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Physical Review A

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

I. I. Fabrikant

Published May 1, 1992• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.45.6404

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•Jan 1, 1995•0 citations
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.
The authors have measured the cross sections for the collisional quenching of highly excited (34<or=n<or=43) S rubidium atoms by ground-state rubidium atoms. The comparison between their data and the values calculated using a theoretical approach that only takes into account the valence electron-ground-state rubidium interaction provides the first experimental estimation of the cross section for the elastic scattering of ultra-low-energy electrons (E approximately=0.01 eV) by rubidium atoms. Their results for the quenching are connected to the available measurements of the self-broadening of the rubidium (5S-nS) lines by using a recent theoretical model: for n approximately 40 the self-broadcasting is essentially due to inelastic collisions. An upper limit is given for the cross section for the isotopic transfer between 85 Rb(nS) and 87 Rb(nS) states due to collisions with ground-state rubidium atoms.
Collisional broadening of nS Rydberg states by K, Rb, and Cs atoms is studied using the adiabatic approach for the $^{3}\mathrm{\ensuremath{\Sigma}}$ quasimolecular state and impulse approximation for all other contributions to the collisional width. The calculations are based on the use of the low-energy phase shifts for electron scattering by alkali metals obtained from ab initio close-coupling calculations and their extrapolation according to the modified effective range theory. We obtain a good agreement for the magnitude of the width with experimental data and satisfactory agreement for the oscillatory part of the width as a function of the principal quantum number. We find that the theory overestimates the amplitude of the oscillations. In the case of Cs as a perturber, the agreement with experimental data is good if we assume the existence of the low-energy 3^{3}3P resonance of ${\mathrm{Cs}}^{\mathrm{\ensuremath{-}}}$. However, recent ab initio bound-state and scattering calculations indicate the existence of the Cs (3{(}^{3}(3P) bound state rather than the resonance.
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 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.
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.