Two-dipole and three-dipole dispersion coefficients for interaction of alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions

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 ${C}_{6}$ and three-dipole ${C}_{9}$ dispersion coefficients involving alkaline-earth-metal atoms with alkaline-earth-metal atoms and alkaline-earth-metal ions. The ${C}_{6}$ and ${C}_{9}$ coefficients are expressed in terms of the dynamic dipole polarizabilities, which are calculated using relativistic methods. Thereafter, the calculated ${C}_{6}$ 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 ${C}_{6}$ coefficients for alkaline-earth-metal atoms with alkaline-earth-metal ions and the ${C}_{9}$ 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., ${\mathrm{Be}}^{+}, {\mathrm{Mg}}^{+}, {\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$, 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.