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Journal of Physics B Atomic Molecular and Optical Physics

Semiclassical calculations of thel-mixing andn,l-changing collisions of Rydberg atoms with rare-gas atoms

Владимир Сергеевич Лебедев, I. I. Fabrikant

Published Jun 14, 1997• 19 citations
Publisher

Abstract

Semiclassical calculations of the quasi-elastic l-mixing and inelastic n,l-changing processes in thermal collisions of a Rydberg sodium atom with rare-gas atoms (Ne, Ar, Kr and Xe) as well as and atoms with Ne are presented in a wide range of principal quantum numbers. The main emphasis is put on the study of the effects in the Rydberg-atom - rare-gas-atom collisions associated with both the short- and long-range (polarization) parts of the electron - perturber interaction. It is shown that the polarization interaction between the highly excited electron and the Ne atom provides the major contribution to the cross section of the l-mixing and n, l -changing transitions. We show that the Ramsauer - Townsend effect in slow electron scattering by the heavy rare-gas atoms significantly affects the values of the cross sections, particularly for the inelastic transitions with large energy transfer. A quantitative explanation of these phenomena is given using the recently developed semiclassical normalized perturbation theory for the Rydberg-atom - neutral collisions combined with the modified effective range theory for scattering of slow electrons by the rare-gas atoms.

DOI
10.1088/0953-4075/30/11/016

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Semiclassical calculations of the quasi-elastic l-mixing and inelastic n,l-changing processes in thermal collisions of a Rydberg sodium atom with rare-gas atoms (Ne, Ar, Kr and Xe) as well as and atoms with Ne are presented in a wide range of principal quantum numbers. The main emphasis is put on the study of the effects in the Rydberg-atom - rare-gas-atom collisions associated with both the short- and long-range (polarization) parts of the electron - perturber interaction. It is shown that the polarization interaction between the highly excited electron and the Ne atom provides the major contribution to the cross section of the l-mixing and n, l -changing transitions. We show that the Ramsauer - Townsend effect in slow electron scattering by the heavy rare-gas atoms significantly affects the values of the cross sections, particularly for the inelastic transitions with large energy transfer. A quantitative explanation of these phenomena is given using the recently developed semiclassical normalized perturbation theory for the Rydberg-atom - neutral collisions combined with the modified effective range theory for scattering of slow electrons by the rare-gas atoms.
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.
A theoretical model for the collision of atoms in high Rydberg states (nl) with neutral atoms or molecules is proposed, based on the assumption that the electron-perturber interaction is of very short range compared with the mean radius of the Rydberg atom. A semiclassical method is used to derive a compact expression for the collision probability. The calculations need total cross sections for the scattering of a free and low-energy electron by the perturber. The model is applied to the calculation of a free and low-energy electron by the perturber. The model is applied to the calculation of cross sections for the quenching of n 2 D or n 2 F Rydberg states of Na and Rb by rare-gas atoms of N 2 . On the whole the calculated cross sections are in reasonable agreement with experimental data for n>10 approximately. The model and the results of the calculations are discussed and compared with other theoretical works.
Coupled-channel calculations for collisions of Na Rydberg atoms with He and Ar have been performed to investigate the effect of the interaction between the Na + core and the rare gas. For n=10, channels corresponding to the levels nd and nf are included, and calculations are reported both with and without terms arising from the core. It is found that the inelastic cross sections (10 to 10f) are insensitive to the core interactions, whereas the elastic cross sections (10d to 10d) may change significantly. This result is consistent with the prediction of the first-order Born approximation.
The author obtains expressions for Rydberg level broadening and shift cross sections and rates suitable for elastic collisions of ground-state rare-gas atoms with Rydberg atoms. The semiclassical impact broadening theory is used. The interaction of a Rydberg atom with a rare-gas atom is approximated by the superposition of polarisation potentials and the Fermi pseudopotential. It is shown that similar expressions for the broadening and shift cross sections due to the perturber-Rydberg-electron interaction can be obtained in the JWKB approximation for the Rydberg-electron wavefunctions and for the square-well model potential. Consequently the shift and width of the Rydberg level are not very sensitive to the shape of the potential but only to its normalisation. Expressions for the shift and width in the square-well potential approximation suitable in the high-density limit of the perturbing atoms are obtained. Limits of the applicability of the expressions for the broadening and shift cross sections are discussed. Calculated broadening and shift rates agree well with experimental results for the broadening and shift of Rydberg levels with small, medium and large principal quantum numbers by all rare gases excepting neon.
A theoretical investigation of quasi-elastic atom-scattering is presented. The transition potential for the system, which consists of an excited atom in a neutral atom in the ground state, is derived and split into short- and long-range parts. A general expression for the leading long-range (two-photon exchange) part of the inelastic potential is obtained and the correct threshold behaviour of the partial-wave amplitude is discussed. The cross sections sigma short (nl to nl') and sigma long (nl to nl') of l-changing collisions of the Rydberg atoms are estimated for large values of n, and small as well as large angular momentum transitions. It is found that sigma short >> sigma long if n 2 q min <<1 r n>>l,l' when n to infinity .
Semi-analytical methods are presented for computing quantum form factors in the general non-hydrogenic case. For transitions between hydrogenic states, semiclassical and quantum form factors are compared in a large domain of momentum transfer. The free electron model is applied to the l-changing Rydberg-atom plus rare-gas collisions between nearly degenerate states on the one hand, and to inelastic n-changing Rydberg-atom plus rare-gas collisions on the other hand. It is shown that the free electron model can be justified in the first case for high values of n(>or=15) and that it breaks down in the second case when large momentum transfers are involved.