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Physical Review A

Classical model for angular momentum mixing of Rydberg states

Charles E. Burkhardt, Jacob J. Leventhal

Published Jan 1, 1991• 10 citations
Publisher

Abstract

A classical model for l mixing of Rydberg states in atomic collisions is described. The primary assumption of the model is that l changing occurs in a single hard-sphere collision between the Rydberg electron and the perturbing atom which is represented by the zero-energy scattering length L. Predictions of the model, which are in the form of cross sections as functions of principal quantum number n, are compared with data for l mixing of Na(nd) and Rb(nf) by rare-gas atoms. Agreement is, in most cases, quite good, comparable with that of other, more sophisticated, models. It is shown that, because the calculation must be carried out in the reference frame of the ion core, the energy deficit between low angular momentum states and the nearest hydrogenic manifold can be made up in a single collision between the Rydberg electron and the perturbing atom, an effect that is analogous to the gravitational slingshot effect used to alter the orbits of a spacecraft under the influence of the Sun's gravitational field. Comparison of data for l mixing by ground-state Rb atoms with model calculations in which L is treated as a free parameter leads to an estimate of 10 a.u. for the zero-energy scattering length of Rb.

DOI
10.1103/physreva.43.110

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Relation between low-energy-electron scattering and l -changing collisions of Rydberg atoms

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Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the $s$-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the $l$-mixing cross section at a particular $n$ is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on $n$. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of $\mathrm{Na}(\mathrm{nd})+\mathrm{He}$, Ne, and Ar are treated as specific examples.

Physical Review A•Mar 1, 1979•55 citations
A classical model for l mixing of Rydberg states in atomic collisions is described. The primary assumption of the model is that l changing occurs in a single hard-sphere collision between the Rydberg electron and the perturbing atom which is represented by the zero-energy scattering length L. Predictions of the model, which are in the form of cross sections as functions of principal quantum number n, are compared with data for l mixing of Na(nd) and Rb(nf) by rare-gas atoms. Agreement is, in most cases, quite good, comparable with that of other, more sophisticated, models. It is shown that, because the calculation must be carried out in the reference frame of the ion core, the energy deficit between low angular momentum states and the nearest hydrogenic manifold can be made up in a single collision between the Rydberg electron and the perturbing atom, an effect that is analogous to the gravitational slingshot effect used to alter the orbits of a spacecraft under the influence of the Sun's gravitational field. Comparison of data for l mixing by ground-state Rb atoms with model calculations in which L is treated as a free parameter leads to an estimate of 10 a.u. for the zero-energy scattering length of Rb.
A coupled-channel approach based on the Arthurs and Dalgarno formalism is presented to describe the scattering of a Rydberg atom and a rare-gas atom. The method permits the calculation of cross sections for changes in the electronic orbital angular momentum of the Rydberg atom. The theory explicitly relates the scattering behavior of the Rydberg state to the electron-rare-gas scattering length. Preliminary results for Na∗(nd){\mathrm{Na}}^{*}(\mathrm{nd})Na∗(nd)+He and Na∗(nf){\mathrm{Na}}^{*}(\mathrm{nf})Na∗(nf)+He are in good agreement with experiment.
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.
Transitions between states with the same principal quantum number n in the collision of a Rydberg atom with an ion are described within the classical approximation for the Rydberg electron. The quantum electron state is represented by an ensemble of classical trajectories. Within the dipole approximation for the interaction the final value of the orbital momentum l is calculated analytically for each initial trajectory in the ensemble. Averaging over the ensemble gives the distribution function over l. For the initial s state of the Rydberg atom the distribution functions are found also for the pairs of variables, namely: {the angular momentum; its projection on the collision velocity}; {projections of the angular momentum and the Runge - Lenz vector on the collision velocity} and {projections of the angular momentum and the Runge - Lenz vector on the plane perpendicular to the collision velocity}. The l-distributions for the orbitally polarized initial p and d Rydberg states with definite projections of the initial angular momentum on the velocity axis are also obtained. The influence of the non-Coulomb core is taken into account by an approximation. The final l-distributions (calculated for the initial s-state) are shifted towards the large-l values as the relative collision velocity vn decreases. Good agreement is achieved with the recent experimental data for Na(28d) and Na(26d) Rydberg atoms.
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 collisional angular-momentum mixing of $n=5\ensuremath{-}15$ Na ddd states with the l>2l>2l>2 states of the same nnn has been studied using He, Ne, and Ar as collision partners. At rare-gas pressures of \ensuremath{\sim}1 Torr, the $l\ensuremath{\ge}2$ states are thoroughly mixed and the mixture decays at the average radiative lifetime of all the $l\ensuremath{\ge}2$ states of the same nnn. Using \ensuremath{\sim}1 Torr of neon to collisionally mix the $l\ensuremath{\ge}2$ states, the average lifetime for $l\ensuremath{\ge}2$ was measured for each nnn and compared to the theoretical prediction for hydrogen, with which it is in excellent agreement. The cross section for lll mixing by each of the gases is found to increase sharply from n=5to10n=5 \mathrm{to} 10n=5to10 and decrease above n=10n=10n=10. The magnitudes of the lll-mixing cross sections are found to correlate with the low-energy scattering lengths of the collision partners.
Collisions of Rydberg atoms with other atoms may induce changes in the electronic orbital angular momentum of the Rydberg state. A theory is presented that expresses the cross section for this process in terms of the sss-wave amplitude for low-energy-electron scattering from the other atom. In its most accurate form, the theory requires a convolution of the electron-scattering amplitude and the initial momentum-space wave function of the Rydberg state. However, an approximate analytic solution is derived in which the lll-mixing cross section at a particular nnn is written as the electron-scattering cross section at the mean electronic kinetic energy of the Rydberg state, multiplied by a scaling function that depends only on nnn. The analytic solution clearly exhibits the asymptotic scaling behavior of the cross sections. Collisions of Na(nd)+He\mathrm{Na}(\mathrm{nd})+\mathrm{He}Na(nd)+He, Ne, and Ar are treated as specific examples.