The equation of state of asymmetric nuclear matter is still controversial, as predictions at subsaturation as well as above normal density widely diverge. We discuss several experimental results measured in heavy-ion collisions with the INDRA array i
n the incident energy range 5-80 MeV/nucleon. In particular an estimate of the density dependence of the symmetry energy is derived from isospin diffusion results compared with a transport code: the potential part of the symmetry energy linearly increases with the density. We demonstrate that isospin equilibrium is reached in mid-central collisions for the two reactions Ni+Au at 52 MeV/nucleon and Xe+Sn at 32 MeV/nucleon. New possible variables and an improved modelization to investigate symmetry energy are discussed.
Decay modes of excited nuclei are investigated in $^{78,82}$Kr + $^{40}$Ca reactions at 5.5 MeV/nucleon. Charged products were measured by means of the $4pi$ INDRA array. Kinetic-energy spectra and angular distributions of fragments with atomic numbe
r 3 $le Z le$ 28 indicate a high degree of relaxation and are compatible with a fission-like phenomenon. Persistence of structure effects is evidenced from elemental cross-sections ($sigma_{Z}$) as well as a strong odd-even-staggering (o-e-s) of the light-fragment yields. The magnitude of the staggering does not significantly depend on the neutron content of the emitting system. Fragment-particle coincidences suggest that the light partners in very asymmetric fission are emitted either cold or at excitation energies below the particle emission thresholds. The evaporation residue cross-section of the $^{78}$Kr + $^{40}$Ca reaction is slightly higher than the one measured in $^{82}$Kr + $^{40}$Ca reaction. The fission-like component is larger by $sim$ 25% for the reaction having the lowest neutron-to-proton ratio. These experimental features are confronted to the predictions of theoretical models. The Hauser-Feshbach approach including the emission of fragments up to $Z$ = 14 in their ground states as well as excited states does not account for the main features of $sigma_{Z}$. For both reactions, the transition-state formalism reasonably reproduces the $Z$-distribution of the fragments with charge 12 $le Z le$ 28. However, this model strongly overestimates the light-fragment cross-sections and does not explain 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 satisfactorily reproduced within the dinuclear system framework which treats the competition between evaporation, fusion-fission and quasifission processes. The model suggests that heavy fragments come mainly from quasifission while light fragments are predominantly populated by fusion. An underestimation of the cross sections for 16 $le Z le$ 22 could signal a mechanism in addition to the capture process.
