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arXiv:1504.05334 · Physical Review A

van der Waals coefficients for positronium interactions with atoms

A. R. Swann, J. A. Ludlow, G. F. Gribakin

Published Jul 6, 2015• 11 citations
arXivHTMLPDF

Abstract

The random-phase approximation with exchange (RPAE) is used with a $B$-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 ${C}_{6}$ 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 ${C}_{6}$ 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 ${C}_{6}$ coefficients for the alkali-metal atoms. Implications of increased ${C}_{6}$ values for Ps scattering from more polarizable atoms are discussed.

DOI
10.1103/physreva.92.012505

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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.
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 C6{C}_{6}C6​ 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 C6{C}_{6}C6​ 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.
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.
Apropos of the growing interest in the study of long-range interactions for their applications in cold-atom physics, we perform theoretical calculations for the two-dipole C6{C}_{6}C6​ and three-dipole C9{C}_{9}C9​ dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The C6{C}_{6}C6​ and C9{C}_{9}C9​ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated C6{C}_{6}C6​ coefficients for the considered alkaline-earth-metal atoms are compared with previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the C6{C}_{6}C6​ coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the C9{C}_{9}C9​ coefficients we perform separate fitting calculations and compare the results. Our calculations match in an excellent manner with the fitting calculations. We also report the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth-metal ions, i.e., Be+,Mg+,Ca+,Sr+{\mathrm{Be}}^{+}, {\mathrm{Mg}}^{+}, {\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}Be+,Mg+,Ca+,Sr+, and Ba+{\mathrm{Ba}}^{+}Ba+, as well as the alkaline-earth-metal atoms, i.e., Be, Mg, Ca, Sr, and Ba. These show good agreement when compared with the available experimental results.
Apropos to the growing interest in the study of long-range interactions which for their applications in cold atom physics, we have performed theoretical calculation for the two-dipole C6C_6C6​ and three-dipole C9C_9C9​ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth ions. The C6C_6C6​ and C9C_9C9​ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated C6C_6C6​ coefficients for the considered alkaline-earth atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the C6C_6C6​ coefficients for alkaline-earth atoms with alkaline-earth ions and the C9C_9C9​ coefficients, we have performed separate fitting calculations and compared. Our calculations match in an excellent manner with the fitting calculations. We have also reported the oscillator strengths for the leading transitions and static dipole polarizabilities for the ground states of the alkaline-earth ions, i.e., Mg+^++, Ca+^++, Sr+^++, and Ba+^++ as well as the alkaline-earth atoms, i.e., Mg, Ca, Sr, and Ba. These, when compared with the available experimental results, show good agreement.
Relativistic many-body calculations of van der Waals coefficients C6{C}_{6}C6​ for dimers correlating to two ground-state alkaline-earth-metal atoms at large internuclear separations are reported. The following values and uncertainties were determined: C6=214(3){C}_{6}=214(3)C6​=214(3) for Be, 627(12) for Mg, 2221(15) for Ca, 3170(196) for Sr, and 5160(74) for Ba in atomic units.