  The in-medium modification of the spectral function of the $\eta'$ meson with
and without the spatial momentum is studied with the $T\rho$ approximation by
employing two phenomenological models for the $\eta'N$ scattering; one is
called coupled channels model and the other the $N(1895)$-dominance model. In
the former model, the $\eta'N$ scattering amplitude is calculated in the
unitarized coupled-channel approach involving the $\eta'N$ channel, while in
the latter model the $\eta'N$ scattering process is dominated by the $N(1895)$
resonance with the spin and parity $J^P=1/2^-$. In the \com{coupled channels
model}, one single peak of the in-medium $\eta'$ mode appears in the spectral
function and the peak position shifts to higher energies along with the
increase of the nuclear density reflecting the repulsive $\eta'N$ scattering
length of the unitarized coupled-channel amplitude. On the other hand, two
branches related to the $\eta'$ and $N(1895)$-hole modes appear in the
$N(1895)$-dominance model. In both models, the shift of the peak position and
the width in the spectral function are a few tens of MeV at the normal nuclear
density for the $\eta'$ meson at rest in the nuclear medium. Once the spatial
momentum is turned on, the peak positions in the spectral function approach the
energies without the nuclear medium effect. Particularly, in the
$N(1895)$-dominance model, the peak strength of the $N(1895)$-hole mode gets
smaller with the finite momentum and the spectral function comes to have one
single peak.
