Tensorial analysis of the long-range interaction between metastable alkaline-earth-metal atoms

Alkaline-earth atoms in their lowest triplet P_2 state are exceptionally long-lived and can be trapped magnetically. The nonspherical atomic structure leads to anisotropic long-range interactions between two metastable alkaline-earth atoms. The anisotropy affects the rotational motion of the diatomic system and couples states of different rotational quantum numbers. We develop a tensorial decomposition of the most important long-range interaction operators, and a systematic inclusion of molecular rotations, in the presence of an external magnetic field. The consequences are illustrated by application to metastable strontium. The coupling among molecular rotational states is demonstrated to induce the formation of a long-range molecular potential well. Its properties vary as a function of magnetic-field strength, thus allowing the scattering length in this state to be tuned. The scattering length of metastable strontium displays a resonance at a field of 339 Gauss.