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Bulletin of the American Physical Society

Energy and angular momentum transfer to Rydberg atoms in collisions with electrons

M. I. Syrkin

Published May 1, 1993• 0 citations
OpenAlex

Abstract

The analytical formulae for the cross-sections with arbitrary change {triangle}n=n{prime}-n and {triangle}1=1{prime}-1 has been obtained in the Born limit. No spin exchange {triangle}S=0: although the total cross-sections n->n are dominated by dipole transitions, the non-dipole transitions {triangle}1>1 can contribute up to 30-50%ER for large {triangle}n>>1. Intercombination transitions {triangle}S=1: the large transfer transitions {triangle}1>>1 are of major importance, as opposed to the previous case.

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The analytical formulae for the cross-sections with arbitrary change {triangle}n=n{prime}-n and {triangle}1=1{prime}-1 has been obtained in the Born limit. No spin exchange {triangle}S=0: although the total cross-sections n->n are dominated by dipole transitions, the non-dipole transitions {triangle}1>1 can contribute up to 30-50%ER for large {triangle}n>>1. Intercombination transitions {triangle}S=1: the large transfer transitions {triangle}1>>1 are of major importance, as opposed to the previous case.
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 intercombination transitions between l-resolved Rydberg levels due to collisions with fast electrons are studied within the Ochkur approximation for principal quantum numbers n\ensuremath{\le}20, where l is the angular momentum. The use of the Heisenberg correspondence principle for radial integrals enables one to obtain analytic expressions for any term in the multipole expansion of the cross section for collisions with an arbitrary n and l change. For transitions involving angular momenta that are small compared to the principal quantum numbers, the semiclassical and the exact results are found to be fairly close, within the accuracy consistent with the Born approximation. As a result, the semiclassical approach furnishes a ready estimate for cross sections, and its validity range proves broad enough to cover the region of large momenta transferred to the atom. The numerical results also confirm that dipole transitions have no dominance over the collisions with other \ensuremath{\Delta}l values, in accord with the general model of intercombination scattering.
Simple analytical expressions for the cross sections of nl to n'l' transitions from Rydberg-neutral inelastic collisions are obtained on the basis of the free electron model for electron-perturber scattering. The dependences of the electron-perturber scattering amplitude on the electron momentum and scattering angle are allowed for. The analytical results agree well with available numerical calculations. The analysis of the equations obtained yields a conclusion that the cross sections at l<or=l' depend weakly on l and l' for degenerate states and are proportional to the statistical weights of the final states for transitions with large energy defects.
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 large enhancement in the resonant collisional energy-transfer process $\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})\ensuremath{\rightarrow}\mathrm{Na}[(n\ensuremath{-}1)p]+\mathrm{Na}(\mathrm{nl})$ or $\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})\ensuremath{\rightarrow}\mathrm{Na}(\mathrm{np})+\mathrm{Na}[(n\ensuremath{-}1)l]$ is observed when the initial ns\mathrm{ns}ns state lies midway between $(n\ensuremath{-}1)p$ and an nl\mathrm{nl}nl state or between np\mathrm{np}np and an $(n\ensuremath{-}1)l$ state. This resonance condition, achieved by the electric field tuning of the levels, leads to large cross sections \ensuremath{\sim} 109{10}^{9}109 A˚2{\mathrm{\AA{}}}^{2}A˚2 and narrow linewidths \ensuremath{\sim} 1 GHz. These cross sections and linewidths are comparable to the previously observed resonant process $\mathrm{Na}(\mathrm{ns})+\mathrm{Na}(\mathrm{ns})\ensuremath{\rightarrow}\mathrm{Na}[(n\ensuremath{-}1)p]+\mathrm{Na}(\mathrm{np})$. We have also observed a similar collisional energy transfer starting from a completely different initial state, i.e., $\mathrm{Na}(15d)+\mathrm{Na}(15d)\ensuremath{\rightarrow}\mathrm{Na}(16f)+\mathrm{Na}(15p)$. In this case the enhancement in the cross section (\ensuremath{\sim} 108{10}^{8}108 A˚2{\mathrm{\AA{}}}^{2}A˚2) is observed at a relatively low electric field \ensuremath{\sim} 17 V/cm.
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.