Energy shift of a depolarizing resonance due to a type-3 Siberian snake

We recently studied the proton beam polarization in the Indiana University Cyclotron Facility Cooler Ring at five energies. We found that the $G\ensuremath{\gamma}=2$ imperfection depolarizing resonance occurred about 1.9 MeV below the expected resonance energy of 108.4 MeV. This energy shift could be due to a shift of about +0.0036 in the spin tune ${\ensuremath{\nu}}_{s}$, which is the number of spin rotations in each turn around the ring. We then demonstrated that this spin tune shift is consistent with the Cooler Ring containing a partial type-3 Siberian snake, which is apparently caused by the magnets that confine the electron and proton beams in the cooling region.