  We investigate the general relativistic collapse of spherically symmetric,
massless spin-1/2 fields at the threshold of black hole formation. A
spherically symmetric system is constructed from two spin-1/2 fields by forming
a spin singlet with no net spin-angular momentum. We study the system
numerically and find strong evidence for a Type II critical solution at the
threshold between dispersal and black hole formation, with an associated mass
scaling exponent $\gamma ~ 0.26$. Although the critical solution is
characterized by a continuously self-similar (CSS) geometry, the matter fields
exhibit discrete self-similarity with an echoing exponent $\Delta ~ 1.34$. We
then adopt a CSS ansatz and reduce the equations of motion to a set of ODEs. We
find a solution of the ODEs that is analytic throughout the solution domain,
and show that it corresponds to the critical solution found via dynamical
evolutions.
