The time-resolved magnetic field effect (TRMFE) method in recombination fluorescence is one of the powerful tools for detecting short-lived radical ions in liquid solutions [1][2][3]. In such experiments, a short pulse of ionizing radiation gives rise to singlet-correlated radical ion pairs in an irradiated solution. Under the action of an external magnetic field, hyperfine coupling (HFC), and paramagnetic relaxation, these radical ion pairs are converted into the triplet state. The change in the population of the singlet state is easily monitored by measuring the fluorescence intensity of excited molecules that are formed upon recombination of singlet pairs.The TRMFE method provides information on the HFC constants, g factors, and paramagnetic relaxation times of radical ions and, sometimes, makes it possible to measure the kinetics of their chemical transformations (see reviews [2,3]). It is worth noting that this method is applicable for studying radical ions whose lifetimes are as short as a few nanoseconds, which makes them undetectable for ESR and even for optically detected ESR.Experimentally, information on spin dynamics is obtained by studying the TRMFE curves plotted as the ratio of the recombination fluorescence intensities measured in the presence and absence of a magnetic field [4][5][6]. Such an approach allows us to eliminate the factor from I ( t ) equal to the radical pair recombination rate, which decreases rapidly with time and is not known with an adequate accuracy. Inasmuch as not all recombining pairs in tracks arise in the spin-correlated state, this ratio takes the form (1)where θ is the fraction of spin-correlated pairs and ( t ) and ( t ) are the probabilities of the pair being found in the singlet state, with the proviso that it was initially prepared in the singlet state, calculated for a zero and a nonzero magnetic field, respectively. In the TRMFE method, the spectral parameters of radical ions are extracted by simulation of the experimental curve using relationship (1), in which the singlet populations are obtained by solving the problem of evolution of the spin state of a radical ion pair in a static external magnetic field and in a zero magnetic field.Only isotropic HFC is significant for radical ions in solutions, and it is believed that the interaction between the spins of radical-ion electrons can be ignored. An exact solution of this problem in an arbitrary magnetic field is known only for HFC with a group of equivalent nuclei in each radical [7][8][9]. This severely limits the application of the TRMFE method and compels one to search for approximate approaches. In particular, for a field that is much stronger than HFC, the solution in the strong-field approximation is known for HFC of an arbitrary type [7,8]. For the spin evolution in a zero field, an exact solution exists for the case of no more than two groups of equivalent nuclei in each of the radicals [10] and a solution in the semiclassical approximation [11] is known for an unresolved ESR spectrum, i.e., in the limit o...