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Journal of Physics B Atomic and Molecular Physics

The long-range contribution to quasi-elastic collisions of atoms

M. Martinis, Hartmut M. Pilkuhn

Published Apr 28, 1982• 0 citations
Publisher

Abstract

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 .

DOI
10.1088/0022-3700/15/8/016

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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 .
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.
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 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.
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.
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.
A general approximate method for computing the cross sections for certain inelastic collision processes is developed. It is based on the possibility of obtaining, with the use of the impact-parameter method, an exact expression for the transition amplitude in a special case. The dependence of the cross section on the parameters of coupling constant, velocity, and energy difference between states is discussed for a two-level model. Detailed calculations are made of cross section for collisions of the type $A(^{2}P_{\frac{3}{2}})+B\ensuremath{\rightleftharpoons}A(^{2}P_{\frac{1}{2}})+B$, where AAA is an excited atom of an alkali metal and BBB is an atom of a noble gas. An Appendix contains a review of the effective long-range interaction of atoms.