  We study systems of few two-component fermions interacting via short-range
interactions within a harmonic-oscillator trap. The dominant interactions,
which are two-body, are organized according to the number of derivatives and
defined in a two-body truncated model space made from a bound-state basis.
Leading-order (LO) interactions are solved for exactly using the formalism of
the No-Core Shell Model, whereas corrections are treated as many-body
perturbations. We show explicitly that next-to-LO and next-to-next-to-LO
interactions improve convergence as the model space increases. We present
results at unitarity for three- and four-fermion systems, which show excellent
agreement with the exact solution (for the three-body problem) and results
obtained by others methods (in the four-body case). We also present results for
finite scattering lengths and non-zero range of the interaction, including (at
positive scattering length) observation of a change in the structure of the
three-body ground state and extraction of the atom-dimer scattering length.
