Conditions for isoscaling in nuclear reactions

With the availability of rare isotope beams as well as detection systems that can resolve the masses and charges of the detected particles, isotope yields become an important observable for studying nuclear collisions of heavy ions @1,2#. This additional freedom on isospin asymmetry allows one to study the properties of bulk nuclear matter that are affected by the nucleon composition of the nuclei such as the isospin dependence of the liquid gas phase transition of nuclear matter @3‐5# and the asymmetry term @ 6‐9 # in the nuclear equation of state. To minimize undesirable complications stemming from the sequential decays of primary unstable fragments, it has been proposed that isospin effects can best be studied by comparing the same observables in two similar reactions that differ mainly in isospin asymmetry @5,7,9#. If two reactions, 1 and 2, have the same temperature but different isospin asymmetry, for example, the ratios of a specific isotope yield with neutron and proton numberN and Z obtained from system 2 and system 1 have been observed to exhibit isoscaling, i.e., exponential dependence of the form @5,7# R21~ N,Z!5Y 2~ N,Z!/Y 1~ N,Z!5C exp~ Na1Zb!, ~1!