  Even though more than 80 years have passed since the discovery of fission,
its microscopic understanding has still been unclear. To clarify the underlying
mechanics of induced fission, we analyze the distribution of a fission width
using a miscropic framework based on a configuration-interaction approach. The
distribution is known to follow a chi-squared distribution, which is
characterized by the effective number of decay channels, $\nu$. We introduce an
effective Hamitonian for the space of compound nucleus states and estimate
$\nu$ from the rank of the imaginary part of the effective Hamiltonian.
Applying the model to $^{235}$U(n,f), we succesfully reproduce the empirical
value of $\nu=2.3\pm1.1$. We also find that $\nu$ is insensitve to the number
of fission channels, which is consistent with an experimental finding.
