  We study the near-threshold photoproduction of $\eta^\prime$ mesons from
nuclei in coincidence with forward going protons in the kinematical conditions
of the Crystal Barrel/TAPS experiment, recently performed at ELSA. The
calculations have been performed within a collision model based on the nuclear
spectral function. The model accounts for both the primary ${\gamma}p \to
{\eta^\prime}p$ process and the two-step intermediate nucleon rescattering
processes as well as the effect of the nuclear $\eta^\prime$ mean-field
potential. We calculate the exclusive $\eta^\prime$ kinetic energy
distributions for the $^{12}$C($\gamma$, ${\eta^\prime}p$) reaction for
different scenarios of $\eta^\prime$ in-medium modification. We find that the
considered two-step rescattering mechanism plays an insignificant role in
${\eta^\prime}p$ photoproduction off the carbon target. We also demonstrate
that the calculated $\eta^\prime$ kinetic energy distributions in primary
photon--proton ${\eta^\prime}p$ production reveal strong sensitivity to the
depth of the real ${\eta^\prime}$ potential at normal nuclear matter density
(or to the ${\eta^\prime}$ in-medium mass shift) in the studied incident photon
energy regime. Therefore, such observables may be useful to help determine the
above ${\eta^\prime}$ in-medium renormalization from the comparison of the
results of our calculations with the data from the CBELSA/TAPS experiment. In
addition, we show that these distributions are also strongly influenced by the
momentum-dependent optical potential, which the outgoing participant proton
feels inside the carbon nucleus. This potential should be taken into account in
the analysis of these data with the aim to obtain information on the
${\eta^\prime}$ modification in cold nuclear matter.

Nuclear Theory;Nuclear Experiment