  We investigate controlled collisions between trapped but separated ultracold
atoms. The interaction between atoms is treated self-consistently using an
energy-dependent delta-function pseudopotential model, whose validity we
establish. At a critical separation, a "trap-induced shape resonance" between a
molecular bound states and a vibrational eigenstate of the trap can occur. This
resonance leads to an avoided crossing in the eigenspectrum as a function of
separation. We investigate how this new resonance can be employed for quantum
control.
