  We consider the classical equations of motion of $SU(2)$ gauge theory,
without a Higgs field, in Minkowski space. We work in the spherical ansatz and
develop a perturbative expansion in the coupling constant $g$ for solutions
which in the far past look like freely propagating spherical shells. The
topological charge $Q$ of these solutions is typically non-integer. We then
show that $Q$ can be expressed as a power series expansion in $g$ which can be
nonzero at finite order. We give an explicit analytic calculation of the order
$g^5$ contribution to $Q$ for specific initial pulses. We discuss the relation
between our findings and anomalous fermion number violation, and speculate on
the physical implications of our results.
