  We derive the ground-state energy for a small number of ultracold atoms in an
isotropic harmonic trap using effective quantum field theory (EFT). Atoms are
assumed to interact through pairwise energy-independent and energy-dependent
delta-function potentials with strengths proportional to the scattering length
$a$ and effective range volume $V$, respectively. The calculations are
performed systematically up to order $l^{-4}$, where $l$ denotes the harmonic
oscillator length. The effective three-body interaction contains a logarithmic
divergence in the cutoff energy, giving rise to a non-universal three-body
interaction in the EFT. Our EFT results are confirmed by nonperturbative
numerical calculations for a Hamiltonian with finite-range two-body Gaussian
interactions. For this model Hamiltonian, we explicitly calculate the
non-universal effective three-body contribution to the energy.
