Prospects of the BECQUEREL experiment devoted to studying, within the relativistic approach, problems of nuclear-cluster physics are discussed. The nuclear track emulsion method used in the present study permits fully investigating relativistic final states in the fragmentation of nuclei. The present study focuses on the dynamics of the formation of a ^8 Be nucleus and the Hoyle state, as well as on searches for the 4 α condensate decaying through them. The development of analysis of exposure to ^84 Kr nuclei at an energy of 950 MeV per nucleon is described in this context. The status of searches for the isobar analog state of the ^13 N nucleus in the fragmentation of ^14 N nuclei at an energy of 2 GeV per nucleon is presented as a continuation of studies of light nuclei.

The first results on analysis of determination of the contribution of decays of unstable 8 Be and 9 B nuclei and the Hoyle 3α-state into the dissociation of 14 N → 3He (+H) are presented. Layers of nuclear track emulsion longitudinally exposed to 2.9 A GeV/ с 14 N nuclei at the JINR Nuclotron are used as the research material. Under the assumption that He and H fragments preserve momentum per nucleon of the primary nucleus, these unstable states are identified by the minimum invariant mass calculated using fragment emission angles.

Status and prospects of nuclear clustering studies by dissociation of relativistic nuclei in nuclear track emulsion are presented. The unstable 8 Be and 9 B nuclei are identified in dissociation of the isotopes 9 Be, 10 B, 10 C and n C, and the Hoyle state in the cases 12 C and 16 O. On this ground searching for the Hoyle state and more complex α -particle states in the dissociation of the heavier nuclei is suggested. A detailed study of a low-density baryonic matter arising in dissociation of the heaviest nuclei is forthcoming long-term problem. An analysis of nuclear fragmentation induced by relativistic muons is proposed to examine the mechanism dissociation.

Production of $\alpha$-particle triples in the Hoyle state (HS) in dissociation of ${}^{12}$C nuclei at 3.65 and 0.42 $A$ GeV in nuclear track emulsion is revealed by the invariant mass approach. Contribution of the HS to the dissociation ${}^{12}$C $\to$ 3$\alpha$ is (11 $\pm$ 3) \%. Reanalysis of data on coherent dissociation ${}^{16}$O $\to$ 4$\alpha$ at 3.65 $A$ GeV is revealed the HS contribution of (22 $\pm$ 2) \%.

The invariant mass method is used to identify the $^8$Be and $^9$B nuclei and Hoyle state formed in dissociation of relativistic nuclei in a nuclear track emulsion. It is shown that to identify these extremely short-lived states in the case of the isotopes $^9$Be, $^{10}$B, $^{10}$C, $^{11}$C, $^{12}$C, and $^{16}$O, it is sufficient to determine the invariant mass as a function of the angles in pairs and triples of He and H fragments in the approximation of the conservation of momentum per nucleon of the parent nucleus. According to the criteria established in this way, the contribution of these three unstable states was evaluated in the relativistic fragmentation of the $^{28}$Si and $^{197}$Au nuclei.