Search for Borromean states in the He-He-Rb triatomic system

We search for the existence of weakly bound He-He-Rb molecules. The He-He-Rb 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 ${}^3\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$, ${}^3\mathrm{He}$-${}^4\mathrm{He}$-${}^{85}\mathrm{Rb}$, and ${}^4\mathrm{He}$-${}^4\mathrm{He}$-${}^{85}\mathrm{Rb}$ trimers, respectively. The bound state for the ${}^3\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$ molecule is a Borromean state found in a realistic molecular systems because there are no bound states in both the ${}^3\mathrm{He}$-${}^3\mathrm{He}$ and ${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$ dimers.

Figure 1

Interatomic potentials for He-He and He-Rb systems.

Figure 2

The lowest hyperspherical potential curves for each of the triatomic systems, ${}^4\mathrm{He}$-${}^4\mathrm{He}$-${}^{85}\mathrm{Rb}$, ${}^4\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$, and ${}^3\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$ trimers. The curves of both the ${}^4\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$ and ${}^4\mathrm{He}$-${}^4\mathrm{He}$-${}^{85}\mathrm{Rb}$ trimers converge to the bound state of the ${}^4\mathrm{He}$-${}^{85}\mathrm{Rb}$ dimer with binding energy of $-10.3$ mK. The curve of ${}^3\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$ trimer converges to zero, the three-body breakup threshold, at large $R$.

Figure 3

The wave functions for the bound states of the ${}^4\mathrm{He}$-${}^4\mathrm{He}$-${}^{85}\mathrm{Rb}$, ${}^4\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$, and ${}^3\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$ trimers. The Borromean state of the ${}^3\mathrm{He}$-${}^3\mathrm{He}$-${}^{85}\mathrm{Rb}$ trimer has an larger spatial extent.