  The paper reports an exact solution for the problem of spin evolution of
radical ion pair in static magnetic and resonant microwave field taking into
account Zeeman and hyperfine interactions and spin relaxation. The values of
parameters that provide one of the four possible types of solution are
analysed. It is demonstrated that in the absence of spin relaxation, besides
the zero field invariant an invariant at large amplitudes of the resonant
microwave field can be found. The two invariants open the possibility for
simple calculation of microwave pulses to control quantum state of the radical
pair. The effect of relaxation on the invariants is analysed and it is shown
that changes in the high field invariant are induced by phase relaxation.
