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Physical Review A

Collisional broadening of Rydberg states by alkali-metal perturbers

V. M. Borodin, I. I. Fabrikant, Andrey K. Kazansky

Published Nov 1, 1991• 21 citations
Publisher

Abstract

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 $^{3}$P resonance of ${\mathrm{Cs}}^{\mathrm{\ensuremath{-}}}$. However, recent ab initio bound-state and scattering calculations indicate the existence of the Cs ${(}^{3}$P) bound state rather than the resonance.

DOI
10.1103/physreva.44.5725

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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.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 10, 2002•4 citations
Collisional broadening of nS Rydberg states by K, Rb, and Cs atoms is studied using the adiabatic approach for the 3\ensuremathΣ^{3}\mathrm{\ensuremath{\Sigma}}3\ensuremathΣ 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 Cs\ensuremath−{\mathrm{Cs}}^{\mathrm{\ensuremath{-}}}Cs\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 use the adiabatic theory in the complex plane of internuclear distance to calculate the Rydberg-state broadening cross sections in the ambient alkali-metal gases. We have found that the imaginary parts of the branch points between the relevant energy curves have an oscillatory structure that is projected into a similar structure in the broadening cross section. The results of the distorted-wave diabatic perturbation theory and the present theory are in excellent agreement for the principal quantum numbers of the Rydberg atoms n30. Unlike the diabatic perturbation theory, the adiabatic approach does not merge with the impulse approximation and fails for higher n.
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.
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.
The adiabatical mechanism of the oscillations of the broadened cross sections produced by collisions of Rydberg alkali atoms with ground-state atoms of an ambient alkali gas is presented. The dependence of the oscillations of the cross sections on the principal quantum number n arises due to the oscillations of the mixing parameter for the pseudocrossing between the 3 P ion state energy curve of the ambient gas atom and the Rydberg state dependent on n. The latter oscillations are generated by the oscillations of the Rydberg electron wavefunction in the coordinate space. The numerical results obtained are in good agreement with the experimental data for different colliding pairs. The matching of the adiabatical picture and the conventional impulse approximation is discussed.
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.