  We present a semiclassical study of the suppression of topology changing,
baryon number violating transitions induced by particle collisions in the
electroweak theory. We find that below the sphaleron energy the suppression
exponent is remarkably close to the analytic estimates based on a low energy
expansion about the instanton. Above the sphaleron energy, the relevant
semiclassical solutions have qualitatively different properties from those
below the sphaleron: they correspond to jumps on top of the barrier. Yet these
processes remain exponentially suppressed, and, furthermore, the tunneling
exponent flattens out in energy. We also derive lower bounds on the tunneling
exponent which show that baryon number violation remains exponentially
suppressed up to very high energies of at least 30 sphaleron masses (250 TeV).
