  Radical pair recombination reactions are known to be sensitive to the
application of both low and high magnetic fields. The application of a weak
magnetic field reduces the singlet yield of a singlet-born radical pair,
whereas the application of a strong magnetic field increases the singlet yield.
The high field effect arises from energy conservation: when the magnetic field
is stronger than the sum of the hyperfine fields in the two radicals, ${\rm
S}\to {\rm T}_{\pm}$ transitions become energetically forbidden, thereby
reducing the number of pathways for singlet to triplet interconversion. The low
field effect arises from symmetry breaking: the application of a weak magnetic
field lifts degeneracies among the zero field eigenstates and increases the
number of pathways for singlet to triplet interconversion. However, the details
of this effect are more subtle, and have not previously been properly
explained. Here we present a complete analysis of the low field effect in a
radical pair containing a single proton, and in a radical pair in which one of
the radicals contains a large number of hyperfine-coupled nuclear spins. We
find that the new transitions that occur when the field is switched on are
between ${\rm S}$ and ${\rm T}_0$ in both cases, and not between ${\rm S}$ and
${\rm T}_{\pm}$ as has previously been claimed. We then illustrate this result
by using it in conjunction with semiclassical spin dynamics simulations to
account for the observation of a biphasic--triphasic--biphasic transition with
increasing magnetic field strength in the magnetic field effect on the
time-dependent survival probability of a photoexcited
carotenoid-porphyrin-fullerene radical pair.
