Constraining the symmetry energy from fragment yields

Abstract

Methods of extraction of the symmetry energy coefficient to temperature ratio from isobaric and isotopic yields of fragments produced in Fermi-energy heavy-ion collisions are discussed. Consistent results are obtained when the hot fragmenting source is well characterized and its excitation energy and isotopic composition are properly taken into account. The results, independent of the mass number of the detected fragments, suggest that their fate is decided very early in the reaction. A comparison to the Statistical Multifragmentation Model (SMM) predictions is also presented. The effort to understand the properties of asymmetric nuclear matter both at normal densities and at densities away from the saturation density has stimulated a growing interest in isospin effects in nuclear reactions. The isotopic distribution of fragments produced in multifragmentation events in central collisions at intermediate energies can probe properties of low density nuclear matter. Different methods to extract the “symmetry energy” coefficient from yield ratios have been proposed. Among those, we focus on three seemingly different approaches: isoscaling [1–4], m-scaling and isobaric yield ratio method [5], and we show that consistent experimental results can be extracted provided that the properties of the hot fragmenting source, such as its isospin composition and excitation energy, are properly taken into account. We remark that experimentally whether the equilibrium process, occurring during the multifragmentation, takes place at constant pressure or volume (freeze-out hypothesis) is not determined. This ambiguity casts some doubts on the derived quantity, i.e. symmetry energy or symmetry enthalpy. Keeping in mind this ambiguity we will refer to the experimentally extracted quantity as the symmetry energy.