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Journal of Physics B Atomic Molecular and Optical Physics

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

Andrey K. Kazansky, Valentin N. Ostrovsky

Published Aug 28, 1996• 18 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/29/16/012

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Journal of Physics B Atomic Molecular and Optical Physics•May 26, 2005•34 citations
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 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.
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.
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.
Processes involving a change of orbital angular momentum l and the dissociation of Rydberg molecules when they collide with inert-gas atoms are considered, using a method based on analyzing the terms of the interacting systems. The proposed method makes it possible to take into account the perturbations in a large group of Rydberg states that weakly penetrate into the ion core and to go beyond the limits of the two-level approximations [R. F. Stebbings and F. B. Dunning, eds., Rydberg States of Atoms and Molecules (Cambridge University Press, Cambridge, 1983; Mir, Moscow, 1985)] widely used in the theory of l mixing with the participation of Rydberg atoms. Using the Na**( nd )+Xe reaction as an example, it is demonstrated that this method gives good results in a wide range of variation of the principal quantum number n of the Rydberg electron ( n ≈10–40). Features of the l mixing and dissociation of Rydberg molecules are studied for the H 2 **+Xe system. It is shown that collisional dissociation occurs by the formation of an intermediate Rydberg state of the molecules, followed by self-decay into a dissociative continuum.
Collisional ionization between two Rydberg atoms in relative motion is examined. A classical trajectory Monte Carlo method is used to determine the cross sections associated with Penning ionization. The dependence of the ionization cross section on the magnitude and the direction of orbital angular momentum of the electrons and the direction of the Laplace-Runge-Lenz vector of the electrons is studied. For a given magnitude of angular momentum, there can exist a difference of a factor of up to $\ensuremath{\sim}2.5$ in the ionization cross section between the orientations with the highest and the lowest ionization cross section. The case of exchange ionization is examined and its dependence on the magnitude of angular momentum is studied.
A stochastic model of associative ionization in collisions of Rydberg atoms with ground-state atoms is presented. The conventional Duman–Shmatov–Mihajlov–Janev (DSMJ) model treats the ionization as excitation of Rydberg electron to the continuum by the electric-dipole field generated by exchange interaction within the quasi-molecular ion. The stochastic model essentially extends this treatment by taking into account redistribution of population over a range of Rydberg states prior to ionization, which is caused by non-adiabatic processes in overlapping multiple level crossings of quasi-molecular Rydberg states. The redistribution is modelled as diffusion of electrons in the Rydberg energy spectrum using a Fokker–Planck-type equation. The process of l -mixing of Rydberg states at large internuclear distances and twisting of the collision trajectories on attractive potentials are taken into account. The choice of the collision velocity distribution is also shown to be important. Associative ionization rates have been calculated for Na**( nl ) + Na collisions with n = 5–25 and l = 0, 1, 2, and compared with the available experimental data and the calculations performed using the nonlinear DSMJ model. At relatively low n the stochastic model yields a substantially better agreement with the experimental data than the DSMJ model, while the results of both models converge at large n .