Effect of superconducting electrons on the energy splitting of tunneling systems

We consider the effect of superconducting electrons on the magnitude of the energy splitting of a tunneling system. A specific example is a hydrogen atom tunneling in niobium. We find that in this case the splitting is roughly 20% smaller in the normal state than in the superconducting state. This difference in the splitting should be observable in neutron scattering and ultrasonic measurements