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We theoretically evaluate the feasibility to form magnetically-tunableFeshbach molecules in collisions between fermionic $^6$Li atoms and bosonicmetastable $^{174}$Yb($^3$P$_2$) atoms. In contrast to the well-studiedalkali-metal atom collisions, collisions with meta-stable atoms are highlyanisotropic. Our first-principle coupled-channel calculation of thesecollisions reveals the existence of broad Feshbach resonances due to thecombined effect of anisotropic-molecular and atomic-hyperfine interactions. Inorder to fit our predictions to the specific positions ofexperimentally-observed broad resonance structures \cite{Deep2015} we optimizedthe shape of the short-range potentials by direct least-square fitting. Thisallowed us to identify the dominant resonance by its leading angular momentumquantum numbers and describe the role of collisional anisotropy in the creationand broadening of this and other resonances.

Magnetic control of ultra-cold $^6$Li and $^{174}$Yb($^3P_2$) atom mixtures with Feshbach resonances