Analysis of fragment yield ratios in the nuclear phase transition

Abstract

The critical phenomenon of the liquid-gas phase transition has been investigated in the reactions $^{78,86}\mathrm{Kr}$$+$$^{58,64}\mathrm{Ni}$ at beam energy of 35 MeV/nucleon using the Landau free energy approach with isospin asymmetry as an order parameter. Fits to the free energy of fragments showed three minima, suggesting that the system is in the regime of a first-order phase transition. The relation m $=$ \ensuremath{-}\ensuremath{\partial}F/\ensuremath{\partial}H, which defines the order parameter and its conjugate field $H$, has been experimentally verified from the linear dependence of the mirror nuclei yield ratio data on the isospin asymmetry of the source. The slope parameter, which is a measure of the distance from a critical temperature, showed a systematic decrease with increasing excitation energy of the source. Within the framework of the Landau free energy approach, isoscaling provided similar results as obtained from the analysis of mirror nuclei yield ratio data. In the present work, it is shown that the external field is primarily related to the minimum of the free energy, which implies a modification of the source concentration \ensuremath{\Delta} used in isospin studies.