Exactly solvable many-particle model of bulk recombination of coupled radical pairs with allowance for singlet-triplet transitions

We have considered a many-particle problem with irreversible bulk recombination of coupled radical pair induced by arbitrary long-range reactive interaction with B reactants residing in the presence of singlet-triplet transitions caused by external magnetic field. If a coupled radical pair is at rest, while B reactants move by stochastic jumps, a many-particle description of the reaction system is given on the level of the Liouville equation for the density matrix. The propagator of the Liouville equation is reduced to that of some integro-differential equation defining all many-particle effects. For the deduced integro-differential equation describing all many-particle effects of the reaction system under discussion the solution in the form of the Neumann series is constructed. In kinetic control region the exact summation of the series has been made, and the analytical expression of the kinetics has been derived. It is shown that this expression coincides with the solution of kinetic equations of traditional approach in the context of the perturbation theory. The decay kinetics of a coupled radical pair is calculated for small concentration of B reactants by binary scaling procedure with allowance for principal order only. This kinetics is shown to coincide with the solution of the kinetic equation derived on the basis of the law of mass action of formal chemical kinetics.