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arXiv:1309.4897 · Physical Review A

van der Waals coefficients for alkali-metal atoms in material media

Bindiya Arora, B. K. Sahoo

Published Feb 18, 2014• 16 citations
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Abstract

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.

DOI
10.1103/physreva.89.022511

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In the present work, we determine the C5{C}_{5}C5​ coefficients along with their uncertainties due to quadrupole polarization effects of all the alkali atoms interacting with a metal (Au), a semiconductor (Si), and four dielectric materials (SiO2,SiNx{\mathrm{SiO}}_{2}, {\mathrm{SiN}}_{x}SiO2​,SiNx​, yttrium aluminum garnet, and sapphire). The required dynamic electric quadrupole (E2E2E2) polarizabilities are evaluated by calculating E2E2E2 matrix elements of a large number of transitions in the alkali atoms by employing a relativistic coupled-cluster method. A significant contribution towards the long-range van der Waals potential is made by the quadrupole polarization effects. Our finding shows that contributions from the C5{C}_{5}C5​ coefficients to the atom-wall interaction potentials are pronounced at short distances (1--10 nm). The C3{C}_{3}C3​ coefficients of a Fr atom interacting with the above material media are also reported. These results could be useful in understanding the interactions of alkali atoms trapped in different material bodies during high-precision measurements.
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.
The van der Waals coefficients, C6,C8,{C}_{6},{C}_{8},C6​,C8​, and C10{C}_{10}C10​ 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, D8{D}_{8}D8​ and the three-body coefficient, C9{C}_{9}C9​ 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.
A systematic study of the leading isotropic van der Waals coefficients for the alkali-metal atom+molecule and molecule+molecule systems is presented. Dipole moments and static and dynamic dipole polarizabilities are calculated employing high-level quantum chemistry calculations. The dispersion, induction, and rotational parts of the isotropic van der Waals coefficient are evaluated. The known van der Waals coefficients are then used to derive characteristics essential for simple models of the collisions involving the corresponding ultracold polar molecules.
The 1%-accurate calculations of the van der Waals interaction between an atom and a cavity wall are performed in the separation region from 3nmto150nm3\phantom{\rule{0.3em}{0ex}}\mathrm{nm}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}150\phantom{\rule{0.3em}{0ex}}\mathrm{nm}3nmto150nm. The cases of metastable He∗{\mathrm{He}}^{*}He∗ and Na atoms near metal, semiconductor, and dielectric walls are considered. Different approximations to the description of wall material and atomic dynamic polarizability are carefully compared. The smooth transition to the Casimir-Polder interaction is verified. It is shown that to obtain accurate results for the atom-wall van der Waals interaction at short separations with an error less than 1% one should use the complete optical-tabulated data for the complex refractive index of the wall material and the accurate dynamic polarizability of an atom. The obtained results may be useful for the theoretical interpretation of recent experiments on quantum reflection and Bose-Einstein condensation of ultracold atoms on or near surfaces of different kinds.
The random-phase approximation with exchange (RPAE) is used with a BBB-spline basis to compute dynamic dipole polarizabilities of noble-gas atoms and several other closed-shell atoms (Be, Mg, Ca, Zn, Sr, Cd, and Ba). From these, values of the van der Waals C6{C}_{6}C6​ constants for positronium interactions with these atoms are determined and compared with existing data. After correcting the RPAE polarizabilities to fit the most accurate static polarizability data, our best predictions of C6{C}_{6}C6​ for Ps--noble-gas pairs are expected to be accurate to within 1%, and to within a few percent for the alkaline-earth metals. We also used accurate dynamic dipole polarizabilities from the literature to compute the C6{C}_{6}C6​ coefficients for the alkali-metal atoms. Implications of increased C6{C}_{6}C6​ values for Ps scattering from more polarizable atoms are discussed.