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Journal of Physics B Atomic Molecular and Optical Physics

Collisional broadening of Rydberg-atom transitions by ground-state alkali atoms

M. E. Henry, Roger M. Herman

Published Jan 10, 2002• 4 citations
Publisher

Abstract

A theory is developed that allows a qualitative explanation and quantitative calculation of the widths and shifts of the two-photon Doppler-free transitions from the ground states of alkali atoms to Rydberg n 2 S and n 2 D states. The widths and shifts result from collisions between Rydberg atoms and ground-state alkali atoms, either of the same or of other species. The collisions are represented by means of a pseudopotential that is a function of theoretically calculated free-electron elastic scattering resonant and nonresonant phase shifts, which depend upon the Rydberg electron momentum. The momentum, in turn, is correlated with the electronic position within the Rydberg atom. This theory assumes classical straight-line trajectories and takes into consideration the multicollisional nature of the Rydberg-electron-perturbing-atom interaction within the Rydberg atom. Impact theory calculations of the linewidths and shifts for K**( n S)-K, K**( n S)-Rb, Rb**( n S)-Rb, Rb**( n S)-K, K**( n D)-K, K**( n D)-Rb, Rb**( n D)-Rb and Rb**( n D)-K show substantial agreement with experiment for 10⩽ n ⩽40.

DOI
10.1088/0953-4075/35/2/312

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Physical Review A•Jun 1, 1995•2 citations
A theory is developed that allows a qualitative explanation and quantitative calculation of the widths and shifts of the two-photon Doppler-free transitions from the ground states of alkali atoms to Rydberg n 2 S and n 2 D states. The widths and shifts result from collisions between Rydberg atoms and ground-state alkali atoms, either of the same or of other species. The collisions are represented by means of a pseudopotential that is a function of theoretically calculated free-electron elastic scattering resonant and nonresonant phase shifts, which depend upon the Rydberg electron momentum. The momentum, in turn, is correlated with the electronic position within the Rydberg atom. This theory assumes classical straight-line trajectories and takes into consideration the multicollisional nature of the Rydberg-electron-perturbing-atom interaction within the Rydberg atom. Impact theory calculations of the linewidths and shifts for K**( n S)-K, K**( n S)-Rb, Rb**( n S)-Rb, Rb**( n S)-K, K**( n D)-K, K**( n D)-Rb, Rb**( n D)-Rb and Rb**( n D)-K show substantial agreement with experiment for 10⩽ n ⩽40.
In this paper we present the results and discuss the applicability of an impact theory of lineshapes, developed by Henry and Herman for the pressure-induced broadening and shifting of transitions from the ground state to various Rydberg states of alkalis, to the situation in which the perturbing atoms are ground-state rare gas atoms. This theory, which has successfully described the collisional broadening of Rydberg states by alkali atoms, can without major alterations predict the widths and shifts of Doppler-free two-photon transitions to n S and n D states of Rb and Na, 6⩽ n ⩽30, perturbed by He, Ne, Ar, Kr and Xe. The results in all cases show reasonable agreement with experiment, with the transitions to Na**( n D) states being somewhat less satisfactory than the others.
The technique of Doppler-free two-photon spectroscopy was used to measure rates for line broadenings and frequency shifts of Rydberg levels with pressure. Measurements were made of spectra of 2S^{2}\mathrm{S}2S and 2D^{2}\mathrm{D}2D states (with n\ensuremath{\sim}10--40) for Rb∗∗{\mathrm{Rb}}^{\mathrm{*}\mathrm{*}}Rb∗∗+Rb and K∗∗{\mathrm{K}}^{\mathrm{*}\mathrm{*}}K∗∗+K, and of 2S^{2}\mathrm{S}2S states (with n=14--29) for K∗∗{\mathrm{K}}^{\mathrm{*}\mathrm{*}}K∗∗+Rb. Large oscillations are observed in both broadening and shift rates for n\ensuremath{\sim}20--30 in all series except for the 2D^{2}\mathrm{D}2D series in Rb∗∗{\mathrm{Rb}}^{\mathrm{*}\mathrm{*}}Rb∗∗+Rb. Overall rates for broadening and shift are compared with a theory based on the ``free-electron'' model. The observed oscillations are inconsistent with theories based on the resonance scattering of the Rydberg electron by the perturbing atom. A possible alternative mechanism related to interference in l-mixing collisions is suggested.
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.
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.
Effective range theory, taking into account the polarisation interaction, is used for the extrapolation of the phaseshifts for the scattering of electrons by heavy alkali atoms to the region of thermal energies. The phaseshifts obtained are used for the calculation of impact broadening and the shift of Rydberg levels by alkali perturbers in the ground state. The parameters of the theory obtained from the ab initio calculations give a good description of the data on broadening and shift in the case of K and Rb. In the case of Cs the parameters have to be somewhat modified to give an agreement with experiment. The phaseshifts are also used for the calculation of the width and shift in the free-electron spin-resonance frequency due to collisions with heavy alkali atoms. The results of calculations are in good agreement with experimental data. The results for total and momentum transfer cross sections for the scattering of electrons with energies from 10 -4 to 10 -1 eV by K, Rb and Cs atoms are presented.
We study the Rydberg-atom--ground-state-atom collisions within the framework of the quasi-free-electron model. We show that the general formulation of the problem based on the three-body Faddeev equations requires the off-shell extension of the two-body amplitude for electron-atom scattering. The two-body off-shell amplitudes for electron scattering by Rb and Cs atoms are calculated using the pseudopotential approach. The cross section for collisional quenching and broadening of Rydberg states due to perturbations by Rb and Cs atoms are calculated, and the results are compared with experimental data. The off-shell extension of the scattering amplitude usually improves agreement with the experiment. However, both on-shell and off-shell results fail in the region of low principal quantum numbers, where the multiscattering effects become important. Our calculations and their comparison with the experiments confirm that the ${\mathrm{Cs}}^{\mathrm{\ensuremath{-}}}$( 3^{3}3P) state is a resonance rather than a bound state.