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Physical Review A

Dipole-allowed and dipole-forbiddenlchange in slow collisions of Na+ with Na(28d) Rydberg atoms

Keith B. MacAdam, R G Rolfes, Xufei Sun, J. Singh, W. L. Fuqua, D. B. Smith

Published Nov 1, 1987• 18 citations
Publisher

Abstract

Both dipole-allowed and dipole-forbidden transitions occur in slow l-change collisions of ${\mathrm{Na}}^{+}$ with Na(28d) Rydberg atoms, despite the validity of the dipole approximation. Measurements of the velocity dependence of the final-state distribution under single-collision conditions are reported. Effects of strong coupling were found, in partial agreement with recent coupled-channel calculations. Microwave-resonance techniques were used to identify the selective-field-ionization signatures of 28f, g, and h states.

DOI
10.1103/physreva.36.4254

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Both dipole-allowed and dipole-forbidden transitions occur in slow l-change collisions of Na+{\mathrm{Na}}^{+}Na+ with Na(28d) Rydberg atoms, despite the validity of the dipole approximation. Measurements of the velocity dependence of the final-state distribution under single-collision conditions are reported. Effects of strong coupling were found, in partial agreement with recent coupled-channel calculations. Microwave-resonance techniques were used to identify the selective-field-ionization signatures of 28f, g, and h states.
The degree of dipole-forbidden l change in Na(26d) and Na(28d) Rydberg atoms caused by slow Na+{\mathrm{Na}}^{+}Na+ ion impact at reduced velocity v\ifmmode \tilde{}\else \~{}\fi{}=0.1--0.9 has been measured. Na+{\mathrm{Na}}^{+}Na+ beam energies 7.3--684 eV were used. Previous measurements were greatly improved by reducing stray electric fields in the Rydberg collision region to about 10 mV/cm. The distributions of final-angular-momentum states were analyzed using directly measured diabatic selective-field-ionization profiles for l=3, 4, and 5. l-change results in Na(26d) and Na(28d) targets are very similar and clearly show an increasing amount of dipole-forbidden behavior for decreasing reduced velocities v\ifmmode \tilde{}\else \~{}\fi{} and partial agreement with the coupled-channel calculation of Beigman and Syrkin (Zh. Eksp. Teor. Fiz. 89, 400 (1985) [Sov. Phys. JETP 62, 226 (1985)]). The dipole-forbidden process is the main channel for angular-momentum change in ion--Rydberg-atom collisions at v\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\le}0.7. At very low energy (v\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\le}0.3) the measurements demonstrate that the final-state distributions are dominated by very high angular-momentum states.
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.
An experimental study of the depopulation of Na(30s) Rydberg atoms under He + ion bombardment has been undertaken to identify the range of collision velocities at which strongly coupled behaviour of the 30s and nearby levels at low velocity changes to predominantly dipole-allowed coupled at high velocity. Ion energies ranged from 700 to 3900 eV corresponding to collision velocities of 2.4 to 5.6 times the mean orbital speed of the excited 30s electron. The ratio of the cross section for the dipole-allowed transitions (30s to 30p and 30s to 29p) to the total depopulation cross section was determined for each collision velocity. (Other dipole-allowed transitions were observed to be negligible.) This ratio was found to increase from only 20% at a reduced velocity of 2.4 to 65% at a reduced velocity of 5.6. The ratio of the two dipole cross sections, sigma (30s-30p)/ sigma (30s-29p), was also determined and compared to calculations based on the dipole approximation with first-order perturbation theory.
The l-changing transitions in collisions of Rydberg atoms with ions, A(nl0{\mathit{nl}}_{0}nl0​)+B+{\mathit{B}}^{+}B+\ensuremath{\rightarrow}A(nl)+B+{\mathit{B}}^{+}B+, are considered within the classical approximation for atomic electron motion. The elliptic orbit of the electron evolves slowly under the influence of the time-dependent electric field exerted by the incident ion. The quantum electron state is represented by an ensemble of classical trajectories. Within the dipole approximation extremely simple analytical formulas for the final-state l-distribution function are obtained for a fixed value of the impact parameter. The influence of the non-Coulomb core is taken into account approximately. The results of our calculations compare favorably with recent experimental data for the Na+{\mathrm{Na}}^{+}Na+(26d, 28d) Rydberg atom. The method can be extended to the calculation of distributions over various observables other than l.
In collisions of Rydberg atoms with charged projectiles at velocities approximately matching the speed of the Rydberg electron vn{v}_{n}vn​ (matching velocity), nnn being the principal quantum number of the Rydberg level, the dipole-forbidden transitions with large angular-momentum transfer $\ensuremath{\Delta}l\ensuremath{\gg}1$ substantially dominate over dipole-allowed transitions $\ensuremath{\Delta}l=1$, although both are induced by the dipole interaction. Here it is shown that as the projectile velocity decreases the adiabatic character of the depopulation depends on the energy distribution of states in the vicinity of the initial level. If the spectrum is close to degeneracy (as for high-lll levels) the dipole-forbidden depopulation prevails practically over the entire low-velocity region, down to velocities $\ensuremath{\sim}{n}^{3}[\frac{\ensuremath{\Delta}E}{\mathrm{Ry}}]{v}_{n}$, where $\ensuremath{\Delta}E$ is the energy spacing adjoining to the level due to either a quantum defect or the relevant level width or splitting, whichever is greater. If the energy gaps are substantial (as for strongly nonhydrogenic sss and ppp levels in alkali-metal atoms), then the fraction of dipole transitions in the total depopulation reaches a flat minimum just below the matching velocity and then grows again, making the progressively increasing contribution to the low-velocity depopulation. The analytic models based on the first-order Born amplitudes (rather than the two-level adiabatic approximation) furnish reasonable estimates of the fractional dipole-allowed and dipole-forbidden depopulations.
Using state-selective field ionization, the state distributions of Rydberg atoms in cold Rydberg gases are measured for various initially excited Rydberg levels, populations, and evolution times. We provide direct experimental evidence for lll-changing collisions that we previously observed indirectly [S. K. Dutta, D. Feldbaum, A. Walz-Flannigan, J. R. Guest, and G. Raithel, Phys. Rev. Lett. 86, 3993 (2001)]. We also observe nnn-mixing and find that its effects are largely in agreement with recent theoretical work on nnn-changing collisions between electrons and Rydberg atoms, thus enabling an estimation of the electron temperature. Unexpectedly large populations of atoms are found in states with principal quantum numbers much lower than that of the initially excited atoms. We explain this observation by collisions between high-lll Rydberg atoms, which are highly polar and can collide due to static electric-dipole forces between them.