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

Abstract

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 $^{40,48}\mathrm{Ca}+\phantom{\rule{0.16em}{0ex}}^{9}\mathrm{Be}/^{181}\mathrm{Ta}$ and $^{58,64}\mathrm{Ni}+\phantom{\rule{0.16em}{0ex}}^{9}\mathrm{Be}/^{181}\mathrm{Ta}$ 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 $(I=N\ensuremath{-}Z)$ of the fragment. For most fragments, ${a}_{p}/T$ falls in the range of $\ensuremath{-}1.0l{a}_{p}/Tl1.0$. Assuming $T\ensuremath{\approx}2.0$ MeV for the intermediate-mass fragments, ${a}_{p}\ensuremath{\sim}2.0$ 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 $y=Cexp(\ensuremath{-}a{T}^{4})$ 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.