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Bulletin of the American Physical Society

Adiabatic complex plane calculations of Rydberg states broadening by Rb and K perturbers

D. B. Khrebtukov, Andrey K. Kazansky, I. I. Fabrikant

Published May 1, 1993• 0 citations
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Abstract

We use the adiabatic theory in the complex plane of internuclear distance to calculate the Rydberg states broadening cross sections in the ambient alkali-metal gases. We find that the imaginary part of the branch point between the relevant energy curves has an oscillatory structure which leads to a similar structure in the broadening cross section. The results are in very good agreement with the distorted wave diabatic perturbation theory for n < 30. However the adiabatic approach fails for higher n.

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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.

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I. I. Fabrikant

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.

Journal of Physics B Atomic and Molecular Physics•May 28, 1986•82 citations
We use the adiabatic theory in the complex plane of internuclear distance to calculate the Rydberg states broadening cross sections in the ambient alkali-metal gases. We find that the imaginary part of the branch point between the relevant energy curves has an oscillatory structure which leads to a similar structure in the broadening cross section. The results are in very good agreement with the distorted wave diabatic perturbation theory for n < 30. However the adiabatic approach fails for higher n.
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.
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.
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.
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.
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.
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.