Fluctuations of fragment observables

This contribution presents a review of our present theoretical as well as experimental knowledge of different fluctuation observables relevant to nuclear multifragmentation. The possible connection between the presence of a fluctuation peak and the occurrence of a phase transition or a critical phenomenon is critically analyzed. Many different phenomena can lead both to the creation and to the suppression of a fluctuation peak. In particular, the role of constraints due to conservation laws and to data sorting is shown to be essential. From the experimental point of view, a comparison of the available fragmentation data reveals that there is a good agreement between different data sets of basic fluctuation observables, if the fragmenting source is of comparable size. This compatibility suggests that the fragmentation process is largely independent of the reaction mechanism (central versus peripheral collisions, symmetric versus asymmetric systems, light ions versus heavy ion induced reactions). Configurational energy fluctuations, that may give important information on the heat capacity of the fragmenting system at the freeze out stage, are not fully compatible among different data sets and require further analysis to properly account for Coulomb effects and secondary decays. Some basic theoretical questions, concerning the interplay between the dynamics of the collision and the fragmentation process, and the cluster definition in dense and hot media, are still open and are addressed at the end of the paper. A comparison with realistic models and/or a quantitative analysis of the fluctuation properties will be needed to clarify in the next future the nature of the transition observed from compound nucleus evaporation to multi-fragment production.Comment: Contribution to WCI (World Consensus Initiative) Book " "Dynamics and Thermodynamics with Nuclear Degrees of Freedom", to appear on Euorpean Physics Journal A as part of the Topical Volume. 9 pages, 12 figure

Statistical description of complex nuclear phases in supernovae and proto-neutron stars

We develop a phenomenological statistical model for dilute star matter at finite temperature, in which free nucleons are treated within a mean-field approximation and nuclei are considered to form a loosely interacting cluster gas. Its domain of applicability, that is baryonic densities ranging from about $\rho>10^8$ g $\cdot$ cm$^{-3}$ to normal nuclear density, temperatures between 1 and 20 MeV and proton fractions between 0.5 and 0, make it suitable for the description of baryonic matter produced in supernovae explosions and proto-neutron stars. The first finding is that, contrary to the common belief, the crust-core transition is not first order, and for all subsaturation densities matter can be viewed as a continuous fluid mixture between free nucleons and massive nuclei. As a consequence, the equations of state and the associated observables do not present any discontinuity over the whole thermodynamic range. We further investigate the nuclear matter composition over a wide range of densities and temperatures. At high density and temperature our model accounts for a much larger mass fraction bound in medium nuclei with respect to traditional approaches as Lattimer-Swesty, with sizeable consequences on the thermodynamic quantities. The equations of state agree well with the presently used EOS only at low temperatures and in the homogeneous matter phase, while important differences are present in the crust-core transition region. The correlation among the composition of baryonic matter and neutrino opacity is finally discussed, and we show that the two problems can be effectively decoupled.Comment: 40 pages, 25 figure

In-medium nuclear cluster energies within the Extended Thomas-Fermi approach

A recently introduced analytical model for the nuclear density profile[1] is implemented in the Extended Thomas-Fermi (ETF) energy density functional. This allows to (i) shed a new light on the issue of the sign of surface symmetry energy in nuclear mass formulas, which is strongly related to the non-uniformity of the isospin asymmetry in finite nuclei, as well as to (ii) evaluate the in-medium corrections to the nuclear cluster energies in thermodynamic conditions relevant for the description of the (proto)-neutron star crust. The ground state configurations of the model are compared to Hartree-Fock calculations in spherical symmetry for some selected isotopic chains, and systematic errors are quantified. The in-medium modification of the nuclear mass due to the presence of a gas component is shown to strongly depend both on the density and the asymmetry of the nucleon gas. This shows the importance of accounting for such effects in the realistic modelizations of the equation of state for core-collapse supernovae and proto-neutron stars.Comment: 15 pages, 9 figure

Tracking energy fluctuations from fragment partitions in the Lattice Gas model

Partial energy fluctuations are known tools to reconstruct microcanonical heat capacities. For experimental applications, approximations have been developed to infer fluctuations at freeze out from the observed fragment partitions. The accuracy of this procedure as well as the underlying independent fragment approximation is under debate already at the level of equilibrated systems. Using a well controlled computer experiment, the Lattice Gas model, we critically discuss the thermodynamic conditions under which fragment partitions can be used to reconstruct the thermodynamics of an equilibrated system.Comment: version accepted for publication in Phys.Rev.

Looking for bimodal distributions in multi-fragmentation reactions

The presence of a phase transition in a finite system can be deduced, together with its order, from the shape of the distribution of the order parameter. This issue has been extensively studied in multifragmentation experiments, with results that do not appear fully consistent. In this paper we discuss the effect of the statistical ensemble or sorting conditions on the shape of fragment distributions, and propose a new method, which can be easily implemented experimentally, to discriminate between different fragmentation scenarii. This method, based on a reweighting of the measured distribution to account for the experimental constraints linked to the energy deposit, is tested on different simple models, and appears to provide a powerful discrimination.Comment: 11 pages, 7 figure

First order phase transitions: equivalence between bimodalities and the Yang-Lee theorem

First order phase transitions in finite systems can be defined through the bimodality of the distribution of the order parameter. This definition is equivalent to the one based on the inverted curvature of the thermodynamic potential. Moreover we show that it is in a one to one correspondence with the Yang Lee theorem in the thermodynamic limit. Bimodality is a necessary and sufficient condition for zeroes of the partition sum in the control intensive variable complex plane to be distributed on a line perpendicular to the real axis with a uniform density, scaling like the number of particles.Comment: 10 pages, no figure

Comment on "Partial energies fluctuations and negative heat capacities" by X. Campi et al

Studying the energy partioning published in nucl-th/0406056v2 we show that the presented results do not fulfill the sum rule due to energy conservation. The observed fluctuations of the energy conservation test point to a numerical problem. Moreover, analysis of the binding energies show that the fragment recognition algorithm adopted by Campi et al. leads with a sizeable probability to fragments containing up to the total mass even for excitation energies as large as 3/4 of the total binding. This surprising result points to another problem since the published inter-fragment energy is not zero while a unique fragment is present. This problem may be due to either the fragment recognition algorithm or to the definition of the inter and intra-fragment energy. These numerical inconsistencies should be settled before any conclusion on the physics can be drawn

Correlations in mesoscopic magnetic systems

The purpose of this proposal is to study the ferro/para phase transition in a mesoscopic Ising-like lattice and in particular demonstrate the existence of a negative magnetic susceptibility in the fixed magnetization ensemble. To this aim we will use the correlation = /N2 where N is the total number of spins for a single cluster, M the total magnetization of the cluster, and the equality holds if we choose r0<Dr<R where r0 is the linear size of a spin site and R is the linear size of a cluster

Clusterized nuclear matter in the (proto-)neutron star crust and the symmetry energy

Though generally agreed that the symmetry energy plays a dramatic role in determining the structure of neutron stars and the evolution of core-collapsing supernovae, little is known in what concerns its value away from normal nuclear matter density and, even more important, the correct definition of this quantity in the case of unhomogeneous matter. Indeed, nuclear matter traditionally addressed by mean-field models is uniform while clusters are known to exist in the dilute baryonic matter which constitutes the main component of compact objects outer shells. In the present work we investigate the meaning of symmetry energy in the case of clusterized systems and the sensitivity of the proto-neutron star composition and equation of state to the effective interaction. To this aim an improved Nuclear Statistical Equilibrium (NSE) model is developed, where the same effective interaction is consistently used to determine the clusters and unbound particles energy functionals in the self-consistent mean-field approximation. In the same framework, in-medium modifications to the cluster energies due to the presence of the nuclear gas are evaluated. We show that the excluded volume effect does not exhaust the in-medium effects and an extra isospin and density dependent energy shift has to be considered to consistently determine the composition of subsaturation stellar matter. The symmetry energy of diluted matter is seen to depend on the isovector properties of the effective interaction, but its behavior with density and its quantitative value are strongly modified by clusterization.Comment: A contribution to the upcoming EPJA Special Volume on Nuclear Symmetry Energ

Modification of magicity towards the dripline and its impact on electron-capture rates for stellar core-collapse

The importance of microphysical inputs from laboratory nuclear experiments and theoretical nuclear structure calculations in the understanding of the core collapse dynamics, and the subsequent supernova explosion, is largely recognized in the recent literature. In this work, we analyze the impact of the masses of very neutron rich nuclei on the matter composition during collapse, and the corresponding electron capture rate. To this aim, we introduce an empirical modification of the popular Duflo-Zuker mass model to account for possible shell quenching far from stability, and study the effect of the quenching on the average electron capture rate. We show that the preeminence of the $N=50$ and $N=82$ closed shells in the collapse dynamics is considerably decreased if the shell gaps are reduced in the region of $^{78}$Ni and beyond. As a consequence, local modifications of the overall electron capture rate up to 30\% can be expected, with integrated values strongly dependent on the stiffness of magicity quenching and progenitor mass and potential important consequences on the entropy generation, the neutrino emissivity, and the mass of the core at bounce. Our work underlines the importance of new experimental measurements in this region of the nuclear chart, the most crucial information being the nuclear mass and the Gamow-Teller strength. Reliable microscopic calculations of the associated elementary rate, in a wide range of temperatures and electron densities, optimized on these new empirical information, will be additionally needed to get quantitative predictions of the collapse dynamics.Comment: 12 pages, 10 figure