An Isoratio Method to Study Free Energy and Temperature Effects in Intermediate Mass Fragments Produced in Heavy-Ion Collisions

An isoratio method, i.e., the isotopic（isotonic） ratio among three isotopes（isotones）, is proposed to study the free energy and temperature effects in the intermediate mass fragments produced in heavy-ion collisions. The parameterizations for the free energy of nucleus at low temperature, which have been proposed in the framework of the density functional theory using the SKM skymre interaction, are adopted to calculate the temperature-dependent free energy of fragment. By analyzing the measured yields of fragments in the 140 A MeV 58,64 Ni +9Be reactions,it is verified that the free energy in the isoratio is almost the same for different reactions. A temperature-dependent pairing-energy is introduced into the parameterizations for free energy, which reveals that the weakened pairing energy at the low temperature accounts for the weakened or disappearing odd-even staggering in isoratio.