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In this work we investigate small clusters of helium atoms using thehyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ atomswith an inter-particle potential which does not present a strong repulsion atshort distances. We use an attractive gaussian potential that reproduces thevalues of the dimer binding energy, the atom-atom scattering length, and theeffective range obtained with one of the widely used He-He interactions, theLM2M2 potential. In systems with more than two atoms we consider a repulsivethree-body force that, by construction, reproduces the trimer binding energy ofthe LM2M2 potential. With this model, consisting in the sum of a two- andthree-body potential, we have calculated the spectrum of clusters formed byfour, five and six helium atoms. We have found that these systems present twobound states, one deep and one shallow close to the threshold fixed by theenergy of the $(A-1)$-atom system. Universal relations between the energies ofthe excited state of the $A$-atom system and the ground state energy of the$(A-1)$-atom system are extracted as well as the ratio between the ground stateof the $A$-atom system and the ground state energy of the trimer.

Spectra of helium clusters with up to six atoms using soft core potentials