  We study systems of few two-component fermions interacting in a Harmonic
Oscillator trap. The fermion-fermion interaction is generated in a finite basis
with a unitary transformation of the exact two-body spectrum given by the Busch
formula. The few-body Schr\"odinger equation is solved with the formalism of
the No-Core Shell Model. We present results for a system of three fermions
interacting at unitarity as well as for finite values of the S-wave scattering
length $a_2$ and effective range $r_2$. Unitary systems with four and five
fermions are also considered. We show that the many-body energies obtained in
this approach are in excellent agreement with exact solutions for the
three-body problem, and results obtained by other methods in the other cases.
