{O}}_{2}O2​, suggests that the accuracy is about a factor of 2.
The title processes are theoretically investigated based on the model in which an excited Rydberg electron behaves as if it were 'free' and slow, with its interaction with the rare-gas atom playing a decisive role. The cross sections of l-changing collisions of the Rydberg atoms with the rare-gas atoms are evaluated for small angular momentum changes. They are compared with experimental data available at present, under the assumption that there is no selection rule for the distribution over the final angular momentum states of the Rydberg atom, and are found to be consistent with experimental findings. The relation between this approach and some others is examined. The possibility of learning about low-energy electron-rare-gas collisions from refined experimental data on the title processes is briefly discussed.
A theory of inelastic n,l-changing and quasielastic l-mixing collisions of Rydberg atoms with the heavy rare-gas atoms is developed. It is based on the semiclassical impact-parameter approach combined with the normalized perturbation theory. Semiclassical formulas for scaled transition probabilities and cross sections as functions of the inelasticity parameter and the collision strength are analyzed. This approach gives a general description of collisional nl\ensuremath{\rightarrow}${\mathit{n}}^{\ensuremath{'}}$ transitions independently of the specific values of the principal quantum number, the relative velocity, and the type of colliding atoms. The energy and angular dependence of the electron-atom scattering amplitude is included in the theory by incorporating the impulse-approximation results in the weak-coupling limit. The Ramsauer-Townsend effect affects significantly the values of the cross sections, especially for the inelastic transitions with large energy transfer. The results obtained are used in calculations of the quenching cross sections for the Rb(nS,nD,nF) atoms in collisions with Ar, Kr, and Xe. Comparison of theory and experiment is made in a wide range of the principal quantum numbers and transition energy defects. \textcopyright{} 1996 The American Physical Society.