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Physical Review A

Angular-momentum distributions following impact of slow ions on Na(nd) Rydberg atoms

Xufei Sun, Keith B. MacAdam

Published May 1, 1993• 39 citations
Publisher

Abstract

The degree of dipole-forbidden l change in Na(26d) and Na(28d) Rydberg atoms caused by slow ${\mathrm{Na}}^{+}$ ion impact at reduced velocity v\ifmmode \tilde{}\else \~{}\fi{}=0.1--0.9 has been measured. ${\mathrm{Na}}^{+}$ 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.

DOI
10.1103/physreva.47.3913

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Andrey K. Kazansky, Valentin N. Ostrovsky

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.

Journal of Physics B Atomic Molecular and Optical Physics•Aug 28, 1996•18 citations
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.
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.
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.
The collisional angular-momentum mixing of the Nand\mathrm{Na}\mathrm{nd}Nand Rydberg states into states of higher angular momentum with Xe as the collisional partner has been studied in zero field and in the presence of a small electric field. The collisional lll-mixing cross section in zero field has been measured for $9\ensuremath{\le}n\ensuremath{\le}23$ using a vapor-cell-fluorescence method and a crossed-beam technique with a selective-field-ionization (SFI) scheme as the state detector. Using the ∣ml∣|{m}_{l}|∣ml​∣ selectivity of the SFI, we have also investigated the final-∣ml∣|{m}_{l}|∣ml​∣-state distribution of the collisionally populated states of l>2l>2l>2. Our measurements suggest that the collisionally populated states have predominantly low ∣ml∣|{m}_{l}|∣ml​∣ values ($|{m}_{l}|\ensuremath{\le}2$). An application of a low electric field (\ensuremath{\sim} 50 V/cm) substantially reduces the collisional population of the low-∣ml∣|{m}_{l}|∣ml​∣ states, thus reducing the total cross section as well.
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.
Ar+{\mathrm{Ar}}^{+}Ar+ and Na+{\mathrm{Na}}^{+}Na+ ion beams bombarding Na ns and np Rydberg-state targets at impact velocities near the Bohr-orbital velocity of the target atoms (i.e., v\ifmmode \tilde{}\else \~{}\fi{}\ensuremath{\approxeq}1) induce transitions to (n-1)l states (l\ensuremath{\ge}2) with larger-than-geometric cross sections. Depopulation of ns states proceeds directly into the full n-1, l\ensuremath{\ge}2 manifold rather than populating the np or (n-1)p states as the first of a sequence of dipole-allowed steps. Depopulation of np states leads to a distribution of final states that is dominated by the nearer or high-l part of the n-1 manifold. n dependences of the cross section for ns depopulation are given at several energies for n=32--41 and at a single energy for np, n=26--32. The absolute cross section for Na(36s) depopulation falls gradually but steadily for reduced velocities v\ifmmode \tilde{}\else \~{}\fi{} increasing from 0.3 to 1.35. Bombardment of Na 39s and 39p states in applied fields 0--18.5 V/cm reveals that the final-state distributions become narrower as manifold states are Stark shifted close to the initial states. No theoretical results are available for direct comparison with these experiments, but the method of coupled channels seems to be the most suitable candidate.
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.