  Nuclei in the $^{135}$I region have been identified as being a possible
bottleneck for the \textit{i} process. Here we present an indirect measurement
for the Maxwellian-averaged cross section of $^{126}\text{Sb}(n,\gamma)$. The
nuclear level density and the $\gamma$-ray strength function of $^{127}$Sb have
been extracted from $^{124}$Sn$(\alpha,p\gamma)^{127}$Sb data using the Oslo
method. The level density in the low-excitation-energy region agrees well with
known discrete levels, and the higher-excitation-energy region follows an
exponential curve compatible with the constant-temperature model. The strength
function between $E_\gamma\approx$ 1.5-8.0 MeV presents several features, such
as an upbend and a possibly double-peaked pygmy-like structure. None of the
theoretical models included in the nuclear reaction code TALYS seem to
reproduce the experimental data. The Maxwellian-averaged cross section for the
$^{126}$Sb$(n,\gamma)^{127}$Sb reaction has been experimentally constrained by
using our level-density and strength-function data as input to TALYS. We
observe a good agreement with the JINA REACLIB, TENDL, and BRUSLIB libraries,
while the ENDF/B-VIII.0 library predicts a significantly higher rate than our
results.
