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The paper reports an exact solution for the problem of spin evolution ofradical ion pair in static magnetic and resonant microwave field taking intoaccount Zeeman and hyperfine interactions and spin relaxation. The values ofparameters that provide one of the four possible types of solution areanalysed. It is demonstrated that in the absence of spin relaxation, besidesthe zero field invariant an invariant at large amplitudes of the resonantmicrowave field can be found. The two invariants open the possibility forsimple calculation of microwave pulses to control quantum state of the radicalpair. The effect of relaxation on the invariants is analysed and it is shownthat changes in the high field invariant are induced by phase relaxation.Comment: 18 pages, 7 figure

Time evolution of the spin state of the radical ion pair in the microwave field: an analytical solution