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Physical Review A

Theory of ion-pair formation in Rydberg-atom–ground-state-atom collisions at thermal energies

D. B. Khrebtukov, I. I. Fabrikant

Published Oct 1, 1996• 9 citations
Publisher

Abstract

We develop the distorted-wave and adiabatic theories of the ion-pair formation in collisions of a Rydberg atom ${\mathit{A}}^{\mathrm{*}\mathrm{*}}$ with a ground-state atom B at thermal collision velocities. The e-B interaction is modeled by a zero-range potential. Both theories give results that are in qualitative agreement with the standard Landau-Zener model, although their prediction for m-changing transitions is different, where m is the projection of the angular momentum. To incorporate these transitions into the adiabatic theory, we take into account the rotation of the internuclear axis before and after a nonadiabatic transition. The m-averaged cross sections are substantially higher than those following from the standard Landau-Zener model, and the distorted-wave results are slightly higher than the adiabatic results with the internuclear-axis rotation taken into account. We apply our results to a description of the McLaughlin and Duquette experiment on ${\mathrm{Ca}}^{+}$-${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ pair formation. The calculated n dependence of the rate for the ion-pair formation is too flat as compared to the experimental observations and does not agree with known values of the electron affinity of Ca. We discuss other possible mechanisms responsible for the ion-pair formation in this process. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2906

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Journal of Physics B Atomic Molecular and Optical Physics•May 26, 2005•34 citations
We develop the distorted-wave and adiabatic theories of the ion-pair formation in collisions of a Rydberg atom A∗∗{\mathit{A}}^{\mathrm{*}\mathrm{*}}A∗∗ with a ground-state atom B at thermal collision velocities. The e-B interaction is modeled by a zero-range potential. Both theories give results that are in qualitative agreement with the standard Landau-Zener model, although their prediction for m-changing transitions is different, where m is the projection of the angular momentum. To incorporate these transitions into the adiabatic theory, we take into account the rotation of the internuclear axis before and after a nonadiabatic transition. The m-averaged cross sections are substantially higher than those following from the standard Landau-Zener model, and the distorted-wave results are slightly higher than the adiabatic results with the internuclear-axis rotation taken into account. We apply our results to a description of the McLaughlin and Duquette experiment on Ca+{\mathrm{Ca}}^{+}Ca+-Ca\ensuremath−{\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}Ca\ensuremath− pair formation. The calculated n dependence of the rate for the ion-pair formation is too flat as compared to the experimental observations and does not agree with known values of the electron affinity of Ca. We discuss other possible mechanisms responsible for the ion-pair formation in this process. \textcopyright{} 1996 The American Physical Society.
This dissertation deals with thermal collisions of highly excited (Rydberg) atoms with atoms in the ground state. The inelastic processes in these collisions manifest themselves mainly in broadening of Rydberg spectral lines. Advancements in tunable laser techniques allowed observation of the ion-pair formation in such collisions as well. Theoretical treatments of these collisions can be separated in two groups according to the principal quantum number n of the Rydberg atom: impulse approximation (n≥30),(n\ge30),(n≥30), and adiabatic approximation (n≤20).(n\le20).(n≤20). Both approaches are presented in application to spectral line broadening. The off-shell modification of the impulse approximation is developed. The pseudopotentials for singlet and triplet electron scattering from Rb and Cs are re-constructed from the phase shift data. These potentials are used to calculate the off-shell amplitudes, which are employed to obtain broadening cross sections. The taking into account of the off-shell effects is shown to improve the agreement with the experiment in the intermediate region of principal quantum number 20<n<30.20 < n < 30.20<n<30. The adiabatic approximation in the framework of Borodin-Kazansky theory is improved to include the exact Coulomb Green's function and the final radius of the ground state atom. The adiabatic theory explains the oscillations with n in the experimental broadening cross sections. The adiabatic theory is developed for the ion-pair formation. The zero-range-potential-Coulomb-field model is employed to generate realistic energy curves. The model allows exact numerical solution, which is used to verify the analytical theory that is set forth to describe the non-adiabatic transitions at large internuclear distances. Adiabatic calculations rely on the complex plane technique that requires the analytical continuation of the energy curves in the complex plane of parameters. Development of the algorithms for the continuation of Mathieu and Whittaker's functions, used in these calculations, constitutes an important methodological achievement of this work. Although all applications of the theories are worked out for alkali-metal atoms, the results can be applied to other atomic species as well.
A simple model potential for the electron-Ca-atom interaction is used to describe the process of charge transfer in Rydberg-atom-calcium-atom collisions. The interaction of the final ionic state with degenerate manifolds of Rydberg covalent states is treated by inclusion of the negative ion decay due to the Coulomb field of the positive ion. This effect leads to a strong reduction of the charge transfer cross section and shifting of the value of the principal quantum number n corresponding to the cross section maximum towards higher n . The rates averaged over the experimental velocity distribution agree quite well with the experimental data and with independent calculations using the Landau-Zener model, although the results of the latter are higher than the present for the charge transfer from s states. The distortion of the classical ion trajectories due to the Coulomb interaction plays a minor role in the calculation of the negative-ion decay probability.
We report the results of comparative studies of ion-pair formation and quenching processes in collisions of Rydberg Li( nl ) and Cs( nl ) atoms with Ca(4s 2 ), Sr(5s 2 ) and Ba(6s 2 ) atoms possessing small electron affinities. Our consideration includes both the cases of selectively excited Rydberg nl -states with small orbital angular momentum ( l ≪ n ) and nearly circular states with l ∼ n − 1. Calculations of the electron-transfer processes are based on the semiclassical theory of nonadiabatic transitions and exact expression for the Rydberg-covalent–ionic coupling terms. Calculations of nonresonant quenching processes are carried out within the framework of the available theory of inelastic and quasielastic transitions between Rydberg-covalent states. The ion-pair formation and resonant quenching cross sections are shown to be significantly dependent not only on the principal quantum number n but also on the orbital angular momentum l and the binding energy of the alkaline-earth anion. For each system under study we find the regions of n in which either the resonant quenching or the ion-pair formation processes are predominant. The relative role of the resonant and nonresonant mechanisms of depopulation of Rydberg states is investigated.
Electron-transfer processes are studied in thermal collisions of Rydberg atoms with alkaline-earth Ca(4s 2), Sr(5s 2), and Ba(6s 2) atoms capable of forming negative ions with a weakly bound outermost p-electron. We consider the ion-pair formation and resonant quenching of highly excited atomic states caused by transitions between Rydberg covalent and ionic terms of a quasi-molecule produced in collisions of particles. The contributions of these reaction channels to the total depopulation cross section of Rydberg states of Rb(nl) and Ne(nl) atoms as functions of the principal quantum number n are compared for selectively excited nl-levels with l ≪ n and for states with large orbital quantum numbers l = n − 1, n − 2. It is shown that the contribution from resonant quenching dominates at small values of n, and the ion-pair formation process begins to dominate with increasing n. The values and positions of the maxima of cross sections for both processes strongly depend on the electron affinity of an alkaline-earth atom and on the orbital angular momentum l of a highly excited atom. It is shown that in the case of Rydberg atoms in states with large l ∼ n − 1, the rate constants of ion-pair formation and collisional quenching are considerably lower than those for nl-levels with l ≪ n.
We formulate the semiclassical close-coupling method for a theoretical description of ion-pair formation in Rydberg-atom--ground-state-atom collisions at thermal energies and apply it to the process $\mathrm{Ca}{(4s}^{2})+{\mathrm{Ne}}^{*}(n)\ensuremath{\rightarrow}{\mathrm{Ca}}^{\ensuremath{-}}{(4s}^{2}4p)+{\mathrm{Ne}}^{+}.$ Our results for the formation of an isolated negative-ion state are very close to those obtained previously using the decay model, although the results for S states are somewhat higher, since the decay model underestimates the survival probability for the ion pair. After the inclusion in our close-coupling calculations of the two fine-structure components of ${\mathrm{Ca}}^{\ensuremath{-}},$ we find that the cross section increases substantially (by about a factor of 2) because of correlation between probabilities for population of two fine-structure sublevels.
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 .