  We present expressions demonstrating that collisional decoherence of
ultracold atoms or molecules in a coherent superposition of non-degenerate
quantum states is suppressed when both the real and imaginary parts of the
scattering lengths for the states in the coherent superposition are equal. We
show that the rate of collisional decoherence can be enhanced or suppressed by
varying an external magnetic field near a Feshbach resonance. For some
resonances, the suppression is very dramatic. We propose a method for measuring
the scattering length of ultracold particles in excited quantum states
exhibiting Feshbach resonances.
