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Annalen der Physik

Lifetimes of Excited Alkalilike Atoms Colliding by Van der Waals Forces with Inert Gas Atoms in the Groundstate

E. Siefart

Published Jan 1, 1982• 0 citations
Publisher

Abstract

Abstract The influence of Van der Waals forces on the lifetime of coherently excited hyperfine‐states |FimFi〉 and |FimFi〉 of alkalilike atoms i by collissions with inert gas atoms j in the groundstate |FjmFi〉 has been examined. To do this the timedependent Schrödinger equation has been solved on taking into account a static magnetic field, a radiation field and a Van der Waals force. Introducing an impact parameter model for the colliding atoms with small scattering angles which form a quasimolecule |μ〉 = |FimFiFjmFi 〉 an expression for the cross section σμμ has been derived which determines the halfwidth Γ μμ of the coherently excited states. On making use of the irreducible tensor representation the calculation of the cross‐section has been reduced to the calculation of multipole transitions. The result has been applied e. g. to the coherently excited 3d104p2P3/2‐states of Cu I colliding by dipole‐dipole interaction with inert gas atoms He I, and Ar I in the ground state. The values agree well with data which have been derived from zero‐level‐crossing experiments.

DOI
10.1002/andp.19824940104

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Canadian Journal of Physics•Apr 1, 1966•38 citations
Abstract The influence of Van der Waals forces on the lifetime of coherently excited hyperfine‐states |FimFi〉 and |FimFi〉 of alkalilike atoms i by collissions with inert gas atoms j in the groundstate |FjmFi〉 has been examined. To do this the timedependent Schrödinger equation has been solved on taking into account a static magnetic field, a radiation field and a Van der Waals force. Introducing an impact parameter model for the colliding atoms with small scattering angles which form a quasimolecule |μ〉 = |FimFiFjmFi 〉 an expression for the cross section σμμ has been derived which determines the halfwidth Γ μμ of the coherently excited states. On making use of the irreducible tensor representation the calculation of the cross‐section has been reduced to the calculation of multipole transitions. The result has been applied e. g. to the coherently excited 3d104p2P3/2‐states of Cu I colliding by dipole‐dipole interaction with inert gas atoms He I, and Ar I in the ground state. The values agree well with data which have been derived from zero‐level‐crossing experiments.
We consider the van der Waals force involving excited atoms in general environments, constituted by magnetodielectric bodies. We develop a dynamical approach studying the dynamics of the atoms and the field, mutually coupled. When only one atom is excited, our dynamical theory suggests that for large distances the van der Waals force acting on the ground-state atom is monotonic, while the force acting in the excited atom is spatially oscillating. We show how this latter force can be related to the known oscillating Casimir-Polder force on an excited atom near a (ground-state) body. Our force also reveals a population-induced dynamics: for times much larger that the atomic lifetime the atoms will decay to their ground states leading to the van der Waals interaction between ground-state atoms.
Abstract We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the and states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only away from these resonances can the van der Waals coefficients, C 6 sp , be defined. We calculate the C 6 coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several , we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms .
We have studied the long-range interaction potentials of the heteronuclear alkali-metal-atom dimers in the case when one of the atoms is in the first excited state (nA{n}_{A}nA​P) and the other is in the ground state (nB{n}_{B}nB​S). The presentation of the general expressions for the interaction energies in the Hund's case (c) is followed by the calculation of the corresponding C6{C}_{6}C6​ constants for all heteronuclear alkali-metal-atom pairs. In the case of heavier perturbers (Rb and Cs) the C6{C}_{6}C6​ constants are found to be significantly influenced by the perturber's fine structure. The van der Waals interaction in the K-Rb system is exceptionally strong resulting in C6{C}_{6}C6​ constants considerably larger than in all other alkali-metal-atom heteronuclear systems. The intermediate-coupling region (ICR) is defined as the region of internuclear separation R where the interaction energy is of the order of the atomic spin-orbit splitting, while the exchange energy is still negligible. Analysis of the general form of the energy matrices in the ICR shows that the homonuclear alkali-metal-atom dimers can be treated as a special case. In the large-R limit, the ICR results reduce to those obtained in Hund's case (c). As an example, we have calculated the ICR interaction potentials of the K-Rb system, taking into account only the leading dipole-dipole interaction. Finally we have discussed the construction of the absorption coefficient in the wings of the resonance lines, both in the impact and in the quasistatic approximation.
Francium has been the least-studied alkali-metal atom until recently. We present accurate calculations for the discrete and continuum optical transitions, and dispersion coefficients for two colliding francium atoms. Spin-orbit coupling is explicitly included and the influence of core polarization on the energies and the electric dipole operator is considered. Predictions for a range of transition amplitudes that are needed for parity violation experiments are made. The van der Waals coefficients for the long-range collision of two-ground-state Fr atoms in different fine-structure levels show a departure from an established trend in other alkali-metal atoms. We comment on the differences.
We investigate the influence of the appearance of excitonic states on van der Waals interactions among two Rydberg atoms. The atoms are assumed to be in different Rydberg states, e.g., in the ∣nsrangle|ns\\rangle∣nsrangle and ∣nprangle|np\\rangle∣nprangle states. The resonant dipole-dipole interactions yield symmetric and antisymmetric excitons, with energy splitting that give rise to new resonances as the atoms approach each other. Only far from these resonances the van der Waals coefficients, C6spC_6^{sp}C6sp​, can be defined. We calculate the C6C_6C6​ coefficients for alkali atoms and present the results for lithium by applying perturbation theory. At short interatomic distances of several mum\\mu mmum, we show that the widely used simple model of two-level systems for excitons in Rydberg atoms breaks down, and the correct representation implies multi-level atoms. Even though, at larger distances one can keep the two-level systems but in including van der Waals interactions among the atoms.
The total cross sections for inelastic collisions between rubidium and inert gas atoms, leading to a transfer of excitation between the 5 2P1/2 and 5 2P3/2 levels in rubidium, have been determined in a study of sensitized fluorescence in rubidium – inert gas mixtures. The experiments were performed at a rubidium vapor pressure of 1.5 × 10−6 mm Hg, at which there is no imprisonment of resonance radiation, and over a range of inert gas pressures extending from 1 to 350 mm Hg. The cross sections Q1(5 2P1/2 → 5 2P3/2) and Q2(5 2P1/2 ← 5 2P3/2) are as follows: Rb–He: 7.6 × 10−18 and 10.3 × 10−18 cm2; Rb–Ne: 1.7 × 10−19 and 2.3 × 10−19 cm2; Rb–A: 1.0 × 10−19 and 1.6 × 10−19 cm2; Rb–Kr: 6.4 × 10−20 and 1.5 × 10−19 cm2; Rb–Xe: 7.9 × 10−20 and 2.1 × 10−19 cm2. The cross sections are subject to two apparent anomalies: they do not vary monotonically with the polarizabilities of the inert gases and not all of their ratios Q1/Q2 have values predicted by the principle of detailed balancing. These properties of the cross sections, as well as a partial disagreement with Franck's rule, are interpreted qualitatively in terms of a "free particle" interaction between the inert gas atoms and the 5 2P orbital electron in rubidium. A competing process involving three-body collisions and the possible formation of Rb – inert gas van der Waals' molecules is also suggested.