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Journal of Physics B Atomic Molecular and Optical Physics

Collisional and thermal ionization of sodium Rydberg atoms: II. Theory fornS,nP andnD states withn= 5–25

K. Miculis, Ilya I. Beterov, Nikolai N. Bezuglov, I. I. Ryabtsev, Denis B. Tretyakov, Aigars Ekers, Andrey N. Klyucharev

Published May 26, 2005• 34 citations
Publisher

Abstract

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 .

DOI
10.1088/0953-4075/38/11/020

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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 .
Collisional and thermal ionization of sodium n S and n D Rydberg atoms with n = 8–20 has been studied. The experiments were performed using a two-step pulsed laser excitation in an effusive atomic beam at atom density of about 2 × 10 10 cm −3 . Molecular and atomic ions from associative, Penning and thermal ionization processes were detected. It was found that the atomic ions were created mainly due to photoionization of Rydberg atoms by photons of blackbody radiation at the ambient temperature of 300 K. Blackbody ionization rates and effective lifetimes of Rydberg states of interest were determined. The molecular ions were found to be from associative ionization in Na( nL ) + Na(3S) collisions. Rate constants of associative ionization have been measured using an original method based on relative measurements of Na + 2 and Na + ion signals.
Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for nSnSnS, nPnPnP, and nDnDnD states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers n=8−−65n=8--65n=8−−65 and at three ambient temperatures of 77, 300, and 600K600\phantom{\rule{0.3em}{0ex}}\mathrm{K}600K. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependences on nnn. The calculated ionization rates are compared with the results of our earlier measurements of BBR-induced ionization rates of Na nSnSnS and nDnDnD Rydberg states with n=8−−20n=8--20n=8−−20 at 300K300\phantom{\rule{0.3em}{0ex}}\mathrm{K}300K. A good agreement for all states except nSnSnS with n>15n>15n>15 is observed. We also present the useful analytical formulas for the quick estimation of BBR ionization rates of Rydberg atoms.
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.
Contemporary views on the formation of dynamic nonlinear resonances in isolated intermediate Rydberg quasi-molecular complexes formed by a single elementary act upon the slow collision highly excited atoms are discussed. A relation between the emergence of dynamic resonance and the quasi-intersection of atomic terms is revealed in the quasi-classical approximation. Relationships between the widths of dynamic resonances and the dipole matrix element leading to the corresponding quasi-intersections are determined. The physical reasons for the dynamic chaos regime are formulated. A quasi-classical statistical description is given of the diffusion ionization of an atomic complex with a dense network of quasi-intersections of terms. Development of the stochastic instability of the Rydberg electron trajectories due charge exchange inside the collision complex is considered. The effect the narrowing region of stochastic motion has when passing through the Coulomb convergence of the levels with a simultaneous drop in the ionization rate of quasi-molecular systems is predicted for external statistical magnetic and electric fields under conditions of Förster resonance.