We consider a trapped dilute gas of
bosons in
interacting via a three-body interaction potential of the form
. In the
limit
,
we prove that every approximate ground state of the system is a convex
superposition of minimizers of a 3D energy-critical nonlinear Schrödinger
functional where the nonlinear coupling constant is proportional to
the scattering energy of the interaction potential. In particular, the
-body
ground state exhibits complete Bose–Einstein condensation if the nonlinear
Schrödinger minimizer is unique up to a complex phase.