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 Ca and 64 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 Weiszäcker-Beth semiclassical mass formula (the symmetry-energy term a sym , the Coulomb-energy term a c , and the pairing-energy term a p ) and the difference between the chemical potential of neutron and proton (µ n − µ p ) are investigated. Simple correlations between (µ n − µ p )/T, a c /T, a sym /T, and a p /T (where T is the temperature), and lnR are obtained. It is suggested that (µ n − µ p )/T, a c /T, a sym /T, and a p /T of neutron-rich nuclei can be extracted using isobaric yield ratios for heavy-ion collisions at intermediate energies.PACS numbers: 21.65. Cd, 21.65.Ef, 21.65.Mn, 25.70.Mn

Finite-size effects in isobaric ratios

“…The equivalent formula derived in Ref. [18] differs from this one by (small) terms involving the entropy of mixing. This small difference is slightly enhanced by factors associated with the pairing term of the binding energy, which we neglect in this work but is considered in Ref.…”

“…This small difference is slightly enhanced by factors associated with the pairing term of the binding energy, which we neglect in this work but is considered in Ref. [18]. However, since we confine our analysis to odd A, and focus on I = 1 and I = −1, all these terms vanish and ln R(1,…”

“…(8) of Ref. [18] because those authors write the Coulomb energy proportional to Z(Z − 1) whereas we use Z 2 . Figure 1 shows R(1, −1, A), calculated for odd-A nuclei, in both the grand-canonical and canonical approaches, at T = This discrepancy is expected since, as discussed, for instance, in Refs.…”

“…In Ref. [18], the method is applied to source systems as small as A 0 = 40, using isobar fragments close to the projectile fragments.…”

Isobaric yield ratio difference between the140AMeVNi58+BeQiao1, Wei2, Ma3 et al. 2015Phys. Rev. C12070View full textAdd to dashboardCite

“…Based on the isobaric yield ratio (IYR), the IBD method provides cancellation of both the system dependence parameters [8][9][10][11], the free energies of isobars [3], and the terms contributing to the free energy of fragments [8,[12][13][14][15][16] in the formula determining the cross sections of fragment. The target dependence of IBD has been studied by investigating the measured fragments in 140A MeV 40,48 Ca and 58,64 Ni projectile fragmentation reactions on the 9 Be and 181 Ta targets [17], which have been performed by Mocko et al at the National Superconducting Cyclotron Laboratory (NSCL) in Michigan State University [18]. In addition, the Shannon information entropy theory is also adopted to explain the IBD method for a better understanding of it [19,20].…”