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Physical Review A

Orientation effects in thermal collisions between ‘‘circular’’–Rydberg-state atoms and ground-state helium

E. de Prunelé

Published Jun 1, 1985• 16 citations
Publisher

Abstract

A general formulation for thermal collisions between a Rydberg-state atom and a ground-state rare-gas atom is developed within the framework of the impulse approximation. This formulation allows calculation of cross sections for state-to-state transitions for an arbitrary initial orientation between the Rydberg-state atom and the relative velocity of the two partners of the collision. It also allows a direct computation of these cross sections averaged over all orientations, a situation corresponding to a cell experiment. In this formulation, the differential cross sections with respect to the modulus of the momentum transfer are obtained analytically in terms of rotation matrix elements. Numerical applications are made for the case of a sodium atom in a ``circular'' Rydberg state (\ensuremath{\Vert}n,l,m〉, with l=m=n-1) colliding with helium. The collisional processes are found to be highly anisotropic. In particular, a selection rule may appear, or disappear, depending upon the initial orientation. The extension to the case where an external electric field is present is also discussed, with special emphasis on symmetry properties.

DOI
10.1103/physreva.31.3593

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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 $(n\ge30),$ and adiabatic approximation $(n\le20).$ 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 $20 < n < 30.$ 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.

•Jan 1, 1995•0 citations
A general formulation for thermal collisions between a Rydberg-state atom and a ground-state rare-gas atom is developed within the framework of the impulse approximation. This formulation allows calculation of cross sections for state-to-state transitions for an arbitrary initial orientation between the Rydberg-state atom and the relative velocity of the two partners of the collision. It also allows a direct computation of these cross sections averaged over all orientations, a situation corresponding to a cell experiment. In this formulation, the differential cross sections with respect to the modulus of the momentum transfer are obtained analytically in terms of rotation matrix elements. Numerical applications are made for the case of a sodium atom in a ``circular'' Rydberg state (\ensuremath{\Vert}n,l,m〉, with l=m=n-1) colliding with helium. The collisional processes are found to be highly anisotropic. In particular, a selection rule may appear, or disappear, depending upon the initial orientation. The extension to the case where an external electric field is present is also discussed, with special emphasis on symmetry properties.
The influence of an external electric field on thermal collisions between a sodium atom excited in a ``circular'' Rydberg state (n=l+1=m+1=20) and a ground-state helium atom is studied numerically within the framework of the impulse approximation. The effect of the field is determined by using parabolic wave functions for the initial and final hydrogenic atomic states. The removal of degeneracy induced by the field appears to have no significant effect for fields in the range of 0--400 V/cm. However, the state-to-state transition cross sections are strongly dependent on the initial orientation as found in previous calculations without electric field.
Alignment and orientation effects in collisions of helium with Rydberg atoms due to the presence of static electric and magnetic fields are predicted. Analytical expressions are obtained for the cross sections of the state-to-state transitions within the manifold with the same principal quantum number. For moderate field-induced inelasticity, the curves of the cross sections vs the fields intensity show modulations that are explained in terms of the phase differences accumulated by the wave functions of the states involved in the collision. Due to the presence of the magnetic field, transitions involving inversion of high magnetic quantum numbers are dramatically quenched. The possibility of observing the predicted effects is discussed. The reported analytical cross sections are expected to help in the understanding of the results.
The title process with simultaneous rotational deexcitation of molecules was investigated theoretically by using the semiquantal approximation. The dipole Born and dipole Glauber differential cross sections were employed for the electron-molecule rotational deexcitation process. Numerical applications were made to the following systems: Xe+CO, HCl, HF, and LiF. A comparative study of the two approximations was carried out concerning the dependences of the cross sections on the following various quantities: n (principal quantum number), J (initial rotational quantum number), \ensuremath{\Delta}J (rotational quantum number change), D (dipole moment), V (relative collision velocity). As the molecular dipole moment becomes larger, there appears a prominent difference in the n dependence of the cross section. The Glauber approximation brings about a decrease in the cross section and yields a sawlike n dependence in contrast to a steplike n dependence in the case of the Born approximation. In the collisions involving lowly excited Rydberg atoms, ionization with simultaneous dipole-forbidden transition of a molecule becomes dominant compared to the ionization with simultaneous dipole-allowed transition. The cross section was found to be inversely proportional to the relative collision velocity; thus the ionization rate becomes independent of temperature. A comparison was also made between the experiment for the ionization rate at 300 K for Xe(27f)+HF and Xe(31f)+HCl.
Recent experimental and theoretical studies of near-resonant energy transfer collisions involving rare-gas atoms and alkali or alkaline earth atoms which have been initially excited to an aligned state via one or more linearly polarized rasters have yielded a wealth of insight into orbital alignment and related effects. We have extended this inquiry to initially aligned Rydberg states, examining state-to-state and alignment-selected cross sections using quantum collision theory augmented by approximations appropriate to the special characteristics of the Rydberg state (e.g., the quasi-free-electron model and the impulse approximation).
The title processes are theoretically investigated based on the model in which an excited Rydberg electron behaves as if it were 'free' and slow, with its interaction with the rare-gas atom playing a decisive role. The cross sections of l-changing collisions of the Rydberg atoms with the rare-gas atoms are evaluated for small angular momentum changes. They are compared with experimental data available at present, under the assumption that there is no selection rule for the distribution over the final angular momentum states of the Rydberg atom, and are found to be consistent with experimental findings. The relation between this approach and some others is examined. The possibility of learning about low-energy electron-rare-gas collisions from refined experimental data on the title processes is briefly discussed.
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.