  The Large Hadron Collider forward (LHCf) experiment is designed to use the
LHC to verify the hadronic-interaction models used in cosmic-ray physics.
Forward baryon production is one of the crucial points to understand the
development of cosmic-ray showers. We report the neutron-energy spectra for LHC
$\sqrt{s}$ = 7 TeV proton--proton collisions with the pseudo-rapidity $\eta$
ranging from 8.81 to 8.99, from 8.99 to 9.22, and from 10.76 to infinity. The
measured energy spectra obtained from the two independent calorimeters of Arm1
and Arm2 show the same characteristic feature before unfolding the difference
in the detector responses. We unfolded the measured spectra by using the
multidimensional unfolding method based on Bayesian theory, and the unfolded
spectra were compared with current hadronic-interaction models. The QGSJET
II-03 model predicts a high neutron production rate at the highest
pseudo-rapidity range similar to our results and the DPMJET 3.04 model
describes our results well at the lower pseudo-rapidity ranges. However no
model perfectly explains the experimental results in the whole pseudo-rapidity
range. The experimental data indicate the most abundant neutron production rate
relative to the photon production, which does not agree with predictions of the
models.
