The isoscaling properties of isotopically resolved projectile residues from peripheral collisions of 86Kr (25 MeV/nucleon), 64Ni (25 MeV/nucleon) and 136Xe (20 MeV/nucleon) beams on various target pairs are employed to probe the symmetry energy coefficient of the nuclear binding energy. The present study focuses on heavy projectile fragments produced in peripheral and semiperipheral collisions near the onset of multifragment emission E*/A = 2-3 MeV). For these fragments, the measured average velocities are used to extract excitation energies. The excitation energies, in turn, are used to estimate the temperatures of the fragmenting quasiprojectiles in the framework the Fermi gas model. The isoscaling analysis of the fragment yields provided the isoscaling parameters alpha which, in combination with temperatures and isospin asymmetries provided the symmetry energy coefficient of the nuclear binding energy of the hot fragmenting quasiprojectiles. The extracted values of the symmetry energy coefficient at this excitation energy range (2-3 MeV/nucleon) are lower than the typical liquid-drop model value ~25 MeV corresponding to ground-state nuclei and show a monotonic decrease with increasing excitation energy. This result is of importance in the formation of hot nuclei in heavy-ion reactions and in hot stellar environments such as supernova.
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