Pairing energy of fragments produced in intermediate-energy heavy-ion collisions

The pairing energy (E-p) of fragments, which is assumed to have a finite temperature in heavy-ion collisions, is obtained using an isobaric yield ratio method in the framework of a modified Fisher model. The fragments in the measured and simulated 140A MeV Ca-40,Ca-48 + Be-9/Ta-181 and Ni-58,Ni-64 + Be-9/Ta-181 reactions have been adopted to perform the analysis. The results show that the ratio of the pairing-energy coefficient to the temperature (a(p)/T) is not significantly influenced by the reaction system, but depends on the neutron excess (I = N-Z) of the fragment. For most fragments, a(p)/T falls in the range of-1.0 < a(p)/T < 1.0. Assuming T approximate to 2.0 MeV for the intermediate-mass fragments, a(p) similar to 2.0 MeV is suggested, which is much smaller than the value in the semiclassical mass formula. For a neutron-rich fragment, E-p may disappear. The results are confirmed by the calculated E-p of some A = 34 isobars using the self-consistent finite-temperature relativistic Hartree-Bogoliubov model with the effective interaction PC-PK1 and the Gogny-pairing interaction D1S. The calculated E-p depends on T in the form of y = C exp(-aT(4)) and E-p goes to zero fast with temperatures at around T = 0.8 MeV. The results are useful for improving the secondary decay simulation for primary fragments in the heavy-ion collisions.