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

Quantum thermodynamics at critical points during melting and solidification processes

We systematically explore and show the existence of finite-temperature continuous quantum phase transition (CTQPT) at a critical point, namely, during solidification or melting such that the first-order thermal phase transition is a special case within CTQPT. Infact, CTQPT is related to chemical reaction where quantum fluctuation (due to wavefunction transformation) is caused by thermal energy and it can occur maximally for temperatures much higher than zero Kelvin. To extract the quantity related to CTQPT, we use the ionization energy theory and the energy-level spacing renormalization group method to derive the energy-level spacing entropy, renormalized Bose-Einstein distribution and the time-dependent specific heat capacity. This work unambiguously shows that the quantum phase transition applies for any finite temperatures.Comment: To be published in Indian Journal of Physics (Kolkata

Echos of the liquid-gas phase transition in multifragmentation

A general discussion is made concerning the ways in which one can get signatures about a possible liquid-gas phase transition in nuclear matter. Microcanonical temperature, heat capacity and second order derivative of the entropy versus energy formulas have been deduced in a general case. These formulas are {\em exact}, simply applicable and do not depend on any model assumption. Therefore, they are suitable to be applied on experimental data. The formulas are tested in various situations. It is evidenced that when the freeze-out constraint is of fluctuating volume type the deduced (heat capacity and second order derivative of the entropy versus energy) formulas will prompt the spinodal region through specific signals. Finally, the same microcanonical formulas are deduced for the case when an incomplete number of fragments per event are available. These formulas could overcome the freeze-out backtracking deficiencies.Comment: accepted to Nuclear Physics

Exotic Hadrons with Hidden Charm and Strangeness

We investigate on exotic tetraquark hadrons of the kind [cs][cbar sbar] by computing their spectrum and decay modes within a constituent diquark-antidiquark model. We also compare these predictions with the present experimental knowledge.Comment: 6 pages, 2 figures, minor changes made, references adde

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

Break-up fragment topology in statistical multifragmentation models

Break-up fragmentation patterns together with kinetic and configurational energy fluctuations are investigated in the framework of a microcanonical model with fragment degrees of freedom over a broad excitation energy range. As far as fragment partitioning is approximately preserved, energy fluctuations are found to be rather insensitive to both the way in which the freeze-out volume is constrained and the trajectory followed by the system in the excitation energy - freeze-out volume space. Due to hard-core repulsion, the freeze-out volume is found to be populated un-uniformly, its highly depleted core giving the source a bubble-like structure. The most probable localization of the largest fragments in the freeze-out volume may be inferred experimentally from their kinematic properties, largely dictated by Coulomb repulsion

Densities and energies of nuclei in dilute matter

We explore the ground-state properties of nuclear clusters embedded in a gas of nucleons with the help of Skyrme-Hartree-Fock microscopic calculations. Two alternative representations of clusters are introduced, namely coordinate-space and energy-space clusters. We parameterize their density profiles in spherical symmetry in terms of basic properties of the energy density functionals used and propose an analytical, Woods-Saxon density profile whose parameters depend, not only on the composition of the cluster, but also of the nucleon gas. We study the clusters' energies with the help of the local-density approximation, validated through our microscopic results. We find that the volume energies of coordinate-space clusters are determined by the saturation properties of matter, while the surface energies are strongly affected by the presence of the gas. We conclude that both the density profiles and the cluster energies are strongly affected by the gas and discuss implications for the nuclear EoS and related perspectives. Our study provides a simple, but microscopically motivated modeling of the energetics of clusterized matter at subsaturation densities, for direct use in consequential applications of astrophysical interest.Comment: 20 pages, incl. 12 figure

Fragment isospin distributions and the phase diagram of excited nuclear systems

Fragment average isospin distributions are investigated within a microcanonical multifragmentation model in different regions of the phase diagram. The results indicate that in the liquid phase $$ versus $Z$ is monotonically increasing, in the phase coexistence region it has a rise and fall shape and in the gas phase it is constant. Deviations from this behavior may manifest at low fragment multiplicity as a consequence of mass/charge conservation. Characterization of the "free" and "bound" phases function of fragment charge reconfirms the neutron enrichment of the "free" phase with respect to the "bound" one irrespectively the localization of the multifragmentation event in the phase diagram.Comment: 23 pages, 12 figure

Impacts of variable renewable energy on wholesale markets and generating assets in the United States: A review of expectations and evidence

We synthesize available literature, data, and analysis on the degree to which growth in variable renewable energy (VRE) has impacted or might in the future impact bulk power system assets, pricing, and costs in the United States. Most studies of future scenarios indicate that VRE reduces wholesale energy prices and capacity factors of thermal generators. Traditional baseload generators are more exposed to these changing market conditions than low-capital cost and more flexible intermediate and peak-load generators. From analysis of historical data we find that VRE is already influencing the bulk power market through changes in temporal and geographic patterns areas with higher levels of VRE. The most significant observed impacts have concentrated in areas with significant VRE and/or nuclear generation along with limited transmission, with negative pricing also often occurring during periods with lower system-wide load. So far, however, VRE, has had a relatively modest impact on historical average annual wholesale prices across entire market regions, at least in comparison to other drivers. The reduction of natural gas prices is the primary contributor to the decline in wholesale prices since 2008. Similarly, VRE impacts on thermal plant retirements have been limited and there is little relationship between the location of recent retirements and VRE penetration levels. Although impacts on wholesale prices have been modest so far, impacts of VRE on the electricity market will be more significant under higher VRE penetrations