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Journal of Physics B Atomic and Molecular Physics

Semiclassical and quantum form factors in Rydberg-neutral collisions

Li Yu Cheng, Henri Van Regemorter

Published Nov 14, 1981• 20 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/14/21/017

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Journal of Physics B Atomic Molecular and Optical Physics•Mar 14, 1991•57 citations
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.
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.
State changing of high-Rydberg atoms by collisions with rare-gas atoms have been theoretically investigated using the free-electron model. The non-selective character of transitions arising from the short range of the interaction between the high-Rydberg atoms and the rare-gas atoms is found to be strongly modified in the following two cases. First, for the high-Rydberg atoms in the circular states with | m |= l ≃ n , it has been found that transitions take place overwhelmingly between the circular states. This propensity rule originates from a highly anisotropic electron-density distribution of the initial circular states. Second, for the high-Rydberg states with large quantum defects (modulo 1), suppression of the yield of the lower angular momentum states have been observed. This cancels out the fair enhancement of the production of the high-Rydberg states with small | m | seen for the hydrogenic case with small quantum defects. It leads to the m distribution of the final states apparently proportional to their statistical weight.
The intercombination transitions between l-resolved Rydberg levels due to collisions with fast electrons are studied within the Ochkur approximation for principal quantum numbers n\ensuremath{\le}20, where l is the angular momentum. The use of the Heisenberg correspondence principle for radial integrals enables one to obtain analytic expressions for any term in the multipole expansion of the cross section for collisions with an arbitrary n and l change. For transitions involving angular momenta that are small compared to the principal quantum numbers, the semiclassical and the exact results are found to be fairly close, within the accuracy consistent with the Born approximation. As a result, the semiclassical approach furnishes a ready estimate for cross sections, and its validity range proves broad enough to cover the region of large momenta transferred to the atom. The numerical results also confirm that dipole transitions have no dominance over the collisions with other \ensuremath{\Delta}l values, in accord with the general model of intercombination scattering.
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.