arXiv:physics/9812028 · Physical Review Letters

High-Precision Calculations of Dispersion Coefficients, Static Dipole Polarizabilities, and Atom-Wall Interaction Constants for Alkali-Metal Atoms

Andrei Derevianko, W. R. Johnson, Marianna S. Safronova, J. F. Babb

Published May 3, 1999• 365 citations

Abstract

The van der Waals coefficients for the alkali-metal atoms from Na to Fr interacting in their ground states are calculated using relativistic ab initio methods. The accuracy of the calculations is estimated by also evaluating atomic static electric-dipole polarizabilities and coefficients for the interaction of the atoms with a perfectly conducting wall. The results are in excellent agreement with the latest data from studies of magnetic field induced Feshbach resonances in ultracold collisions of Na and of Rb atoms. For Cs we provide critically needed data for ultracold collision studies.

DOI: 10.1103/physrevlett.82.3589

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arXiv:physics/9812028 · Physical Review Letters

High-Precision Calculations of Dispersion Coefficients, Static Dipole Polarizabilities, and Atom-Wall Interaction Constants for Alkali-Metal Atoms

Andrei Derevianko, W. R. Johnson, Marianna S. Safronova, J. F. Babb

Published May 3, 1999• 365 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.82.3589

Related papers

Semiempirical calculation of van der Waals coefficients for alkali-metal and alkaline-earth-metal atoms

J. Mitroy, M. W. J. Bromley

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The van der Waals coefficients,

{C}_{6},{C}_{8},

and

{C}_{10}

for the alkali-metal (Li, Na, K, and Rb) and alkaline-earth-metal (Be, Mg, Ca, and Sr) atoms are estimated by a combination of ab initio and semiempirical methods. Polarizabilities and atom-wall coefficients are given as a diagnostic check, and the lowest order nonadiabatic dispersion coefficient,

{D}_{8}

and the three-body coefficient,

{C}_{9}

are also presented. The dispersion coefficients are in agreement with the available relativistic many-body perturbation theory calculations. The contribution from the core was included by using constrained sum rules involving the core polarizability and Hartree-Fock expectation values to estimate the f-value distribution.

The

{C}_{3}

coefficients and their ratios for the alkali-metal atoms are determined very accurately by taking into account the optical properties of the atoms and four distinct types of trapping materials such as Au (metal), Si (semiconductor), vitreous

{\text{SiO}}_{2}

(dielectric), and

{\text{SiN}}_{x}

(dielectric). Dynamic dipole polarizabilities are calculated precisely for the alkali-metal atoms that produce

{C}_{3}

coefficients in a perfectly conducting medium within 0.2% accuracy. Thus, uncertainties from the atomic polarizabilities in the evaluation of the material-dependent

{C}_{3}

coefficients are small and accuracies of these

{C}_{3}

values mainly rely on the used optical data which are not taken into account in the present work. Our findings are in very good agreement with the available measurements, but they differ by around 10% from the previously reported high-precision calculations in heavy atoms for the perfect conductors. We also revisit the dispersion coefficients for the alkali-metal dimers and evaluate them using the above dynamic dipole polarizabilities which provide slightly different error bars than the other reported precise results. These coefficients are fitted into a ready-to-use functional form to aid the experimentalists in finding out the interaction potential only with the knowledge of atom-wall distance.

The long-range part of the interatomic interactions plays a substantial role in the collisional dynamics of ultracold gases. Here, we report on the calculation of the isotropic and anisotropic

{C}_{6}

coefficients characterizing the van der Waals interaction between dysprosium or erbium atoms in the two lowest energy levels and the ground-state alkali-metal (Li, Na, K, Rb, Cs, Fr) or alkaline-earth-metal (Be, Mg, Ca, Sr, Ba) atoms. The calculations are done using the integral of dynamic dipole polarizabilities at so-called imaginary frequencies of the two interacting atoms. For all atom pairs, we find that the isotropic

{C}_{6}

coefficients are two or three orders of magnitude larger than the anisotropic ones. Those coefficients are essential for modeling collisional properties of heteronuclear quantum mixtures containing highly magnetic dysprosium or erbium atoms and alkali-metal or alkaline-earth-metal atoms.