The transverse-momentum distributions and correlation characteristics of relativistic $alpha$ particles from the coherent dissociation of a carbon nucleus into three $alpha$ particles at 4.5 GeV/$c$ are studied in lead-enriched emulsion. Comparative analysis of data obtained in ordinary and lead-enriched emulsion stacks is performed. It is shown that the statistical model of rapid fragmentation does not describe the momentum and correlation characteristics of a $alpha$ particles in the rest frame of the carbon nucleus. The estimated decay temperature of $^{12}$C is weakly dependent on the target atomic mass. It is shown that the carbon nucleus undergoing fragmentation acquires angular momentum in the collision.
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