Experimental studies ofN/Zequilibration in peripheral collisions using fragment yield ratios

Abstract

Peripheral collisions of $^{40}\mathrm{Ca}$ and $^{48}\mathrm{Ca}$ projectiles at 32 MeV/nucleon on $^{112}\mathrm{Sn}$ and $^{124}\mathrm{Sn}$ targets were studied in this work. The fragments of the projectile-like source (quasiprojectile) were collected with a charged-particle multidetector array. The average value of the neutron-to-proton ratio $N/Z$ of the quasiprojectiles formed in the reactions was determined with two approaches. The first is a direct reconstruction approach using isotopically resolved fragments and is hindered by undetected neutrons leading to lower $N/Z$ values. The second approach, based on the assumption of early fragment formation, employs yield ratios of fragment isobars and is not hindered by undetected neutrons. Using this approach, the amount of $N/Z$ mixing that occurred in the quasiprojectiles (compared to a fully $N/Z$ equilibrated system) was found to be approximately $53%$. The experimental results were compared with model calculations. First, the phenomenological DIT (deep inelastic transfer) model was used, followed by the statistical multifragmentation model (SMM). The results of these calculations are in close agreement with the data and indicate that the mean number of undetected neutrons increases with the $N/Z$ of the composite system, accounting for the difference observed between the two approaches of quasiprojectile $N/Z$ determination. Second, the microscopic transport model IBUU (isospin-dependent Boltzmann-Uehling-Uhlenbeck) was employed, providing preliminary results in reasonable agreement with the data. The determination of the degree of $N/Z$ equilibration employing the present fragment yield ratio approach may provide a valuable probe to study the isospin part of the nuclear equation of state in conjunction with detailed microscopic models of the collisions in the Fermi energy regime.