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

TL;DR

This paper presents theoretical calculations of long-range dispersion coefficients ($C_6$ and $C_9$) for alkaline-earth atoms and ions, using relativistic methods, with results validated against existing data and new oscillator strengths and polarizabilities reported.

Contribution

It provides new calculated dispersion coefficients involving alkaline-earth atoms and ions, along with oscillator strengths and polarizabilities, filling gaps where experimental data was unavailable.

Findings

Calculated $C_6$ and $C_9$ coefficients match fitting calculations.

Reported oscillator strengths and polarizabilities agree with experimental data.

Provided data enhances understanding of long-range interactions in cold atom physics.

Abstract

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 $C_6$ and three-dipole $C_9$ dispersion coefficients involving alkaline-earth atoms with alkaline-earth atoms and alkaline-earth 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 atoms among themselves are compared with the previously reported values. Due to unavailability of any other earlier theoretical or experimental results, for the $C_6$ coefficients for alkaline-earth atoms with alkaline-earth ions and the $C_9$ 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.