  The possible occurence of highly deformed configurations in the $^{40}$Ca
di-nuclear system formed in the $^{28}$Si + $^{12}$C reaction is investigated
by analyzing the spectra of emitted light charged particles. Both inclusive and
exclusive measurements of the heavy fragments (A $\geq$ 10) and their
associated light charged particles (protons and $\alpha$ particles) have been
made at the IReS Strasbourg {\sc VIVITRON} Tandem facility at bombarding
energies of $E_{lab}$ ($^{28}$Si) = 112 MeV and 180 MeV by using the {\sc
ICARE} charged particle multidetector array. The energy spectra, velocity
distributions, in-plane and out-of-plane angular correlations of light charged
particles are compared to statistical-model calculations using a consistent set
of parameters with spin-dependent level densities. This spin dependence
approach suggests the onset of large nuclear deformation in $^{40}$Ca at high
spin. This conclusion might be connected with the recent observation of
superdeformed bands in the $^{40}$Ca nucleus. The analysis of $\alpha$
particles in coincidence with $^{32}$S fragments suggests a surprisingly strong
$^{8}$Be cluster emission of a binary nature.
