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In the events of peripheral dissociation of relativistic nuclei in thenuclear track emulsion, it is possible to study the emerging ensembles of Heand H nuclei, including those from decays of unstable $^{8}$Be and $^{9}$Bnuclei, as well as the Hoyle state. These extremely short-lived states areidentified by invariant masses calculated from the angles in 2$\alpha$-pairs,2$\alpha p$- and 3$\alpha$-triplets in the approximation of conservation ofmomentum per nucleon of the primary nucleus. In the same approach, it ispossible to search for more complex states. This paper explores the correlationbetween the formation of $^{8}$Be nuclei and the multiplicity of accompanying$\alpha$-particles in the dissociation of relativistic $^{16}$O, $^{22}$Ne,$^{28}$Si, and $^{197}$Au nuclei. On the above basis, estimates of thiscorrelation are presented for the unstable $^{9}$B nucleus and the Hoyle state.The enhancement in the $^{8}$Be contribution to dissociation with the$\alpha$-particle multiplicity has been found. Decays of $^{9}$B nuclei andHoyle states follow the same trend.

Correlation in formation of $^{8}$Be nuclei and $\alpha$-particles in fragmentation of relativistic nuclei