Isobaric yield ratios in heavy-ion reactions, and symmetry energy of neutron-rich nuclei at intermediate energies

Abstract

The isobaric yield ratios of the fragments produced in the neutron-rich $^{48}\mathrm{Ca}$ and $^{64}\mathrm{Ni}$ projectile fragmentation are analyzed in the framework of a modified Fisher model. The correlations between the isobaric yield ratios ($R$) and the energy coefficients in the Weisz\"acker-Beth semiclassical mass formula (the symmetry-energy term ${a}_{\mathrm{sym}}$, the Coulomb-energy term ${a}_{c}$, and the pairing-energy term ${a}_{p}$) and the difference between the chemical potentials of the neutron and proton (${\ensuremath{\mu}}_{n}\ensuremath{-}{\ensuremath{\mu}}_{p}$) are investigated. Simple correlations between $({\ensuremath{\mu}}_{n}\ensuremath{-}{\ensuremath{\mu}}_{p})/T$, ${a}_{c}/T$, ${a}_{\mathrm{sym}}/T$, and ${a}_{p}/T$ (where $T$ is the temperature), and $\mathrm{ln}R$ are obtained. It is suggested that $({\ensuremath{\mu}}_{n}\ensuremath{-}{\ensuremath{\mu}}_{p})/T$, ${a}_{c}/T$, ${a}_{\mathrm{sym}}/T$, and ${a}_{p}/T$ of neutron-rich nuclei can be extracted using isobaric yield ratios for heavy-ion collisions at intermediate energies.