Multi-alpha Boson Gas state in Fusion Evaporation Reaction and Three-body Force

The experimental evidence for the $\alpha$ Boson gas state in the ${}^{11}$C+${}^{12}$C$\to$${}^{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.