The energies and geometry of the ${}^{24}$Mg-He${}_2$ and ${}^{40}$Ca-He${}_2$ triatomic complexes are studied using the hyperspherical coupled-channel method. With pairwise He-$X$ (where $X$ denotes Mg or Ca) potentials, we find that the ${}^{24}$Mg-${}^4$He${}_2$ and ${}^{24}$Mg-${}^3$He-${}^4$He systems possess two bound states and the ${}^{24}$Mg-${}^3$He${}_2$ system possesses one, while the ${}^{40}$Ca-${}^4$He${}_2$, ${}^{40}$Ca-${}^3$He${}_2$, and ${}^{40}$Ca-${}^3$He-${}^4$He systems are found to support four, three, and three bound states, respectively. The different energies and geometric behaviors are reported when the He atom changes from ${}^3$He to ${}^4$He for the He-He-${}^{24}$Mg (${}^{40}$Ca) isotopic combinations. We also study structures of excited states and find that for some excited states, they are quite different from the ground states.

• Received 29 May 2013

DOI:https://doi.org/10.1103/PhysRevA.88.042503