  \noindent A formalism based on path-integral expression of time-evolution
operator during tunneling at a finite energy proposed by the authors is applied
to $SU(2)$ gauge-Higgs system to produce Higgs particles with $\Delta B=1$.
Instead of starting from instanton tunneling at the zero energy, a classical
bounce solution giving sphaleron (instanton) action at high (low) energies is
used as the tunneling configuration. Fourier transform of the bounce
configuration in coherent state expression at the entrance and exit of the
tunneling plays an important role. Numerical results at various energies for
$M_H/M_W=1 \sim 2 $ are given. Though the cross section with $\Delta B=1$
results from a severe cancellation of several large quantities in the leading
order as occured in the instanton calculus, it seems unlikely that the cross
section grows as largely as to reach unitarity bound at energies $E \leq
E_{sph}$. It is pointed out that the actual value $g^2=0.418$ of the $SU(2)$
gauge coupling constant may be too large to take the weak coupling limit.}
