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Journal of Physics B Atomic and Molecular Physics

Analytical expressions for cross sections of Rydberg-neutral inelastic collisions

B. Kaulakys

Published Mar 28, 1985• 60 citations
Publisher

Abstract

The author obtains simple analytical expressions for the cross sections of the state-changing and ionisation collisions of Rydberg atoms with neutral atomic particles due to the Rydberg-electron-perturber interaction. The theoretical investigation is based on the impulse approximation and binary encounter approach for the form factor. The earlier results of Alekseev and Sobel'man (1965) and Omont (1977) turn out to be the limiting cases of the author's expressions. The calculated quenching cross sections for the Rydberg states agree well with experimental results and numerical calculations.

DOI
10.1088/0022-3700/18/6/004

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Physical Review A•Dec 1, 1984•40 citations
The author obtains simple analytical expressions for the cross sections of the state-changing and ionisation collisions of Rydberg atoms with neutral atomic particles due to the Rydberg-electron-perturber interaction. The theoretical investigation is based on the impulse approximation and binary encounter approach for the form factor. The earlier results of Alekseev and Sobel'man (1965) and Omont (1977) turn out to be the limiting cases of the author's expressions. The calculated quenching cross sections for the Rydberg states agree well with experimental results and numerical calculations.
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.
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.
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.
The theory of impact broadening of the isolated spectral lines of the Rydberg atomic series perturbed by neutral particles is developed within the framework of the impulse approximation. The analysis of the broadening process is based on the consideration of the inelastic nl to n' transitions between highly excited states of the Rydberg atom. The role of the potential and resonance scattering of the quasifree electron by a perturbing particle in the impact broadening of the Rydberg nl levels is investigated. It is shown that the general expressions for the broadening cross sections presented in this paper contain the results of asymptotic Alekseev and Sobel'man theory (1965) as special cases. Both elastic and inelastic scattering contributions of the perturber by the parent core of Rydberg atom to the broadening cross sections are also considered within the framework of the 'shake' model. The results obtained are used for a quantitative explanation of experimental data on the broadening of Rydberg atomic levels perturbed by alkali-metal atoms. The energies and widths of the 3 P resonances on the quasidiscrete levels of the negative K - and Rb - ions are determined.
The results of theoretical investigations of the excitation, quenching, ionization and broadening of the Rydberg atomic levels in inelastic collisions with ground‐state atoms of buffer or parent gases are presented. The different physical mechanisms of these processes due to the scattering of the perturbing neutral particle on the quasifree electron and on the core of the Rydberg atom are considered. In particular the role of the potential and resonance scattering of the slow electron on the perturbing atoms in the quenching and broadening processes is discussed. The effects of the nonadiabatic transfer of the Rydberg electron energy to the kinetic energy of the colliding atoms and to the energy of the electronic shell of the quasimolecular ion are also considered. The results of calculations of the cross sections and the rate constants of the quenching, boradening and ionziation processes for some physcial systems are presented and are compared with available experimental data.
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.