  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.
