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Journal of Physics B Atomic and Molecular Physics

Thermal collisions of high Rydberg atoms with neutral particles. I. General theory and modified impulse approximation

Yukap Hahn

Published Mar 28, 1981• 22 citations
Publisher

Abstract

A general theoretical formulation of the Rydberg-atom-neutral-atom inelastic processes is presented in order to define precisely the physical content of the simple impulse picture and to develop a systematic correction procedure. A simple modification of the impulse amplitude is then introduced to incorporate the distortion effect caused by the presence of the core of Rydberg atom. A preliminary calculation provides a reasonable description of the inelastic scattering involving low principal quantum numbers as well.

DOI
10.1088/0022-3700/14/6/011

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For pt.I see ibid., vol.14, p.985 (1981). A general theory of the Rydberg atom inelastic scattering by perturber atoms has been developed previously, in which the leading term is the simple impulse amplitude, followed by the various correction terms. Theoretical estimates of these correction terms are presented in this paper, resulting in a general scaling formula. The non-impulse correction to the impulse approximation varies as n -2 at large principal quantum number n and depends on the signature of the electron-perturber scattering length. The distortion correction due to the interaction between the perturber and the Rydberg atomic core is large for the intermediate values of n<or approximately=20 behaves as n -4 , and depends on the perturber-core total cross section. The scaling formula derived here has been tested for the scattering systems consisting of Na and Rb targets and inert gas perturbers.

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M. Raymond Flannery

A new theoretical method outlined here for an important inelastic mechanism based on A-B + encounters in A-B(n) thermal collisions indicates a substantial contribution to l-changing transitions which therefore cannot be viewed as proceeding via (e-A) encounters alone. Recent descriptions of l-changing thermal collisions which are based on an (e-A) impulse treatment appear defective in that they disregard certain impulse validity criteria and yield results which greatly exceed the upper limit specified by the basic impulse expression, and do not recognise the above important inelastic mechanism associated with the non-inertiality of the core.

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Impulse-approximation analysis of collisions between Rydberg and ground-state rubidium atoms at thermal energies

I. I. Fabrikant

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Physical Review A•May 1, 1992•17 citations
A general theoretical formulation of the Rydberg-atom-neutral-atom inelastic processes is presented in order to define precisely the physical content of the simple impulse picture and to develop a systematic correction procedure. A simple modification of the impulse amplitude is then introduced to incorporate the distortion effect caused by the presence of the core of Rydberg atom. A preliminary calculation provides a reasonable description of the inelastic scattering involving low principal quantum numbers as well.
For pt.I see ibid., vol.14, p.985 (1981). A general theory of the Rydberg atom inelastic scattering by perturber atoms has been developed previously, in which the leading term is the simple impulse amplitude, followed by the various correction terms. Theoretical estimates of these correction terms are presented in this paper, resulting in a general scaling formula. The non-impulse correction to the impulse approximation varies as n -2 at large principal quantum number n and depends on the signature of the electron-perturber scattering length. The distortion correction due to the interaction between the perturber and the Rydberg atomic core is large for the intermediate values of n<or approximately=20 behaves as n -4 , and depends on the perturber-core total cross section. The scaling formula derived here has been tested for the scattering systems consisting of Na and Rb targets and inert gas perturbers.
The validity of the impulse approximation (IA) in thermal Rydberg-neutral collisions rests critically on the semiclassical nature of the Coulomb binding potential. The authors have shown that the IA is valid in both thermal and high-Rydberg-neutral collisions by estimating the second-order terms of the IA. The authors have also indicated that the thermal quasielastic state-changing collisions of the high-Rydberg atoms with the neutrals can be viewed as proceeding via the Rydberg electron-neutral encounters. The core effect proposed by Flannery (1982) is shown to be unimportant for the case of thermal quasielastic Rydberg-neutral collisions.
The theory of the J-mixing process for thermal collisions between Rydberg atoms and neutral particles has been developed in the impulse approximation using the formalism of spherical tensor operators and the WKB approximation. The authors have derived a simple formula for the cross section of inelastic nlJ to nlJ' transitions, which provides the dependence on the principal n and orbital l quantum numbers, relative velocity V and the energy defect of the fine-structure splitting. The analytical results obtained are in good agreement with the available experimental data and numerical calculations.
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 new theoretical method outlined here for an important inelastic mechanism based on A-B + encounters in A-B(n) thermal collisions indicates a substantial contribution to l-changing transitions which therefore cannot be viewed as proceeding via (e-A) encounters alone. Recent descriptions of l-changing thermal collisions which are based on an (e-A) impulse treatment appear defective in that they disregard certain impulse validity criteria and yield results which greatly exceed the upper limit specified by the basic impulse expression, and do not recognise the above important inelastic mechanism associated with the non-inertiality of the core.
The impulse approximation for the Rydberg atom-atom collisions is analyzed on the basis of the Faddeev equations. A modified expression is derived for the cross sections, including the interference between the Rydberg-electron--perturber scattering and the ion-core--perturber scattering. This expression is used for the calculations of the collisional quenching and elastic scattering in Rb(nS)-Rb and Rb(nP)-Rb collisions. We use the electron-Rb scattering phase shifts obtained from ab initio close-coupling calculations and their extrapolation, applying the modified effective-range theory. Our results show that the impulse approximation agrees with the experimental data for the quenching cross sections at n>20 but underestimates the quenching cross sections at lower n. The position of the maximum of the cross section is in good agreement with experimental data. We also obtain reasonable results for the elastic cross section at n>20, but for the lower n the results are too large. The interference effect plays a minor role in the process, which means that simultaneous electron-perturber and ion-perturber interaction is unlikely.