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Journal of Physics B Atomic Molecular and Optical Physics

Inelastic transitions between the fine-structure components of Rydberg atoms in collisions with neutral particles

Владимир Сергеевич Лебедев

Published Mar 14, 1992• 9 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/25/5/003

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Physical Review A•Aug 1, 1992•4 citations
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.
A theory of inelastic n,l-changing and quasielastic l-mixing collisions of Rydberg atoms with the heavy rare-gas atoms is developed. It is based on the semiclassical impact-parameter approach combined with the normalized perturbation theory. Semiclassical formulas for scaled transition probabilities and cross sections as functions of the inelasticity parameter and the collision strength are analyzed. This approach gives a general description of collisional nl\ensuremath{\rightarrow}${\mathit{n}}^{\ensuremath{'}}$ transitions independently of the specific values of the principal quantum number, the relative velocity, and the type of colliding atoms. The energy and angular dependence of the electron-atom scattering amplitude is included in the theory by incorporating the impulse-approximation results in the weak-coupling limit. The Ramsauer-Townsend effect affects significantly the values of the cross sections, especially for the inelastic transitions with large energy transfer. The results obtained are used in calculations of the quenching cross sections for the Rb(nS,nD,nF) atoms in collisions with Ar, Kr, and Xe. Comparison of theory and experiment is made in a wide range of the principal quantum numbers and transition energy defects. \textcopyright{} 1996 The American Physical Society.
Simple analytical formulas are given that allow the rapid estimation of cross sections for lll mixing, nnn changing, and ionization of Rydberg atoms with atomic and molecular targets. These formulas are derived by using the quasifree-electron model and the impulse approximation. The lll dependence of the cross section is accounted for only via the atomic energy. The quasielastic process of angular-momentum mixing caused by either the short- or long-range interaction between the Rydberg electron and the neutral perturber is studied and the corresponding cross sections are evaluated. The Rydberg-atom---molecule inelastic transitions (nnn changing and ionization) caused by the ${e}^{\ensuremath{-}}$-dipole or ${e}^{\ensuremath{-}}$-quadrupole interaction are investigated. It is shown that the nnn-changing reactions occur via quasiresonant internal-energy transfer between the two colliding partners. The influence of the relevant physical parameters is clearly stated for the three types of interaction (short-range, ${e}^{\ensuremath{-}}$-dipole, ${e}^{\ensuremath{-}}$-quadrupole). Comparison with more sophisticated approaches and experimental data shows that the accuracy of the formulas is about a factor of 2.
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.
Simple analytical expressions for the cross sections of nl to n'l' transitions from Rydberg-neutral inelastic collisions are obtained on the basis of the free electron model for electron-perturber scattering. The dependences of the electron-perturber scattering amplitude on the electron momentum and scattering angle are allowed for. The analytical results agree well with available numerical calculations. The analysis of the equations obtained yields a conclusion that the cross sections at l<or=l' depend weakly on l and l' for degenerate states and are proportional to the statistical weights of the final states for transitions with large energy defects.
We have presented a theoretical description of J-mixing (the transfer of excitation between fine structure) cross sections of a Rydberg Cs atom induced by thermal collisions with noble-gas atoms. The theory is based on the application of impulse approximation theory and a kind of model-potential wave function. The results agree well with available recent experimental values for He, Ne, and Ar atoms. But for the heavier noble-gas atoms Kr and Xe, the theoretical cross sections are larger than the experimental ones.