The existence of small helium clusters containing a variable number of ${}^{\mathrm{4}}\mathrm{H}\mathrm{e}$ and ${}^{\mathrm{3}}\mathrm{H}\mathrm{e}$ atoms is studied within a variational Monte Carlo calculation employing the Aziz HFD-B(HE) pair interaction. The clusters ${{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}_2$ support one and two ${}^{\mathrm{3}}\mathrm{H}\mathrm{e}$ atoms; however, the system with three ${}^{\mathrm{3}}\mathrm{H}\mathrm{e}$ atoms is metastable, and the next bound system requires at least 18 fermions. All clusters obtained by adding ${}^{\mathrm{3}}\mathrm{H}\mathrm{e}$ atoms to the trimer ${{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}_3$ and the tetramer ${{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}_4$ are bound, but the clusters ${{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}_3$-${{}^{\mathrm{3}}\mathrm{H}\mathrm{e}}_{3,4,5}$ and ${{}^{\mathrm{4}}\mathrm{H}\mathrm{e}}_{3,4}$-${{}^{\mathrm{3}}\mathrm{H}\mathrm{e}}_9$ are metastable. All remaining clusters with three or more bosons and any number of fermions are stable.

• Received 19 June 2002

DOI:https://doi.org/10.1103/PhysRevLett.89.193401