Nuclear dynamics on coupled potential surfaces can lead to bound states embedded in the continuum. For one type of conical intersection situation, an explicit proof is presented that such states exist. Non-Born-Oppenheimer effects are responsible for the binding of these states. Once the Born-Oppenheimer approximation is introduced, these states at best become resonances which decay via potential tunneling. The tunneling is completely suppressed by the coupling between the electronic states. A numerical example is given.
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