The possible occurrence 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, and both 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. The analysis suggests the onset of large nuclear deformation in $^{40}$Ca at high spin.
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