Abstract
We investigate for the existence of the weakly bound He-He-Ca molecules. By employing the best empirical interaction between each pair of particles, the Schr\"odinger equation for the triatomic system is solved using hyperspherical coordinates in the adiabatic approximation. The bound states are found for each of the ${}^{3}$He-${}^{3}$He-${}^{40}$Ca, ${}^{3}$He-${}^{4}$He-${}^{40}$Ca, and ${}^{4}$He-${}^{4}$He-${}^{40}$Ca trimers, respectively. The binding energies of such molecules are estimated. We discuss the features of the channel functions associated with the hyperspherical potential curves of each system to obtain insight into the geometry of the molecules.
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