Delta function model for the helium trimer: origin of three-body forces

The Dirac bubble potential, previously used to model the helium dimer, is applied to the trimer. It is shown that the quantum mechanical kinetic energy operator for a three-body system contains terms over and above the analogues of classical pairwise contributions. The additional terms, the ‘Borromean couplings’, are responsible for a dramatic increase in the binding energy of the trimer. For example, ⁴He₃ is bounded by two orders of magnitude more strongly than ⁴He₂, 279 mK versus 1.31 mK, respectively, according to our calculations. Moreover, the trimer is considerably more compact than the dimer, with (r₁₂) decreasing to 9.01 Å from 51.9 Å.