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We report results for the ground-state energy and structural properties ofsmall $^4$He-T$\downarrow$ clusters consisting of up to 4 T$\downarrow$ and 8$^4$He atoms. These results have been obtained using very well-known$^4$He-$^4$He and T$\downarrow$-T$\downarrow$ interaction potentials andseveral models for the $^4$He-T$\downarrow$ interatomic potential. All thecalculations have been performed with variational and diffusion Monte Carlomethods. It takes at least three atoms to form a mixed bound state. Inparticular, for small clusters the binding energies are significantly affectedby the precise form of the $^4$He-T$\downarrow$ interatomic potential but thestability limits remain unchanged. The only exception is the$^4$He$_2$T$\downarrow$ trimer whose stability in the case of the weakest$^4$He-T$\downarrow$ interaction potential is uncertain, while it seems stablefor other potentials. The mixed trimer $^4$He(T$\downarrow$)$_2$, a candidatefor Borromean state, is not bound. All other studied clusters are stable. Someof the weakest bound clusters can be classified as quantum halos, as aconsequence of having high probability of being in a classically forbiddenregion.

Ground state of small mixed helium and spin-polarized tritium clusters: a quantum Monte Carlo stud