  The semiclassical, dynamical description of diffraction dissociation of
weakly bound nuclei is applied to analyze the decay-energy spectra of $^{15}$C
that have been measured at 68 MeV/nucleon on a Pb target. The optical
potentials that are used to describe the nuclear interaction of $^{15}$C with
the target nucleus are realistic because the fits to the two measured spectra,
one with a small and one with a very large acceptance angle, are consistent and
of similar quality. The cross section for the radiative neutron capture on
$^{14}$C to the 1/2$^+$ ground state of $^{15}$C is deduced from the analysis.
When combined with an estimated contribution from the capture to the 5/2$^+$
excited state of $^{15}$C, an excellent agreement with a recent direct capture
measurement is achieved.
