$α$-particle condensate states in $^{16}$O

The existence of a rotational band with the $α$+$^{12}$C($0_2^+$) cluster structure, in which three $α$ particles in $^{12}$C($0_2^+$) are locally condensed, is demonstrated near the four-$α$ threshold of $^{16}$O in agreement with experiment. This is achieved by studying structure and scattering for the $α$+$^{12}$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-$α$ threshold in $^{16}$O suggests that it could be a candidate for the superfluid state in $α$-particle condensation.

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