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Physical Review A

Long-range diatomic s+p potentials of heavy rare gases

M. R. Doery, Edgar J. D. Vredenbregt, J. G. C. Tempelaars, Herman C. W. Beijerinck, BOUDEWIJN J. VERHAAR

Published May 1, 1998• 17 citations
Publisher

Abstract

We examine the long-range part of the rare-gas diatomic potentials that connect to the $R{(n\ensuremath{-}{1)p}^{5}\mathrm{ns}}+R{(n\ensuremath{-}{1)p}^{5}\mathrm{np}}$ atomic states in the separated atom limit ($n=3,$ 4, 5, and 6 for Ne, Ar, Kr, and Xe, respectively). We obtain our potentials by diagonalization of a Hamiltonian matrix containing the atomic energies and the electric dipole-dipole interaction, with experimentally determined parameters (atomic energies, lifetimes, transition wavelengths, and branching ratios) as input. Our numerical studies focus on Ne and Kr in this paper, but apply in principle to all other rare gases lacking hyperfine structure. These diatomic potentials are essential for applications in which homonuclear rare-gas pairs interact at large internuclear separations, greater than about 20 Bohr radii. Among such applications are the study of cold atomic collisions and photoassociative spectroscopy.

DOI
10.1103/physreva.57.3603

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We examine the long-range part of the rare-gas diatomic potentials that connect to the R(n\ensuremath−1)p5ns+R(n\ensuremath−1)p5npR{(n\ensuremath{-}{1)p}^{5}\mathrm{ns}}+R{(n\ensuremath{-}{1)p}^{5}\mathrm{np}}R(n\ensuremath−1)p5ns+R(n\ensuremath−1)p5np atomic states in the separated atom limit (n=3,n=3,n=3, 4, 5, and 6 for Ne, Ar, Kr, and Xe, respectively). We obtain our potentials by diagonalization of a Hamiltonian matrix containing the atomic energies and the electric dipole-dipole interaction, with experimentally determined parameters (atomic energies, lifetimes, transition wavelengths, and branching ratios) as input. Our numerical studies focus on Ne and Kr in this paper, but apply in principle to all other rare gases lacking hyperfine structure. These diatomic potentials are essential for applications in which homonuclear rare-gas pairs interact at large internuclear separations, greater than about 20 Bohr radii. Among such applications are the study of cold atomic collisions and photoassociative spectroscopy.
We present semiempirical calculations of long-range van der Waals interactions for two interacting metastable rare-gas atoms Ne through Xe. Dispersion coefficients C6{C}_{6}C6​ are obtained for homonuclear molecular potentials asymptotically connecting to the ns(3/2)2+ns(3/2)2{\mathrm{ns}(3/2)}_{2}{+ns(3/2)}_{2}ns(3/2)2​+ns(3/2)2​ atomic states. The estimated uncertainty of the calculated C6{C}_{6}C6​ dispersion coefficients is 4%.
Semiclassical calculations of the quasi-elastic l-mixing and inelastic n,l-changing processes in thermal collisions of a Rydberg sodium atom with rare-gas atoms (Ne, Ar, Kr and Xe) as well as and atoms with Ne are presented in a wide range of principal quantum numbers. The main emphasis is put on the study of the effects in the Rydberg-atom - rare-gas-atom collisions associated with both the short- and long-range (polarization) parts of the electron - perturber interaction. It is shown that the polarization interaction between the highly excited electron and the Ne atom provides the major contribution to the cross section of the l-mixing and n, l -changing transitions. We show that the Ramsauer - Townsend effect in slow electron scattering by the heavy rare-gas atoms significantly affects the values of the cross sections, particularly for the inelastic transitions with large energy transfer. A quantitative explanation of these phenomena is given using the recently developed semiclassical normalized perturbation theory for the Rydberg-atom - neutral collisions combined with the modified effective range theory for scattering of slow electrons by the rare-gas atoms.
The term long-range interactions refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds of Bohr radii. The energies involved are much smaller than the usual chemical bond energies. However, they are comparable with the typical kinetic energies of particles in an ultracold gas (T ≪ 1 K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases sheds a new light on the well-established topic of long-range interactions, because (i) the interacting atoms and molecules can be prepared in a well-defined quantum (electronic, vibrational, rotational, fine or hyperfine), ground or excited level; and (ii) long-range interactions can be tailored at will using external electromagnetic fields. In this chapter, we present the essential concepts and mathematical relations to calculate long-range potential energies. We start by deriving the multipolar expansion of the electrostatic interaction energy between classical charge distributions, both in Cartesian coordinates for pedagogical purpose, and in spherical coordinates for practical use. Then we combine multipolar expansion and quantum perturbation theory, to obtain the general first- and second-order energy corrections, including the well-known van der Waals energy. We consider two central examples in the current context of ultracold gases: (i) a pair of alkali metal atoms and (ii) a pair of alkali metal heteronuclear diatomic molecules in the presence of an electric field. We highlight the key role of the total angular momenta of the interacting particles and of the complex, irrespective of their electronic or nuclear, orbital or spin nature.
A new laser spectroscopic technique has been demonstrated for examining the structure of alkali--rare gas diatomic electronic states near the classical limit. In two-color experiments, Rb--Ar or Rb--Kr thermal pairs are excited by freeleftarrowleftarrowleftarrowfree or boundleftarrowleftarrowleftarrowfree transitions while monitoring the amplified spontaneous emission produced on the Rb D1_11​ or D2_22​ lines. Spectra observed lying within 10 cm−1^{-1}−1 of the separated atom limit for the A2Pi1/2^{2}Pi_{1/2}2Pi1/2​ states of Rb--Ar and Rb--Kr will be presented and discussed.
The term "long-range interactions" refers to electrostatic and magnetostatic potential energies between atoms and molecules with mutual distances ranging from a few tens to a few hundreds Bohr radii. The involved energies are much smaller than the usual chemical bond energies. However, they are comparable with the typical kinetic energies of particles in an ultracold gas (T≪1KT\ll 1KT≪1K), so that the long-range interactions play a central role in its dynamics. The progress of research devoted to ultracold gases shed a new light on the well-established topic of long-range interactions, because: (i) the interacting atoms and molecules can be prepared in a well-defined quantum (electronic, vibrational, rotational, fine or hyper-fine), ground or excited level; and (ii) long-range interactions can be tailored at will using external electromagnetic fields. In this chapter, we present the essential concepts and mathematical relations to calculate long-range potential energies. We start with deriving the multipolar expansion of the electrostatic interaction energy between classical charge distributions, both in Cartesian coordinates for pedagogical purpose, and in spherical coordinates for practical use. Then we combine multipolar expansion and quantum perturbation theory, to obtain the general first- and second-order energy corrections, including the well-known van der Waals energy. We consider two central examples in the current context of ultracold gases: (i) a pair of alkali-metal atoms and (ii) a pair of alkali-metal heteronuclear diatomic molecules submitted to an electric field. We highlight the key role of the total angular momenta of the interacting particles and of the complex, irrespective of their electronic or nuclear, orbital or spin nature.