The article is dedicated to the experimental study in the relativistic approach to the problems of nuclear cluster physics for the prospects of the BECQUEREL experiment. The nuclear emulsion method applied in this experiment makes it possible to study thoroughly the relativistic final states in the fragmentation of nuclei. The focus of the presented research is the dynamics of emergence of the 8 Be nucleus and the Hoyle state, as well as the search for the 4α-particle condensate decaying via the above nuclear states. In this context, the analysis of exposure to 84 Kr nuclei at 950 MeV/nucleon is shown. As a continuation of the study of light nuclei, we have demonstrated the search for the isobar-analogue state of the 13 N nucleus in the fragmentation of 14 N nuclei at 2 GeV/nucleon.