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Physical Review A

Inelastic and quasielastic collisions of Rydberg atoms with the heavy rare-gas atoms

Владимир Сергеевич Лебедев, I. I. Fabrikant

Published Oct 1, 1996• 26 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.54.2888

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Physical Review A•Jun 1, 1991•10 citations
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}n\ensuremath′{\mathit{n}}^{\ensuremath{'}}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.
Semiclassical calculations of the quasi-elastic l-mixing and inelastic n,l-changing processes in thermal collisions of a Rydberg sodium atom with rare-gas atoms (Ne, Ar, Kr and Xe) as well as and atoms with Ne are presented in a wide range of principal quantum numbers. The main emphasis is put on the study of the effects in the Rydberg-atom - rare-gas-atom collisions associated with both the short- and long-range (polarization) parts of the electron - perturber interaction. It is shown that the polarization interaction between the highly excited electron and the Ne atom provides the major contribution to the cross section of the l-mixing and n, l -changing transitions. We show that the Ramsauer - Townsend effect in slow electron scattering by the heavy rare-gas atoms significantly affects the values of the cross sections, particularly for the inelastic transitions with large energy transfer. A quantitative explanation of these phenomena is given using the recently developed semiclassical normalized perturbation theory for the Rydberg-atom - neutral collisions combined with the modified effective range theory for scattering of slow electrons by the rare-gas atoms.
For $20\ensuremath{\le}n\ensuremath{\le}45$, two types of quasielastic state-changing-collisional (QESCC) processes, i.e., (i) lll-changing and (ii) nnn-and lll-changing processes, have been theoretically investigated based on the free-electron model in which an excited Rydberg electron behaves as if it were "free" and slow with its interaction with a rare-gas atom playing a decisive role. It is shown that a parameter ${u}_{min}[=\frac{\ensuremath{\nu}{\ensuremath{\nu}}^{\ensuremath{'}}\ensuremath{\Delta}E{a}_{0}}{(\ensuremath{\hbar}V)}]$ is quite useful for characterizing both of these QESCC processes in a unified way where $\ensuremath{\nu}(\ensuremath{\simeq}{\ensuremath{\nu}}^{\ensuremath{'}})$ is an effective principal quantum number of the initial (final) state, $\ensuremath{\Delta}E$ is an energy defect, and VVV is a relative velocity. It is theoretically found that higher-angular-momentum states are dominantly populated in the final channel of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ such as in the nnn- and lll-changing collision of Rb∗∗(ns)+He{\mathrm{Rb}}^{**}(\mathrm{ns})+\mathrm{He}Rb∗∗(ns)+He. This is in contrast with the uniform distribution over the final angular-momentum states for the usual lll-changing processes, i.e., ${u}_{min}\ensuremath{\lesssim}1$. The calculated cross sections of these QESCC processes with $1<{u}_{min}\ensuremath{\lesssim}\ensuremath{\nu}$ are found to be in reasonable agreement with experimental findings available at present.
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.
A theoretical model for the collision of atoms in high Rydberg states (nl) with neutral atoms or molecules is proposed, based on the assumption that the electron-perturber interaction is of very short range compared with the mean radius of the Rydberg atom. A semiclassical method is used to derive a compact expression for the collision probability. The calculations need total cross sections for the scattering of a free and low-energy electron by the perturber. The model is applied to the calculation of a free and low-energy electron by the perturber. The model is applied to the calculation of cross sections for the quenching of n 2 D or n 2 F Rydberg states of Na and Rb by rare-gas atoms of N 2 . On the whole the calculated cross sections are in reasonable agreement with experimental data for n>10 approximately. The model and the results of the calculations are discussed and compared with other theoretical works.
Simple analytical formulas are given that allow the rapid estimation of cross sections for lll mixing, nnn changing, and ionization of Rydberg atoms with atomic and molecular targets. These formulas are derived by using the quasifree-electron model and the impulse approximation. The lll dependence of the cross section is accounted for only via the atomic energy. The quasielastic process of angular-momentum mixing caused by either the short- or long-range interaction between the Rydberg electron and the neutral perturber is studied and the corresponding cross sections are evaluated. The Rydberg-atom---molecule inelastic transitions (nnn changing and ionization) caused by the ${e}^{\ensuremath{-}}$-dipole or ${e}^{\ensuremath{-}}$-quadrupole interaction are investigated. It is shown that the nnn-changing reactions occur via quasiresonant internal-energy transfer between the two colliding partners. The influence of the relevant physical parameters is clearly stated for the three types of interaction (short-range, ${e}^{\ensuremath{-}}$-dipole, ${e}^{\ensuremath{-}}$-quadrupole). Comparison with more sophisticated approaches and experimental data shows that the accuracy of the formulas is about a factor of 2.
Using the wave functions of the multichannel-quantum-defect theory, a semiclassical theory for both elastic and inelastic collisional cross sections of Rydberg atoms, in which there can be more than one valence electron, with ground-state rare-gas atoms is obtained. Especially the noble-gas-induced broadening cross sections of Rydberg series in alkaline-earth atoms can be calculated. An application of theory is shown to explain the irregular broadening rates of Sr 5sns 1^{1}1S0{\mathit{S}}_{0}S0​ series due to collision with Xe, and a good agreement between theory and experiment is achieved.