556 research outputs found

### 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

### 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

### Analytical mass formula and nuclear surface properties in the ETF approximation

The problem of the determination of the nuclear surface and surface symmetry
energy is addressed in the framework of the Extended Thomas Fermi (ETF)
approximation using Skyrme functionals. We propose an analytical model for the
density profiles with variationally determined diffuseness parameters. For the
case of symmetric nuclei, the resulting ETF functional can be exactly
integrated, leading to an analytical formula expressing the surface energy as a
function of the couplings of the energy functional. The importance of non-local
terms is stressed, which cannot be simply deduced from the local part of the
functional. In the case of asymmetric nuclei, we propose an approximate
expression for the diffuseness and the surface energy. These quantities are
analytically related to the parameters of the energy functional. In particular,
the influence of the different equation of state parameters can be explicitly
quantified. Detailed analyses of the different energy components
(local/non-local, isoscalar/isovector, surface/curvature and higher order) are
also performed. Our analytical solution of the ETF integral improves over
previous models and leads to a precision better than 200 keV per nucleon in the
determination of the nuclear binding energy for dripline nuclei.Comment: 27 pages, 18 figures, submitted to PR

### 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

### 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

### Multifragmentation and the symmetry term of the nuclear equation of state

We investigate the possibility to extract the symmetry energy from
multifragmentation data. The applicability of the grandcanonical formula
earlier proposed by Ono {\it et al.} [Phys. Rev. C {\bf 68}, 051601(R)] in the
case of finite excited nuclei is tested within a microcanonical framework.
Relatively good results are obtained except for large residual nuclei,
especially when large sources are highly excited. Effects of secondary particle
emission and the extent in which relevant information may be inferred from
experimental observables are finally discussed.Comment: 13 pages, 4 figure

### Unified treatment of sub-saturation stellar matter at zero and finite temperature

The standard variational derivation of stellar matter structure in the
Wigner-Seitz approximation is generalized to the finite temperature situation
where a wide distribution of different nuclear species can coexist in the same
density and proton fraction condition, possibly out of $\beta$-equilibrium. The
same theoretical formalism is shown to describe on one side the single-nucleus
approximation (SNA), currently used in most core collapse supernova
simulations, and on the other side the nuclear statistical equilibrium (NSE)
approach, routinely employed in r- and p-process explosive nucleosynthesis
problems. In particular we show that in-medium effects have to be accounted for
in NSE to have a theoretical consistency between the zero and finite
temperature modeling. The bulk part of these in-medium effects is analytically
calculated and shown to be different from a van der Waals excluded volume term.
This unified formalism allows controlling quantitatively the deviations from
the SNA in the different thermodynamic conditions, as well as having a NSE
model which is reliable at any arbitrarily low value of the temperature, with
potential applications for neutron star cooling and accretion problems. We
present different illustrative results with several mass models and effective
interactions, showing the importance of accounting for the nuclear species
distribution even at temperatures lower than 1 MeV.Comment: 26 pages, 17 figures; submitted to 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

### 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.

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