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 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 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, and
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 and the three-body coefficient,
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.
The van der Waals coefficients, from
C11 through to
C16 resulting from second-, third-, and fourth-order perturbation theory are estimated for the alkali-metal (Li, Na, K, and Rb) atoms. The dispersion coefficients are also computed for all possible combinations of the alkali-metal atoms and hydrogen. The parameters are determined from sum rules after diagonalizing a semiempirical fixed core Hamiltonian in a large basis. Comparisons of the radial dependence of the
Cn∕rn potentials give guidance as to the radial regions in which the various higher-order terms can be neglected. It is seen that including terms up to
C10∕r10 results in a dispersion interaction that is accurate to better than 1% whenever the inter-nuclear spacing is larger than
20a0. This level of accuracy is mainly achieved due to the fortuitous cancellation between the repulsive
(C11,C13,C15) and attractive
(C12,C14,C16) dispersion forces.
We study the van der Waals interaction between Rydberg alkali-metal atoms with fine structure (
n2Lj; $L\ensuremath{\le}2$) and heteronuclear alkali-metal dimers in the ground rovibrational state ($X^{1}\mathrm{\ensuremath{\Sigma}}^{+}$;
v=0,J=0). We compute the associated
C6 dispersion coefficients of atom-molecule pairs involving
133Cs and
85Rb atoms interacting with KRb, LiCs, LiRb, and RbCs molecules. The obtained dispersion coefficients can be accurately fitted to a state-dependent polynomial
O(n7) over the range of principal quantum numbers $40\ensuremath{\le}n\ensuremath{\le}150$. For all atom-molecule pairs considered, Rydberg states
n2Sj and
n2Pj result in attractive
1/R6 potentials. In contrast,
n2Dj states can give rise to repulsive potentials for specific atom-molecule pairs. The interaction energy at the LeRoy distance approximately scales as ${n}^{\ensuremath{-}5}$ for
n>40. For intermediate values of $n\ensuremath{\lesssim}40$, both repulsive and attractive interaction energies of the order of 10--$1000\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ can be achieved with specific atomic and molecular species. The accuracy of the reported
C6 coefficients is limited by the quality of the atomic quantum defects, with relative errors $\mathrm{\ensuremath{\Delta}}{C}_{6}/{C}_{6}$ estimated to be no greater than 1% on average.
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.