  We consider the problem of cold atomic collisions in tight traps, where the
absolute scattering length may be larger than the trap size. As long as the
size of the trap ground state is larger than a characteristic length of the van
der Waals potential, the energy eigenvalues can be computed self-consistently
from the scattering amplitude for untrapped atoms. By comparing with the exact
numerical eigenvalues of the trapping plus interatomic potentials, we verify
that our model gives accurate eigenvalues up to milliKelvin energies for single
channel s-wave scattering of $^{23}$Na atoms in an isotropic harmonic trap,
even when outside the Wigner threshold regime. Our model works also for
multi-channel scattering, where the scattering length can be made large due to
a magnetically tunable Feshbach resonance.
