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Physical Review A

Theory of slow-atom collisions

Bo Gao

Published Sep 1, 1996• 51 citations
Publisher

Abstract

A general theory of slow-atom collisions is presented with special emphasis on the effects of nuclear statistics and atomic fine and/or hyperfine structures. Symmetry properties of the collision complex and correlations between the molecular states and the separated-atom states are carefully examined. The frame transformations between various angular momentum coupling schemes are derived, which, in combination with the multichannel quantum defect theory, provides a solid foundation for the computation and the physical interpretation of slow-atom collision processes. The theory reduces to those of Stoof et al. [Phys. Rev. B 38, 4688 (1988)] and Zygelman et al. [Phys. Rev. A 49, 2587 (1994); 50, 3920 (1994)] in their respective ranges of validity. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.2022

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A general theory of slow-atom collisions is presented with special emphasis on the effects of nuclear statistics and atomic fine and/or hyperfine structures. Symmetry properties of the collision complex and correlations between the molecular states and the separated-atom states are carefully examined. The frame transformations between various angular momentum coupling schemes are derived, which, in combination with the multichannel quantum defect theory, provides a solid foundation for the computation and the physical interpretation of slow-atom collision processes. The theory reduces to those of Stoof et al. [Phys. Rev. B 38, 4688 (1988)] and Zygelman et al. [Phys. Rev. A 49, 2587 (1994); 50, 3920 (1994)] in their respective ranges of validity. \textcopyright{} 1996 The American Physical Society.
We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential and both the energy and angular momentum insensitivities of the short-range parameters. The theory provides an accurate and complete account of scattering processes, including shape and Feshbach resonances, in terms of a few parameters such as the singlet and triplet scattering lengths. As an example, results for $^{23}\mathrm{Na}\ensuremath{-}^{23}\mathrm{Na}$ scattering are presented and compared to close-coupling calculations.
We extend the powerful formalism of multichannel quantum defect theory combined with a frame transformation to ultracold atom-molecule collisions in magnetic fields. By solving the coupled-channel equations with hyperfine and Zeeman interactions omitted at short range, the extended theory enables a drastically simplified description of the intricate quantum dynamics of ultracold molecular collisions in terms of a small number of short-range parameters. We apply the formalism to ultracold Mg+NH collisions in a magnetic field, achieving a 10^{4}-fold reduction in computational effort.
A theory of electron-impact excitation of atoms in which fine structure is included as a perturbation is presented in detail. Hyperfine structure is included in the target atom but neglected in the electron-atom interaction. Expressions for electron-photon angular-correlation parameters and scattering cross sections are derived in terms of products of complex scattering amplitudes, with emphasis on electron-sodium excitation. Examples are given in which zero-field quantum beats may be observed in electron-photon angular-correlation and differential-cross-section measurements. Some of the interference terms are only observable in angular-correlation experiments. Examples are also given of partial cross sections for electron-impact excitation of state-to-state hyperfine levels in terms of direct- and exchange-scattering amplitudes plus additional terms due to the inclusion of fine-structure effects. The expressions given allow a comparison between the various possible scattering experiments.
Very briefly described is research conducted on the following topics: Fine structure and Zeeman effect of helium; Zeeman and Stark effect of positronium; hyperfine structure of the muonic helium atom; Lamb shifts of hydrogenic ions of high Z; nonadiabatic effects in slow atomic collisions; quenching of the metastable 2S state of muonic hydrogen and the muonic helium ion; two photon absorption; and quantization of electrodynamics hyperboloids and generalization of the effective action for electrodynamics.
We study atom-molecule inelastic scattering in a trapped alkali metal gas at ultracold temperature. We derive the atom-molecule Hamiltonian in the presence of hyperfine interactions and introduce angular momentum coupling schemes suited to the description of the short-and long-range physics of the collision. We provide a first estimate of the relative importance of rotational, hyperfine-changing, and spin-changing transitions within a simple rigid-rotor model. We also investigate the occurrence of resonance phenomena near the atom-molecule energy threshold.