  The statistical model of compound-nucleus reactions predicts that the
fluctuations of the partial $\gamma$-decay widths for a compound-nucleus
resonance are governed by the Porter-Thomas distribution (PTD), and that
consequently the distribution of total $\gamma$-decay widths is very narrow.
However, a recent experiment [Koehler, Larsen, Guttormsen, Siem, and Guber,
Phys. Rev. C 88, 041305(R) (2013)] reported large fluctuations of the total
$\gamma$-decay widths in the $^{95}$Mo$(n,\gamma)^{96}$Mo* reaction, contrary
to this expectation. Furthermore, in recent theoretical works it was argued
that sufficiently strong channel couplings can cause deviations of the partial
width distributions from PTD. Here, we investigate whether the combined
influence of a large number of nonequivalent $\gamma$-decay channels, each of
which couples weakly to the compound-nucleus resonances, can modify the
statistics of the partial widths. We study this effect in neutron scattering
off $^{95}$Mo within a random-matrix model that includes coupling to the
entrance neutron channel and to the large number of $\gamma$ channels. Using
realistic coupling parameters obtained from empirical models for the level
density and the $\gamma$ strength function, we find that the PTD describes well
the distribution of partial widths for all decay channels, in agreement with
the statistical-model expectation. Furthermore, we find that the width of the
distribution of the total $\gamma$-decay widths is insensitive to wide
variations in the parameters of the $\gamma$ strength function, as well as to
deviations of the partial-width distributions from the PTD. Our results rule
out an explanation of the recent experimental data within a statistical-model
description of the compound nucleus.
