  The longitudinal relaxation time of the magnetization of a system of two
exchange coupled spins subjected to a strong magnetic field is calculated
exactly by averaging the stochastic Gilbert-Landau-Lifshitz equation for the
magnetization, i.e., the Langevin equation of the process, over its
realizations so reducing the problem to a system of linear
differential-recurrence relations for the statistical moments (averaged
spherical harmonics). The system is solved in the frequency domain by matrix
continued fractions yielding the complete solution of the two-spin problem in
external fields for all values of the damping and barrier height parameters.
The magnetization relaxation time extracted from the exact solution is compared
with the inverse relaxation rate from Langer's theory of the decay of
metastable states, which yields in the high barrier and intermediate-to-high
damping limits the asymptotic behaviour of the greatest relaxation time.
