  We consider a spin-boson model in which a spin 1 system is coupled to an
oscillator. A unitary transformation is applied which allows a separation of
terms responsible for the Bloch-Siegert shift, and terms responsible for the
level splittings at anticrossings associated with Bloch-Siegert resonances.
When the oscillator is highly excited, the system can maintain resonance for
sequential multiphoton transitions. At lower levels of excitation, resonance
cannot be maintained because energy exchange with the oscillator changes the
level shift. An estimate for the critical excitation level of the oscillator is
developed.
