  A consistent description of the $ d d \rightarrow$
$^{4}\hspace{-0.03cm}\mbox{He} \eta$ and $ d d \rightarrow$
($^4$He$\eta$)$_{bound} \rightarrow X $ cross sections was recently proposed
with a broad range of real ($V_{0}$) and imaginary (W0), $\eta$-$^4$He optical
potential parameters leading to a good agreement with the d d -> 4He eta data.
Here we compare the predictions of the model below the $\eta$ production
threshold, with the WASA-at-COSY excitation functions for the dd -> 3He N pi
reactions to put stronger constraints on (V0, W0). The allowed parameter space
(with |V_0| < \sim 60 MeV and |W_0| < \sim 7 MeV estimated at 90% CL ) excludes
most optical model predictions of eta-4He nuclei except for some loosely bound
narrow states.
