  We examine the possible existence of quadrupole resonances in exotic atoms
containing odd-$A$ nuclei. We find that the spin-flip of the de-exciting exotic
particle can induce a resonance, altering the orbital angular momentum of the
nucleus by one quanta. This process results in an excited nucleus with a
suppression in x-ray photon emissions during the exotic atom cascade. We
provide specific cases of antiprotonic atoms of stable elements where this
resonance effect is expected to occur. The study of this phenomena may provide
insight into the strong interaction of deeply bound antiprotonic states in the
proximity of the unpaired nucleon, and serve as a tool for probing short-lived
excited nuclear states.
