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Decay modes of excited nuclei are investigated in $^{78,82}$Kr + $^{40}$Careactions at 5.5 MeV/nucleon. Charged products were measured by means of the$4\pi$ INDRA array. Kinetic-energy spectra and angular distributions offragments with atomic number 3 $\le Z \le$ 28 indicate a high degree ofrelaxation and are compatible with a fission-like phenomenon. Persistence ofstructure effects is evidenced from elemental cross-sections ($\sigma_{Z}$) aswell as a strong odd-even-staggering (o-e-s) of the light-fragment yields. Themagnitude of the staggering does not significantly depend on the neutroncontent of the emitting system. Fragment-particle coincidences suggest that thelight partners in very asymmetric fission are emitted either cold or atexcitation energies below the particle emission thresholds. The evaporationresidue cross-section of the $^{78}$Kr + $^{40}$Ca reaction is slightly higherthan the one measured in $^{82}$Kr + $^{40}$Ca reaction. The fission-likecomponent is larger by $\sim$ 25% for the reaction having the lowestneutron-to-proton ratio. These experimental features are confronted to thepredictions of theoretical models. The Hauser-Feshbach approach including theemission of fragments up to $Z$ = 14 in their ground states as well as excitedstates does not account for the main features of $\sigma_{Z}$. For bothreactions, the transition-state formalism reasonably reproduces the$Z$-distribution of the fragments with charge 12 $\le Z \le$ 28. However, thismodel strongly overestimates the light-fragment cross-sections and does notexplain the o-e-s of the yields for 6 $\le Z \le$ 10. The shape of the whole$Z$-distribution and the o-e-s of the light-fragment yields are satisfactorilyreproduced within the dinuclear system framework which treats the competitionbetween evaporation, fusion-fission and quasifission processes. The modelsuggests that heavy fragments come mainly from quasifission while lightfragments are predominantly populated by fusion. An underestimation of thecross sections for 16 $\le Z \le$ 22 could signal a mechanism in addition tothe capture process.

Decay of excited nuclei produced in $^{78,82}$Kr + $^{40}$Ca reactions at 5.5 MeV/nucleon