Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Floquet analysis of inelastic collisions of ions with Rydberg atoms

M. J. Cavagnero

Published Oct 1, 1995• 9 citations
Publisher

Abstract

The theory of Demkov et al. (Zh. Eksp. Teor. Fiz. 66, 125 (1974) [Sov. Phys. JETP 39, 57 (1974)]) for collisional mixing of degenerate states of a hydrogenlike target is generalized to nonhydrogenic targets parametrized by a set of quantum defects, {${\mathrm{\ensuremath{\mu}}}_{\mathit{l}}$}, with l the orbital angular-momentum quantum number of the Rydberg electron. Schr\"odinger's equation is written in periodic form in the impact-parameter approximation by using the angle of rotation of the internuclear line, as opposed to the time, as the independent variable. Quasiperiodic solutions are constructed by Floquet analysis, as in studies of Rydberg-state mixing by oscillatory fields, leading to an infinite-dimensional eigenvalue equation whose eigenvectors and eigenvalues determine the evolution operator of the collision system. An initial application to ``l-mixing collisions'' of ions with alkali-metal atoms indicates that dipole-forbidden transitions dominate depopulation cross sections at intermediate collision speeds.

DOI
10.1103/physreva.52.2865

Related papers

Rydberg-atom - ion collision: classical theory of intrashell transitions

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

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

Xufei Sun, Keith B. MacAdam

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.

Physical Review A•May 1, 1993•39 citations

Inelastic Transitions Induced by Collisions of Rydberg Atom (Ion) with Charged Particles

Владимир Сергеевич Лебедев, И. Л. Бейгман

Springer eBooks•Jan 1, 1998•1 citation

Multilevel effects on the balance of dipole-allowed to dipole-forbidden transitions in Rydberg atoms induced by a dipole interaction with slow charged projectiles

M. I. Syrkin

In collisions of Rydberg atoms with charged projectiles at velocities approximately matching the speed of the Rydberg electron ${v}_{n}$ (matching velocity), $n$ 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-$l$ 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 $s$ and $p$ 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.

Physical Review A•Feb 1, 1996•6 citations

Long-range interactions and dynamics of excited atoms

Sigrid Ina Simonsen

A study of the dynamics of excited hydrogenic atoms, with emphasis on analytical and numerical calculations of the time-independent and the time-dependent Schrõdinger equation. A short description of Rydberg atoms and their applications is also present in the thesis.

•Jun 10, 2010•0 citations

l-changing collisions in the intermediate Rydberg states of lithium

Mimoun Harnafi, Bernard Dubreuil

l-mixing collisions Li(${n}^{2}$D)+X\ensuremath{\rightarrow}Li(${n}^{2}$L,L>2)+X induced in Rydberg states of lithium (n=4,5,...,13) by rare-gas atoms or Li ground-state atoms are studied in a heat-pipe arrangement. The l-mixing cross sections deduced from the time analysis of the ${n}^{2}$D laser-induced fluorescence agree with experimental values obtained with the heavier alkali-metal atoms and with different theoretical models developed for quasielastic Rydberg-electron--target collisions. Quenching of the ${n}^{2}$D fluorescence at higher rare-gas pressures is interpreted as inelastic collisional transfer of the L\ensuremath{\ge}1 mixed states to the nonhydrogenic S sublevel. Finally the radiative lifetimes of the ${n}^{2}$D states and ${n}^{2}$L mixed states with L\ensuremath{\ge}1 are deduced, respectively, from the low-pressure limit and intermediate-pressure study of the ${n}^{2}$D fluorescence relaxation rate.

Physical Review A•Mar 1, 1985•9 citations
The theory of Demkov et al. (Zh. Eksp. Teor. Fiz. 66, 125 (1974) [Sov. Phys. JETP 39, 57 (1974)]) for collisional mixing of degenerate states of a hydrogenlike target is generalized to nonhydrogenic targets parametrized by a set of quantum defects, {\ensuremathμl{\mathrm{\ensuremath{\mu}}}_{\mathit{l}}\ensuremathμl​}, with l the orbital angular-momentum quantum number of the Rydberg electron. Schr"odinger's equation is written in periodic form in the impact-parameter approximation by using the angle of rotation of the internuclear line, as opposed to the time, as the independent variable. Quasiperiodic solutions are constructed by Floquet analysis, as in studies of Rydberg-state mixing by oscillatory fields, leading to an infinite-dimensional eigenvalue equation whose eigenvectors and eigenvalues determine the evolution operator of the collision system. An initial application to ``l-mixing collisions'' of ions with alkali-metal atoms indicates that dipole-forbidden transitions dominate depopulation cross sections at intermediate collision speeds.
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.
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.
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.
l-mixing collisions Li(n2{n}^{2}n2D)+X\ensuremath{\rightarrow}Li(n2{n}^{2}n2L,L>2)+X induced in Rydberg states of lithium (n=4,5,...,13) by rare-gas atoms or Li ground-state atoms are studied in a heat-pipe arrangement. The l-mixing cross sections deduced from the time analysis of the n2{n}^{2}n2D laser-induced fluorescence agree with experimental values obtained with the heavier alkali-metal atoms and with different theoretical models developed for quasielastic Rydberg-electron--target collisions. Quenching of the n2{n}^{2}n2D fluorescence at higher rare-gas pressures is interpreted as inelastic collisional transfer of the L\ensuremath{\ge}1 mixed states to the nonhydrogenic S sublevel. Finally the radiative lifetimes of the n2{n}^{2}n2D states and n2{n}^{2}n2L mixed states with L\ensuremath{\ge}1 are deduced, respectively, from the low-pressure limit and intermediate-pressure study of the n2{n}^{2}n2D fluorescence relaxation rate.