  We clarify the confusion in a recent paper by Aurenche, Zakharov and Zaraket
(AZZ) \cite{azz} over the procedure and region of validity of the collinear
approximation in the twist expansion approach to induced gluon emission in
deeply inelastic scattering (DIS) off a nucleus target. We point out that, in
this approach to the semi-inclusive spectrum, the transverse momentum
$\vec\ell_\perp$ of the induced gluon must be fixed in the collinear expansion
in the transverse momentum $\vec k_\perp$ of the initial partons, therefore the
result is valid for $<k_\perp^2> \ll \ell_\perp^2 \ll Q^2$. In the twist-four
contribution, one can single out the double-hard term corresponding to
collinear quark-gluon Compton scattering which can be calculated independently
of the collinear expansion approach. We will discuss the connection between the
collinear approximation in the twist expansion approach and the small $k_T$
approximation of the results in the Light-Cone Path Integral (LCPI) and
Gyulassy-Levai-Vitev (GLV) opacity expansion approach. We point out the
misconstrued variable change by AZZ before the $k_T$ expansion in LCPI and
opacity expansion approach, without which one obtains the same result for the
induced gluon spectrum under collinear approximation as in the twist expansion
approach. We also show that corrections beyond the collinear approximation to
the transverse momentum integrated gluon spectrum within the static potential
model in the GLV approach give rise to a logarithmic factor difference from the
result of collinear approximation.
