  An extensive, growing body of work has been penned on cosmologies that
include one or more sterile neutrinos. Early entries in the literature
formulated a Boltzmann-like equation describing sterile-neutrino production in
a way that bypasses the numerical tracking of high-frequency complex phases,
and meticulous quantum-kinetic analyses shortly thereafter put the formula on
firmer ground. A new and more direct derivation is given here, showing that the
equation follows almost immediately from a quantum relaxation-time
approximation and an expansion in the mixing angle. Besides reproducing the
desired result, the relaxation ansatz captures to a high degree of accuracy the
interlaced dynamics of oscillations, decoherence, and plasma repopulation.
Successes and limitations of the semiclassical equation are illustrated
numerically and are shown to reflect the accuracy of the approximations
employed in the derivation. The inclusion of interactions among the sterile
neutrinos is also briefly addressed.
