The adiabatic hyperspherical method is used to investigate the spectru
m of the helium trimer and to explore effects on the spectrum of varyi
ng the helium masses as well as the interaction strength. When a reali
stic helium dimer potential is adopted, only two isotopic combinations
are observed to have three-body bound states: He-4(3) and He-4(2) He-
3. By artificially adjusting the dimer potential, we also determine th
e range of interaction strengths for which halo states can result. The
existence of Efimov states for both physical and unphysical systems i
s also examined.