  Using Path Integral Monte Carlo, we have calculated exchange frequencies as
electrons undergo ring exchanges of 2, 3 and 4 electrons in a ``clean'' 3d
Wigner crystal (bcc lattice) as a function of density. We find pair exchange
dominates and estimate the critical temperature for the transition to
antiferromagnetic ordering to be roughly $1 \times 10^{-8}$Ry at melting. In
contrast to the situation in 2d, the 3d Wigner crystal is different from the
solid bcc 3He in that the pair exchange dominates because of the softer
interparticle potential. We discuss implications for the magnetic phase diagram
of the electron gas.
