The exclusive photoproduction reaction $\gamma p \rightarrow \psi(2S) p$
has been studied with the ZEUS detector in $ep$ collisions at HERA
using an integrated luminosity of 333~pb$^{-1}$, in the kinematic range
$30 < W < 180$~GeV, $Q^2 < 1$~GeV$^2$, $|t| < 5$~GeV$^2$,
where $W$ is the photon proton centre-of-mass energy,
$Q^2$ - the photon virtuality and $t$ - four-momentum transfer at the proton vertex.
The $\psi(2S)$ mesons were identified via the decay channels:
$\psi(2S) \rightarrow \mu^+ \mu^-$ and $J/\psi\, \pi^+ \pi^-$ with $J/\psi \rightarrow \mu^+ \mu^-$.
The ratio of the production cross sections $R = \sigma(\psi(2S)) / \sigma(J/\psi)$
was measured as a function of $W$, for three $W$ intervals: $30 < W < 80$~GeV, $80 < W <
130$~GeV and $130 < W < 180$~GeV and in the whole kinematic
range accessible in this analysis.
The advantage of including the 4-prong final state channel is its negligible
background in the respective invariant mass distribution and small systematic
uncertainty due to the branching ratio (BR) comparing to the BR of direct
decay of $\psi(2S)$ into a muon pair. The presented analysis is complementary to
already published ZEUS measurement of the same quantity as a function of $Q^2$
in deep-inelastic (DIS) channel.