The richness of the data set, collected by the INDRA collaboration during the last twenty years, enabled us to build a set of caloric curves for nuclei of various sizes, by using, for the first time, a single experimental set-up and a single experimental protocol. We will therefore present the different caloric curves ($E^{\ast}-T$) obtained by a new calorimetry, for Quasi-Projectiles produced by symmetric or quasi symmetric reactions at different incident energies (Au+Au, Xe+Sn, Ni+Ni). For all these systems, a clear change of the de-excitation process of hot nuclei is observed but this one is neither a plateau nor a back-bending, but a sudden change of slope.
Simulations based on experimental data obtained from multifragmenting quasifused nuclei produced in central 129Xe + natSn collisions have been used to deduce event by event freeze-out properties on the thermal excitation energy range 4-12 AMeV. From these properties and temperatures deduced from proton transverse momentum fluctuations constrained caloric curves have been built. At constant average volumes caloric curves exhibit a monotonous behaviour whereas for constrained pressures a backbending is observed. Such results support the existence of a first order phase transition for hot nuclei.
Simulations based on experimental data obtained from multifragmenting quasi-fused nuclei produced in central $^{129}$Xe + $^{nat}$Sn collisions have been used to deduce event by event freeze-out properties in the thermal excitation energy range 4-12 AMeV [Nucl. Phys. A809 (2008) 111]. From these properties and the temperatures deduced from proton transverse momentum fluctuations, constrained caloric curves have been built. At constant average volumes caloric curves exhibit a monotonic behaviour whereas for constrained pressures a backbending is observed. Such results support the existence of a…
A basic feature of the nuclear equation of state is not yet understood: the dependence of the nuclear caloric curve on the neutron-proton asymmetry. Predictions of theoretical models differ on the magnitude and even the sign of this dependence. In this work, the nuclear caloric curve is examined for fully reconstructed quasi-projectiles around mass A=50. The caloric curve extracted with the momentum quadrupole fluctuation thermometer shows that the temperature varies linearly with quasi-projectile asymmetry (N-Z)/A. An increase in asymmetry of 0.15 units corresponds to a decrease in temperatur…
The role played by the heaviest fragment in partitions of multifragmenting hot nuclei is emphasized. Its size/charge distribution (mean value, fluctuations and shape) gives information on properties of fragmenting nuclei and on the associated phase transition.
Recent advancement on the knowledge of multifragmentation and phase transition for hot nuclei is reported. It concerns i) the influence of radial collective energy on fragment partitions and the derivation of general properties of partitions in presence of such a collective energy, ii) a better knowledge of freeze-out properties obtained by means of a simulation based on all the available experimental information and iii) the quantitative study of the bimodal behaviour of the heaviest fragment charge distribution for fragmenting hot heavy quasi-projectiles which allows, for the first time, to …
Recent important progress on the knowledge of multifragmentation and phase transition for hot nuclei, thanks to the high detection quality of the INDRA array, is reported. It concerns i) the radial collective energies involved in hot fragmenting nuclei/sources produced in central and semi- peripheral collisions and their influence on the observed fragment partitions, ii) a better knowledge of freeze-out properties obtained by means of a simulation based on all the available experimental information and iii) the quantitative study of the bimodal behaviour of the heaviest fragment distribution f…
Statistical and dynamical aspects in the decay of hot neutron-rich nuclei
在反应40，48 Ca +27 Al中产生的热准射弹中观察到了化学势演化中的同位旋不对称相变信号，证实了在较轻的28 Si +112，124 Sn系统中的类似观察。随着质量的增加，二次发射对热准粒子的性质影响越来越大。热力学观测值对两个反应40、48Ca + 27Al中不同数量的丢失中子不敏感，因此提供了中子动态发射的信号，这可能与射弹和靶之间非常富含中子的低密度区域（颈部）的形成有关。
A rather new approach employing Monte Carlo GEANT simulation for converting the experimentally measured fold distribution to angular momentum distribution has been described. The technique has been successfully utilized to measure the angular momentum of the compound nucleus formed in the reaction 4He + 115In --> 119Sb at E_Lab = 35 MeV. A 50 element gamma multiplicity filter, fabricated in-house, was used to measure experimentally the required fold distribution. The present method has been compared with the other ones exiting in the literature and relative merits have been discussed.
In the domain of Fermi energy, the hot nucleus temperature can be determined by using the energy spectra of evaporated light charged particles. But this method of measurement is not without difficulties both theoretical and experimental. The presented study aims to disentangle the respective influences of different factors on the quality of this measurement : the physics, the detection (a 4? detector array as INDRA) and the experimental procedure. This analysis demonstrates the possibility of determining from an energy spectrum, with an accuracy of about 10 %, the true apparent temperature fel…
In nuclear thermodynamics, the determination of the excitation energy of hot nuclei is a fundamental experimental problem. Instrumental physicists have been trying to solve this problem for several years by building the most exhaustive 4Pi detector arrays and perfecting their calorimetry techniques. In a recent paper, a proposal for a new calorimetry, called "3D calorimetry", was made. It tries to optimize the separation between the particles and fragments emitted by the Quasi-Projectile and the other possible contributions. This can be achieved by determining the experimental probability for …
The pairing gaps, heat capacities and level densities are calculated within the BCS-based quasiparticle approach including the effect of thermal fluctuations on the pairing field within the pairing model plus noncollective rotation along the z axis for $^{60}$Ni and $^{72}$Ge nuclei. The analysis of the numerical results obtained shows that, in addition to the pairing gap, the heat capacity can also serve as a good observable to detect the appearance of the pairing reentrance in hot rotating nuclei, whereas such signature in the level density is rather weak.
Nuclear expansion and symmetry energy of hot nuclei
本文研究了在束流能量为30、40和47 MeV/核子时，在$^{58}$ Ni + $^{58}$ Ni、$^{58}$ Fe + $^{58}$ Ni和$^{58}$ Fe + $^{58}$ Fe反应中热核的对称性能量随激发能的降低。据观察，这种减少主要是膨胀增加或密度降低的结果，而不是温度升高。计算结果与最近报道的微观计算的基础上的Escheras-Fermi方法是一致的。提出了一个研究不同质量区有限核对称能的经验关系式。
In 129 Xe+ nat Sn central collisions from 8 to 25 MeV/A, the three-fragment exit channel occurs with a significant cross section. We show that these fragments arise from two successive binary splittings of a heavy composite system. The sequence of fragment production is determined. Strong Coulomb proximity effects are observed in the three-fragment final state. A comparison with Coulomb trajec-tory calculations shows that the time scale between the consecutive break-ups decreases with increasing bombarding energy, becoming quasi-simultaneous above excitation energy E * = 4.0$\pm$0.5 MeV/A. Thi…
By using freeze-out properties of multifragmenting hot nuclei produced in quasifusion central $^{129}$Xe+$^{nat}$Sn collisions at different beam energies (32, 39, 45 and 50 AMeV) which were estimated by means of a simulation based on experimental data collected by the $4π$ INDRA multidetector, heat capacity in the thermal excitation energy range 4 - 12.5 AMeV was calculated from total kinetic energies and multiplicities at freeze-out. The microcanonical formulation was employed. Negative heat capacity which indicates a first order phase transition for finite systems is observed and confirms pr…
The fusion-by-diffusion model proposed by Swiatecki {\it et al.} [Phys. Rev. C71, 014602 (2005)] has provided a simple and convenient tool to estimate evaporation residue cross sections for superheavy nuclei. I extend this model by taking into account deformation of the target nucleus, and discuss the role of orientation of deformed target in hot fusion reactions at energies around the Coulomb barrier. To this end, I introduce an injection point for the diffusion process over an inner barrier which depends on the orientation angle. I apply this model to the $^{48}$Ca+$^{248}$Cm reaction and sh…
When two heavy ions near the Fermi energy collide, a warm and low-density region can form in which fragments appear. This region is mainly dominated by proton (p) and alpha particles. In such an environment, the alphas interact with each other, and especially through strong resonances, form complex systems such as 8Be and 12C. Our experiments show that in the reactions 70(64)Zn(64Ni)+70(64)Zn(64Ni) at E/A=35 MeV/nucleon levels of 8Be appear around relative energies Eij=0.092 MeV, 3.03 MeV as well as above 10 MeV and 100 MeV. For the 3 alpha systems, multi resonance processes give rise to excit…
The pairing correlations in hot nuclei $^{162}$Dy are investigated in terms of the thermodynamical properties by covariant density functional theory. The heat capacities $C_V$ are evaluated in the canonical ensemble theory and the paring correlations are treated by a shell-model-like approach, in which the particle number is conserved exactly. A S-shaped heat capacity curve, which agrees qualitatively with the experimental data, has been obtained and analyzed in details. It is found that the one-pair-broken states play crucial roles in the appearance of the S shape of the heat capacity curve. …
The phonon damping model (PDM) is extended to include the effect of angular momentum at finite temperature. The model is applied to the study of damping of giant dipole resonance (GDR) in hot and noncollectively rotating spherical nuclei. The numerical results obtained for Mo88 and Sn106 show that the GDR width increases with both temperature T and angular momentum M. At T > 4 MeV and M<= 60 hbar the increase in the GDR width slows down for Sn106, whereas at M<= 80 hbar the GDR widths in both nuclei nearly saturate. By adopting the nuclear shear viscosity extracted from fission data at T= 0, i…
An abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation in the Fermi energy domain. On the other hand finite size effects are predicted to strongly reduce this abnormal production. High statistics quasifusion hot nuclei produced in central collisions between Xe and Sn isotopes at 32 and 45 AMeV incident energies have been used to definitively establish, through the experimental measurement of charge correlations, the presence of spinodal instabilities. N/Z influence was als…
The Green-Kubo relation and fluctuation-dissipation theorem are employed to calculate the shear viscosity $η$ of a finite hot nucleus directly from the width and energy of the giant dipole resonance (GDR) of this nucleus. The ratio $η/s$ of shear viscosity $η$ to entropy density $s$ is extracted from the experimental systematics of the GDR in copper, tin and lead isotopes at finite temperature $T$. These empirical results are then compared with the predictions by several independent models, as well as with almost model-independent estimations. Based on these results, it is concluded that the r…
A study of fusion-evaporation and (partly) fusion-fission channels for the $^{88}$Mo compound nucleus, produced at different excitation energies in the reaction $^{48}$Ti + $^{40}$Ca at 300, 450 and 600 MeV beam energies, is presented. Fusion-evaporation and fusion-fission cross sections have been extracted and compared with the existing systematics. Experimental data concerning light charged particles have been compared with the prediction of the statistical model in its implementation in the Gemini++ code, well suited even for high spin systems, in order to tune the main model parameters in …
In the domain of Fermi energy, it is extremely complex to isolate experimentally fragments and particles issued from the cooling of a hot nucleus produced during a heavy ion collision. This paper presents a new method to characterize more precisely hot Quasi-Projectiles. It tries to take into account as accurately as possible the distortions generated by all the other potential participants in the nuclear reaction. It is quantitatively shown that this method is a major improvement respect to classic calorimetries used with a 4$π$ detector array. By detailing and deconvolving the different step…
By using freeze-out properties of multifragmenting hot nuclei produced in quasifusion central $^{129}$Xe+$^{nat}$Sn collisions at different beam energies (32, 39, 45 and 50 AMeV) which were estimated by means of a simulation based on experimental data collected by the $4π$ INDRA multidetector, heat capacity in the thermal excitation energy range 4 - 12.5 AMeV was calculated from total kinetic energies and multiplicities at freeze-out. The microcanonical formulation was employed. Negative heat capacity which signs a first order phase transition for finite systems is observed and confirms previo…
The thermodynamics of pairing phase-transition in nuclei is studied in the canonical ensemble and treating the pairing correlations in a finite-temperature variation after projection BCS approach (FT-VAP). Due to the restoration of particle number conservation, the pairing gap and the specific heat calculated in the FT-VAP approach vary smoothly with the temperature, indicating a gradual transition from the superfluid to the normal phase, as expected in finite systems. We have checked that the predictions of the FT-VAP approach are very accurate when compared to the results obtained by an exac…
The empirical heat capacities of $^{93-98}$Mo nuclei are re-investigated by using the latest updated and recommended nuclear level density (NLD) data below the neutron binding energy $B_n$ combined with the back-shifted Fermi-gas (BSFG) model for the energy region above $B_n$. For the latter, the BSFG formula with energy-dependent level density parameter is used and the new parameterization has been carried out in order to obtain the best fit to the new NLD data in the whole data range. The results obtained show that the S-shaped heat capacity, a fingerprint of the pairing phase transition, is…
This review article takes stock of the progress made in understanding the phase transition in hot nuclei and highlights the coherence of observed signatures
The formation of excited compound nucleus (CN) and its statistical decay is investigated within the dinuclear system (DNS) model.The initial DNS is formed in the entrance channel when the projectile is captured by a target, and then the evolution of DNS in mass asymmetry coordinate leads to formation of the hot CN. The emission barriers for complex fragments were calculated within the DNS model by using the double folding procedure for the interaction potential. It is shown that cross sections for complex fragment emission become larger when excited CN is more neutron deficient. This approach …
The machine-learning techniques have shown their capability for studying phase transitions in condensed matter physics. Here, we employ the machine-learning techniques to study the nuclear liquid-gas phase transition. We adopt an unsupervised learning and classify the liquid and gas phases of nuclei directly from the final state raw experimental data of heavy-ion reactions. Based on a confusion scheme which combines the supervised and unsupervised learning, we obtain the limiting temperature of the nuclear liquid-gas phase transition. Its value $9.24\pm0.04~\rm MeV$ is consistent with that obt…
