The Hoyle state in relativistic dissociation of light nuclei

In the context of the search for triples of relativistic $\alpha$-particles in the Hoyle state, the analysis of available data on the dissociation of the nuclei ${}^{12}$C, ${}^{16}$O and ${}^{22}$Ne in the nuclear emulsion was carried out. The Hoyle state is identified by the invariant mass calculated from pair angles of expansion in $\alpha$-triples in the approximation of the conservation of the momentum per nucleon of the parent nucleus. The contribution of the Hoyle state to the dissociation of ${}^{12}$C $\to$ 3$\alpha$ is 11%. In the case of the coherent dissociation of ${}^{16}$O $\to$ 4$\alpha$ it reaches 22% when the portion of the channel ${}^{16}$O $\to$ 2${}^8$Be is equal to 5%.