  In November 2010, we performed a search for a $^{4}\mbox{He}$-$\eta$ bound
state by measuring the excitation function for the $dd\rightarrow$
$^{3}\mbox{He} n \pi{}^{0}$ and $dd\rightarrow$ $^{3}\mbox{He} p \pi{}^{-}$
reactions in the vicinity of the $\eta$ production threshold with the WASA
detector.~The experiment was carried out using a deuteron COSY beam and
deuteron pellet target. The beam momentum varied continuously in each of
acceleration cycle from 2.127 GeV/c to 2.422 GeV/c, which corresponds to a
range of excess energy $Q$ $\in$(-70,30)MeV. This dissertation is about the
search for $^{4}\mbox{He}$-$\eta$ bound state in $dd\rightarrow$ $^{3}\mbox{He}
n \pi{}^{0}$ reaction. The excitation function for the process was determined
after identification of all outgoing particles and the application of the
selection conditions based on Monte Carlo simulations of $\eta$-mesic helium
production and its decay via excitation of the $N^{*}$ resonance. No narrow
structure of the $\eta$-mesic helium was observed in the excitation function.
The upper limit of the total cross section for the bound state formation and
its decay in $dd\rightarrow({}^{4}\mbox{He}$-$\eta)_{bound} \rightarrow$
$^{3}\mbox{He} n \pi{}^{0}$ process was determined on the 90% confidence level.
It varies from 21 to 36 nb for the bound state width ranging from 5 MeV to 50
MeV, respectively. However, an indication for a broad state was observed. The
kinematic region, where we expect the evidence of the signal from the bound
state, cannot be fully described only by the combination of the considered
background processes. In contrast, the experimental excitation function is very
well fitted by the background contributions for the region where the signal is
not expected.
