  Low-energy neutron-${}^{19}$C scattering is studied in the three-body
  $n + n + {}^{18}$C model using a realistic $nn$ potential and a number of
shallow and deep $n$-${}^{18}$C potentials, the latter supporting deeply-bound
Pauli-forbidden states that are projected out. Exact Faddeev-type three-body
scattering equations for transition operators including two- and three-body
forces are solved in the momentum-space partial-wave framework. Phase shift,
inelasticity parameter, and cross sections are calculated. For the elastic
$n$-${}^{19}$C scattering in the $J^\Pi=0^+$ partial wave the signatures of the
Efimov physics, i.e., the pole in the effective-range expansion and the elastic
cross section minimum, are confirmed for both shallow and deep models, but with
clear quantitative differences between them, indicating the importance of a
proper treatment of deeply-bound Pauli-forbidden states. In contrast, the
inelasticity parameter is mostly correlated with the asymptotic normalization
coefficient of the ${}^{19}$C bound state. Finally, in the regime of very weak
${}^{19}$C binding and near-threshold (bound or virtual) excited ${}^{20}$C
state the standard Efimovian behaviour of the $n$-${}^{19}$C scattering length
and cross section was confirmed, resolving the discrepancies between earlier
studies by other authors [I. Mazumdar, A. R. P. Rau, V. S. Bhasin, Phys. Rev.
Lett. 97 (2006) 062503; M. T. Yamashita, T. Frederico, L. Tomio, Phys. Rev.
Lett. 99 (2007) 269201].
