$\alpha$-particle condensate states in ${}^{16}$O

The existence of a rotational band with the $\alpha$+${}^{12}$C($0_2^{+}$) cluster structure, in which three $\alpha$ particles in ${}^{12}$C($0_2^{+}$) are locally condensed, is demonstrated near the four-$\alpha$ threshold of ${}^{16}$O in agreement with experiment. This is achieved by studying structure and scattering for the $\alpha$+${}^{12}$C($0_2^{+}$) system in a unified way. A drastic reduction (quenching) of the moment of the inertia of the $0^{+}$ state at 15.1 MeV just above the four-$\alpha$ threshold in ${}^{16}$O suggests that it could be a candidate for the superfluid state in $\alpha$-particle condensation.