  Possibilities of observing a signal of an $\eta ^{\prime} n$ bound state are
investigated by considering photoproductions of the $\eta$ and $\eta ^{\prime}$
mesons on a deuteron target with forward proton emission. For this purpose, we
take the $\eta ^{\prime} n$ interaction from the linear sigma model with a
coupling to $\eta n$, in which an $s$-wave $\eta ^{\prime} n$ bound state can
be dynamically generated, and we fix the $\gamma p \to \eta p$ and $\eta
^{\prime} p$ scattering amplitudes so as to reproduce the experimental cross
sections with forward proton emission. By using these $\gamma p \to \eta ^{(
\prime )} p$ and $\eta ^{( \prime )} n \to \eta ^{( \prime )} n$ amplitudes, we
calculate cross sections of the $\gamma d \to \eta n p$ and $\eta ^{\prime} n
p$ reactions with forward proton emission in single and $\eta ^{(\prime
)}$-exchange double scattering processes. As a result, we find that the signal
of the $\eta ^{\prime} n$ bound state can be seen below the $\eta ^{\prime} n$
threshold in the $\eta n$ invariant mass spectrum of the $\gamma d \to \eta n
p$ reaction and is comparable with the contribution from the quasifree $\eta
^{\prime}$ production above the $\eta ^{\prime} n$ threshold. We also discuss
the behavior of the signal of the $\eta ^{\prime} n$ bound state in several
experimental conditions and model parameters.
