Measuring the Temperature of Hot Nuclear Fragments

A new thermometer based on fragment momentum fluctuations is presented. This thermometer exhibited residual contamination from the collective motion of the fragments along the beam axis. For this reason, the transverse direction has been explored. Additionally, a mass dependence was observed for this thermometer. This mass dependence may be the result of the Fermi momentum of nucleons or the different properties of the fragments (binding energy, spin etc..) which might be more sensitive to different densities and temperatures of the exploding fragments. We expect some of these aspects to be smaller for protons (and/or neutrons); consequently, the proton transverse momentum fluctuations were used to investigate the temperature dependence of the source

Isoscaling of mass A≃40 reconstructed quasiprojectiles from collisions in the Fermi energy regime

Isoscaling studies of fragments with Z=1-8 from reconstructed quasiprojectiles of mass A≃40 from the Ar40+Sn124, 112Sn and Ca40+Sn124, 112Sn reactions at beam energy of 45 MeV/nucleon were performed. After initial efforts to obtain isoscaling with the " traditional" approach of using pairs of systems differing in their isospin asymmetry (or neutron-to-proton ratio N/Z), " intra-system" isoscaling for each of these four systems was obtained using fragment sources restricted in two narrow N/Z regions (one neutron-rich and one neutron-poor). The observed isoscaling behavior was excellent and the isoscaling parameter α was found to decrease with increasing excitation energy. Corrections due to undetected neutrons were also taken into account in the source N/Z determination by using the theoretical models DIT (Deep Inelastic Transfer) and SMM (Statistical Multifragmentation Model) along with a software replica of the experimental setup. These corrections were applied to the determination of the parameter Δ (expressing the difference in the isospin asymmetry of the two sources used in the isoscaling). The reduced isoscaling parameter α/Δ was obtained and found to decrease as the excitation energy of the quasiprojectile source increases, in good agreement with recent work on reconstructed mass A≃80 quasiprojectiles. This decrease of α/Δ may point to a decrease of the symmetry energy coefficient with increasing excitation energy. © 2010 Elsevier B.V

Multifragmentation of reconstructed quasi-projectiles in the mass region A 3∼0

The production of fragments from a broad range of reconstructed quasi-projectiles obtained in the interaction of 32S (45 MeV/nucleon) with 112Sn was studied. A good description of the experimental data on the multifragmentation of these light quasi-projectiles with a model framework based on deep inelastic transfer followed by SMM (statistical multifragmentation model) was obtained. The charge and mass distributions of the observed fragments show that the break-up of a given quasi-projectile source is highly correlated to its isospin composition. The sensitivity of the hot primary fragments to the symmetry energy was investigated in detail. It was found that for the present light systems (A30), a good description of the experimental data on the charge distributions, the N/Z distributions and the isotopic distributions of the fragments is obtained by the SMM calculations involving the standard (Csym = 25 MeV), as well as, a reduced value of the symmetry energy (Csym = 8 MeV). However, the reduced value of the symmetry energy appears to provide a better description of the isotopic distributions in most of the cases. This is in agreement with an overall reduction of the symmetry energy of primary fragments indicated by a number of multifragmentation studies of heavier systems. © 2012 IOP Publishing Ltd

Analysis of fragment yield ratios in the nuclear phase transition

The critical phenomenon of the liquid-gas phase transition has been investigated in the reactions Kr78,86+Ni58,64 at beam energy of 35 MeV/nucleon using the Landau free energy approach with isospin asymmetry as an order parameter. Fits to the free energy of fragments showed three minima, suggesting that the system is in the regime of a first-order phase transition. The relation m=-∂F/∂H, which defines the order parameter and its conjugate field H, has been experimentally verified from the linear dependence of the mirror nuclei yield ratio data on the isospin asymmetry of the source. The slope parameter, which is a measure of the distance from a critical temperature, showed a systematic decrease with increasing excitation energy of the source. Within the framework of the Landau free energy approach, isoscaling provided similar results as obtained from the analysis of mirror nuclei yield ratio data. In the present work, it is shown that the external field is primarily related to the minimum of the free energy, which implies a modification of the source concentration Δ used in isospin studies. © 2011 American Physical Society

Measuring the temperature of hot nuclear fragments

A new thermometer based on fragment momentum fluctuations is presented. This thermometer exhibited residual contamination from the collective motion of the fragments along the beam axis. For this reason, the transverse direction has been explored. Additionally, a mass dependence was observed for this thermometer. This mass dependence may be the result of the Fermi momentum of nucleons or the different properties of the fragments (binding energy, spin, etc.) which might be more sensitive to different densities and temperatures of the exploding fragments. We expect some of these aspects to be smaller for protons (and/or neutrons); consequently, the proton transverse momentum fluctuations were used to investigate the temperature dependence of the source. © 2010 Elsevier B.V

Experimental studies of N/Z equilibration in peripheral collisions using fragment yield ratios

Peripheral collisions of Ca40 and Ca48 projectiles at 32 MeV/nucleon on Sn112 and Sn124 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. © 2010 The American Physical Society

Investigation of transverse collective flow of intermediate mass fragments

The transverse flow of intermediate mass fragments (IMFs) has been investigated for the 35 MeV/u 70Zn+70Zn, 64Zn+64Zn, and 64Ni+64Ni systems. A transition from the IMF transverse flow strongly depending on the mass of the system, in the most violent collisions, to a dependence on the charge of the system, for the peripheral reactions, is shown. This transition was shown to be sensitive to the density dependence of the symmetry energy using the antisymmetrized molecular-dynamics model. The results present an observable, the IMF transverse flow, that can be used to probe the nuclear equation of state. Comparison with the simulation demonstrated a preference for a stiff density dependence of the symmetry energy. © 2010 The American Physical Society

Constraining the symmetry term in the nuclear equation of state at subsaturation densities and finite temperatures

Methods of extraction of the symmetry energy (or enthalpy) coefficient to temperature ratio from isobaric and isotopic yields of fragments produced in Fermi-energy heavy-ion collisions are discussed. We show that the methods are consistent when the hot fragmenting source is well characterized and its excitation energy and isotopic composition are properly taken into account. The results are independent of the mass number of the detected fragments, which suggests that their fate is decided very early in the reaction. © 2012 American Physical Societ

Transverse collective flow and midrapidity emission of isotopically identified light charged particles

The transverse flow and relative midrapidity yield of isotopically identified light charged particles (LCPs) has been examined for the 35 MeV/nucleon 70Zn+70Zn, 64Zn+64Zn, and 64Ni+64Ni systems. A large enhancement of the midrapidity yield of the LCPs was observed relative to the yield near the projectile rapidity. In particular, this enhancement was increased for the more neutron-rich LCPs demonstrating a preference for the production of neutron-rich fragments in the midrapidity region. Additionally, the transverse flow of the LCPs was extracted, which provides insight into the average movement of the particles in the midrapidity region. Isotopic and isobaric effects were observed in the transverse flow of the fragments. In both cases, the transverse flow was shown to decrease with an increasing neutron content in the fragments. A clear inverse relationship between the transverse flow and the relative midrapidity yield is shown. The increased relative midrapidity emission produces a decreased transverse flow. The stochastic mean-field model was used for comparison to the experimental data. The results showed that the model was able to reproduce the general isotopic and isobaric trends for the midrapidity emission and transverse flow. The sensitivity of these observables to the density dependence of the symmetry energy was explored. The results indicate that the transverse flow and midrapidity emission of the LCPs are sensitive to the denisty dependence of the symmetry energy. © 2011 American Physical Society

Quantum suppression of fluctuations and temperatures of reconstructed A ∼ 30 quasi-projectiles

Suppression of multiplicity fluctuations has been observed for three light fermions (protons, tritons and 3He) in the multifragmentation of reconstructed hot quasi-projectiles produced in collisions of 32S (45 MeV/nucleon) with 112Sn. This suppression, predicted by recent calculations, is attributed to Pauli blocking and has also been observed in experiments with trapped Fermi gases. Experimental results on nuclear temperature and density employing a quantal approach based on momentum and multiplicity fluctuations are also presented. The extracted temperatures show a noticeable reduction when compared to a similarly derived classical method. This reduction in temperature is in agreement with previous predictions indicating that classically derived methods overpredict nuclear temperature as they do not take into account the Fermi motion of the nucleons. The present results underline the role of quantum statistics in nuclear disassembly and suggest the need for proper quantum treatment when dealing with the thermodynamic properties of fragmenting heavy ions. © 2014 IOP Publishing Ltd