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Journal of Physics B Atomic and Molecular Physics

Thermal collisions of high-Rydberg atoms with neutral particles. II. Higher-order corrections to the impulse approximation

Yukap Hahn

Published Feb 28, 1982• 17 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/15/4/013

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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.
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.
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 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.
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 validity of the impulse approximation (IA) in thermal Rydberg-neutral collisions rests critically on the semiclassical nature of the Coulomb binding potential. The authors have shown that the IA is valid in both thermal and high-Rydberg-neutral collisions by estimating the second-order terms of the IA. The authors have also indicated that the thermal quasielastic state-changing collisions of the high-Rydberg atoms with the neutrals can be viewed as proceeding via the Rydberg electron-neutral encounters. The core effect proposed by Flannery (1982) is shown to be unimportant for the case of thermal quasielastic Rydberg-neutral collisions.
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.