  The experimental evidence for the $\alpha$ Boson gas state in the
$^{11}$C+$^{12}$C$\rightarrow$$^{23}$Mg$^{\ast}$ fusion evaporation reaction is
presented. By measuring the $\alpha$ emission spectrum with multiplicity 2 and
3, we provide insight into the existence of a three-body force among $\alpha$
particles. The observed spectrum exhibited distinct tails corresponding to
$\alpha$ particles emitted in pairs and triplets consistent well with the
model-calculations of AV18-UX and chiral effective field theory of NV2-3-la*,
indicating the formation of $\alpha$ clusters with three-body force in the
Boson gas state.
