A perturbation theory treatment of oscillating magnetic fields in the radical pair mechanism

This paper describes an application of time-dependent perturbation theory to the calculation of singlet-to-triplet yields in radical pair reactions for oscillating magnetic fields. It outlines an iterative approach, based on the Schrödinger equation, that should hold for any order of perturbation theory and then gives explicit expressions up to second order in the oscillating field strength for the dependence of the singlet-to-triplet yield on the frequency of the oscillating field. It then compares this method to other methods, namely, numerical integration and the rotating frame treatment, and gives sample results for exponential and Noyes time-dependences. Finally, assuming the radical pair mechanism can explain certain magnetic field effects in biology, this paper discusses several counterintuitive behaviors of the singlet-to-triplet yields that may account for conflicts in the magnetic field bioeffects literature.