Bose–Einstein condensation of five \(\alpha \) clusters in \(^{20}\)Ne and supersolidity

Abstract

We show that the five \(\alpha \) cluster states recently observed in \(^{20}\)Ne, slightly above the five \(\alpha \) threshold energy, are Bose–Einstein condensates of five \(\alpha \) clusters. The states are described well using a superfluid cluster model, where the order parameter is defined. We suggest that the five \(\alpha \) states are fragmented. Theory predicts the emergence of a five \(\alpha \) rotational roton band characterized by a large moment of inertia. This band is formed through roton excitations of the five \(\alpha \) BEC vacuum and possesses dual properties of superfluidity and crystallinity, a property of supersolidity. The persistent existence of such a roton band is discussed and confirmed for the four \(\alpha \) condensate above the four \(\alpha \) threshold in \(^{16}\)O and the three \(\alpha \) condensate above the three \(\alpha \) threshold in \(^{12}\)C.