Search for weakly bound states of the He-He-Be triatomic system

We search for the existence of weakly bound He-He-Be molecules. The He-He-Be molecule is treated as a three-body system. By using hyperspherical coordinates, the Schrödinger equation for the triatomic system is solved in the adiabatic approximation. A bound state is found for each of the ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$, ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}\text{−}{}^9\mathrm{Be}$, and ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}\text{−}{}^9\mathrm{Be}$ trimers.

Figure 1

Interatomic potentials for the He-He and He-Be systems.

Figure 2

The lowest hyperspherical potential curves for each of the triatomic systems, ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}\text{−}{}^9\mathrm{Be}$, ${}^4\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$, and ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$ trimers. The curves of both the ${}^4\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$, and ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}\text{−}{}^9\mathrm{Be}$ trimers converge to the bound state of the ${}^4\mathrm{He}\text{−}{}^9\mathrm{Be}$ dimer with binding energy of $2.45\mathrm{K}$. The curve of ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$ trimer converges to the bound state of the ${}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$ dimer with binding energy of $1.85\mathrm{K}$.

Figure 3

The wave functions for the bound states of the ${}^4\mathrm{He}\text{−}{}^4\mathrm{He}\text{−}{}^9\mathrm{Be}$, ${}^4\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$, and ${}^3\mathrm{He}\text{−}{}^3\mathrm{He}\text{−}{}^9\mathrm{Be}$ trimers. The hyperadial axis has a logarithmic scale. The three bound states have almost the same spatial extent.