The helium trimer has no bound rotational excited states

Abstract

We have searched for bound states of helium trimers with nonzero angular momenta. Including only pair interactions between helium atoms, we solved the Schrödinger equation in hyperspherical coordinates in the adiabatic approximation. From the resulting potential curves - which are mostly repulsive for nonzero angular momenta - we conclude that there are no bound rotational excited states in any of the isotopes of the helium trimer. The symmetry properties of the trimer wavefunctions in the body-fixed frame are also analysed.