Photoproduction of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>η</mml:mi></mml:math>-Mesic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mrow><mml:mi>He</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mn>3</mml:mn></mml:mmultiscripts></mml:math>

The photoproduction of $\ensuremath{\eta}$-mesic $^{3}\mathrm{He}$ has been investigated using the TAPS calorimeter at the Mainz Microtron accelerator facility MAMI. The total inclusive cross section for the reaction $\ensuremath{\gamma}^{3}\mathrm{He}\ensuremath{\rightarrow}\ensuremath{\eta}X$ has been measured for photon energies from threshold to 820 MeV. The total and angular differential coherent $\ensuremath{\eta}$ cross sections have been extracted up to energies of 745 MeV. A resonancelike structure just above the $\ensuremath{\eta}$ production threshold with an isotropic angular distribution suggests the existence of a resonant quasibound state. This is supported by studies of a competing decay channel of such a quasibound $\ensuremath{\eta}$-mesic nucleus into ${\ensuremath{\pi}}^{0}pX$. A binding energy of $(\ensuremath{-}4.4\ifmmode\pm\else\textpm\fi{}4.2)\text{ }\text{ }\mathrm{MeV}$ and a width of ($25.6\ifmmode\pm\else\textpm\fi{}6.1)\text{ }\text{ }\mathrm{MeV}$ is deduced for the quasibound $\ensuremath{\eta}$-mesic state in $^{3}\mathrm{He}$.

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