  We report the observation of vortex formation upon the absorption of a
thermal neutron in a rotating container of superfluid $^3$He-B. The nuclear
reaction n + $^3$He = p + $^3$H + 0.76MeV heats a cigar shaped region of the
superfluid into the normal phase. The subsequent cooling of this region back
through the superfluid transition results in the nucleation of quantized
vortices. Depending on the superflow velocity, sufficiently large vortex rings
grow under the influence of the Magnus force and escape into the container
volume where they are detected individually with nuclear magnetic resonance.
The larger the superflow velocity the smaller the rings which can expand. Thus
it is possible to obtain information about the morphology of the initial defect
network. We suggest that the nucleation of vortices during the rapid cool-down
into the superfluid phase is similar to the formation of defects during
cosmological phase transitions in the early universe.
