  We present a new method for calculating the product yield of a radical pair
recombination reaction in the presence of a weak time-dependent magnetic field.
This method successfully circumvents the computational difficulties presented
by a direct solution of the Liouville-von Neumann equation for a long-lived
radical pair containing many hyperfine-coupled nuclear spins. Using a modified
formulation of Floquet theory, treating the time-dependent magnetic field as a
perturbation, and exploiting the slow radical pair recombination, we show that
one can obtain a good approximation to the product yield by considering only
nearly-degenerate sub-spaces of the Floquet space. Within a significant
parameter range, the resulting method is found to give product yields in good
agreement with exact quantum mechanical results for a variety of simple model
radical pairs. Moreover it is considerably more efficient than the exact
calculation, and it can be applied to radical pairs containing significantly
more nuclear spins. This promises to open the door to realistic theoretical
investigations of the effect of radiofrequency electromagnetic radiation on the
photochemically induced radical pair recombination reactions in the avian
retina which are believed to be responsible for the magnetic compass sense of
migratory birds.
