arXiv subjects

F. Matera

Publications and source records attributed to F. Matera.

At least 19 recordsLinked to original sources

arXiv2017

Low-energy modes of spin-imbalanced Fermi gases in BCS phase

The low-energy modes of a spin-imbalanced superfluid Fermi gas in the Bardeen-Cooper-Schrieffer (BCS) side are studied. The gas is assumed to be sufficiently dilute so that the pairing of atoms can be considered effective only in s-wave between fermions of different internal state. The order parameter at equilibrium is determined by the mean-field approximation, while the properties of the collective modes are calculated within a Gaussian approximation for the fluctuations of the order parameter. In particular we investigate the effects of asymmetry between the populations of the two different components and of temperature on the frequency and damping of collective modes. It is found that the temperature does not much affect the frequency and the damping of the modes, whereas an increase of the imbalance shifts the frequency toward lower values and enhances the damping sensitively. Besides the Bogoliubov-Anderson phonons, we observe modes at zero frequency for finite values of the wave-number. These modes indicate that an instability develops driving the system toward two separate phases, normal and superfluid.

cond-mat.quant-gas↗

arXiv2016

Pairing effects on neutrino transport in low-density stellar matter

We investigate the impact of pairing correlations on neutrino transport in stellar matter. Our analysis is extended to nuclear matter conditions where large density fluctuations develop, associated with the onset of the liquid-vapor phase transition, and clustering phenomena occur. Within a thermodynamical treatment, we show that at moderate temperatures, where pairing effects are still active, the scattering of neutrinos in the nuclear medium is significantly affected by pairing correlations, which increase the neutrino trapping, thus modifying the cooling mechanism, by neutrino emission, of neutron stars.

nucl-th↗

arXiv2012

Influence of vector interactions on the hadron-quark/gluon phase transition

The hadron-quark/gluon phase transition is studied in the two-phase model. As a further study of our previous work, both the isoscalar and isovector vector interactions are included in the Polyakov loop modified Nambu--Jona-Lasinio model (PNJL) for the quark phase. The relevance of the exchange (Fock) terms is stressed and suitably accounted for. The calculation shows that the isovector vector interaction delays the phase transition to higher densities and the range of the mixed phase correspondingly shrinks. Meanwhile the asymmetry parameter of quark matter in the mixed phase decreases with the strengthening of this interaction channel. This leads to some possible observation signals being weakened, although still present. We show that these can be rather general effects of a repulsion in the quark phase due to the symmetry energy. This is also confirmed by a simpler calculation with the MIT--Bag model. However, the asymmetry parameter of quark matter is slightly enhanced with the inclusion of the isoscalar vector interaction, but the phase transition will be moved to higher densities. The largest uncertainty on the phase transition lies in the undetermined coupling constants of the vector interactions. In this respect new data on the mixed phase obtained from Heavy Ion Collisions at Intermediate Energies appear very important.

nucl-th↗

arXiv2011

BCS and BEC p-wave pairing in Bose-Fermi gases

The pairing of fermionic atoms in a mixture of atomic fermion and boson gases at zero temperature is investigated. The attractive interaction between fermions, that can be induced by density fluctuations of the bosonic background, can give rise to a superfluid phase in the Fermi component of the mixture. The atoms of both species are assumed to be in only one internal state, so that the pairing of fermions is effective only in odd-l channels. No assumption about the value of the ratio between the Fermi velocity and the sound velocity in the Bose gas is made in the derivation of the energy gap equation. The gap equation is solved without any particular "ansatz" for the pairing field or the effective interaction. The p-wave superfluidity is studied in detail. By increasing the strength and/or decreasing the range of the effective interaction a transition of the fermion pairing regime, from the Bardeen-Cooper-Schrieffer state to a system of tightly bound couples can be realized. These composite bosons behave as a weakly-interacting Bose-Einstein condensate.

cond-mat.quant-gas↗

arXiv2010

Self-consistency and collective effects in semiclassical pairing theory

A simple model, in which nuclei are represented as homogeneous spheres of symmetric nuclear matter, is used to study the effects of a self-consistent pairing interaction on the nuclear response. Effects due to the finite size of nuclei are suitably taken into account. The semiclassical equations of motion derived in a previous paper for the time-dependent Hartree-Fock-Bogoliubov problem are solved in an improved (linear) approximation in which the pairing field is allowed to oscillate and to become complex. The new solutions are in good agreement with the old ones and also with the result of well-known quantum approaches. The role of the Pauli principle in eliminating one possible set of solutions is also discussed. The pairing-field fluctuations have two main effects: they restore the particle-number symmetry which is broken in the constant-$Δ$ approximation and introduce the possibility of collective eigenfrequencies of the system due to the pairing interaction. A numerical study with values of parameters appropriate for nuclei, shows an enhancement of the density-density strength function in the region of the low-energy giant octupole resonance, while no similar effect is present in the region of the high-energy octupole resonance and for the giant monopole and quadrupole resonances.

nucl-th↗

arXiv2008

Density dependence of isospin observables in spinodal decomposition

Isotopic fluctuations in fragment formation are investigated in a quasi-analytical description of the spinodal decomposition scenario. By exploiting the fluctuation-dissipation relations the covariance matrix of density fluctuations is derived as a function of the wave vector for nuclear matter at given values of density, charge asymmetry, temperature, and of the time that the system spends in the instability region. Then density fluctuations in ordinary space are implemented with a Fourier transform performed in a finite cubic lattice. Inside this box, domains with different density coexist, from which clusters of nucleons eventually emerge. Within our approach, the isotopic distributions are determined by the N/Z ratio of the leading unstable isoscalarlike mode and by isovectorlike fluctuations present in the matter undergoing the spinodal decomposition. Hence the average value of the N/Z ratio of clusters and the width of the relative distribution reflect the properties of the symmetry energy. Generating a large number of events, these calculations allow a careful investigation of the cluster isotopic content as a function of the cluster density. A uniform decrease of the average charge asymmetry and of the width of the isotopic distributions with increasing density is observed. Finally we remark that the results essentially refer to the early break--up of the system.

nucl-th↗

arXiv2007

Kinetic equation for finite systems of fermions with pairing

The solutions of the Wigner-transformed time-dependent Hartree--Fock--Bogoliubov equations are studied in the constant-$Δ$ approximation. This approximation is known to violate particle-number conservation. As a consequence, the density fluctuation and the longitudinal response function given by this approximation contain spurious contributions. A simple prescription for restoring both local and global particle-number conservation is proposed. Explicit expressions for the eigenfrequencies of the correlated systems and for the density response function are derived and it is shown that the semiclassical analogous of the quantum single--particle spectrum has an excitation gap of $2Δ$, in agreement with the quantum result. The collective response is studied for a simplified form of the residual interaction.

nucl-th↗

arXiv2006

An extended Vlasov equation with pairing correlations

A simplified version of the Wigner--transformed time--dependent Hartree--Fock--Bogoliubov equations, leading to a solvable model for finite systems of fermions with pairing correlations, is introduced. In this model, pairing correlations result in a coupling of the Vlasov--type equation for the normal phase--space density with that for the imaginary part of the anomalous density. The effect of pairing correlations on the linear response of the system is studied for a finite one--dimensional system and an explicit expression for the correlated propagator is given.

nucl-th↗

arXiv2005

Collective motion in finite Fermi systems within Vlasov dynamics

A semiclassical theory of linear response in finite Fermi systems, based on the Vlasov equation, and its applications to the study of isoscalar vibrations in heavy nuclei are reviewed. It is argued that the Vlasov equation can be used to study the response of small quantum systems like (heavy) nuclei in regimes for which the finite size of the system is more important than the collisions between constituents. This requires solving the linearized Vlasov equation for finite systems, however, in this case the problem of choosing appropriate boundary conditions for the fluctuations of the phase-space-density is non-trivial. Calculations of the isoscalar response functions performed by using different boundary conditions, corresponding to fixed and moving nuclear surface, are compared for different multipoles and it is found that, in a sharp-surface model, the moving-surface boundary conditions give better agreement with experiment. The semiclassical strength functions given by this theory are strikingly similar to the results of analogous quantum calculations, in spite of the fact that shell effects are not included in the theory, this happens because of a well known close relation between classical trajectories and shell structure.

nucl-th↗

arXiv2005

Isospin fluctuations in spinodal decomposition

We study the isospin dynamics in fragment formation within the framework of an analytical model based on the spinodal decomposition scenario. We calculate the probability to obtain fragments with given charge and neutron number, focussing on the derivation of the width of the isotopic distributions. Within our approach this is determined by the dispersion of N/Z among the leading unstable modes, due to the competition between Coulomb and symmetry energy effects, and by isovector-like fluctuations present in the matter that undergoes the spinodal decomposition. Hence the widths exhibit a clear dependence on the properties of the Equation of State. By comparing two systems with different values of the charge asymmetry we find that the isotopic distributions reproduce an isoscaling relationship.

nucl-th↗

arXiv2004

Unified semiclassical approach to isoscalar collective modes in heavy nuclei

A semiclassical model based on the solution of the Vlasov equation for finite systems with a sharp moving surface has been used to study the isoscalar quadrupole and octupole collective modes in heavy spherical nuclei. Within this model, a unified description of both low-energy surface modes and higher-energy giant resonances has been achieved by introducing a coupling between surface vibrations and the motion of single nucleons. Analytical expressions for the collective response functions of different multipolarity can be derived by using a separable approximation for the residual interaction between nucleons. The response functions obtained in this way give a good qualitative description of the quadrupole and octupole response in heavy nuclei. Although shell effects are not explicitly included in the theory, our semiclassical response functions are very similar to the quantum ones. This happens because of the well known close relation between classical trajectories and shell structure. The role played by particular nucleon trajectories and their connection with various features of the nuclear response is displayed most clearly in the present approach, we discuss in some detail the damping of low-energy octupole vibrations and give an explicit expression showing that only nucleons moving on triangular orbits can contribute to this damping.

nucl-th↗

arXiv2004

Fragmentation path of excited nuclear systems

We perform a study of the fragmentation path of excited nuclear sources, within the framework of a stochastic mean-field approach. We consider the reaction $^{129}$Xe + $^{119}$Sn at two beam energies: 32 and 50 MeV/A, for central collisions. It is observed that, after the compression phase the system expands towards a dilute configuration from which it may recontract or evolve into a bubble-like structure. Then fragments are formed through the development of volume and/or surface instabilities. The two possibilities co-exist at 32 MeV/A, leading to quite different fragment partitions, while at 50 MeV/A the hollow configuration is observed in all events. Large variances are recovered in a way fully consistent with the presence of spinodal decomposition remnants. Kinematical properties of fragments are discussed and suggested as observables very sensitive to the dominant fragment production mechanism. A larger radial collective flow is observed at 50 MeV/A, in agreement with experiments.

nucl-th↗

arXiv2003

Fermion pairing in Bose-Fermi mixtures

An effective interaction between fermions in a Bose-Fermi mixture is derived. It is induced by density fluctuations of the bosonic background. The contributions from states containing both one and two virtual phonons are taken into account self-consistently. The time dependence of the effective interaction has been removed by assuming that the velocity of the fermions at the Fermi surface is much larger than the sound velocity in the Bose gas. The fermions are considered in only one magnetic state, so that pairing can be effective only in odd-l channels. It has been found that the onset of the superconducting phase can occur at temperatures (> 100nK) of the same order of magnitude as the Fermi temperature (300nK), and the energy gap in the excitation spectrum is a small fraction (1%) of the Fermi energy.

cond-mat.soft↗

arXiv2003

Octupole response and stability of spherical shape in heavy nuclei

The isoscalar octupole response of a heavy spherical nucleus is analyzed in a semiclassical model based on the linearized Vlasov equation. The octupole strength function is evaluated with different degrees of approximation. The zero-order fixed-surface response displays a remarkable concentration of strength in the $1\hbarω$ and $3\hbarω$ regions, in excellent agreement with the quantum single-particle response. The collective fixed-surface response reproduces both the high- and low-energy octupole rsonances, but not the low-lying $3^{-}$ collective states, while the moving-surface response function gives a good qualitative description of all the main features of the octupole response in heavy nuclei. The role of triangular nucleon orbits, that have been related to a possible instability of the spherical shape with respect to octupole-type deformations, is discussed within this model. It is found that, rather than creating instability, the triangular trajectories are the only classical orbits contributing to the damping of low-energy octupole excitations.

nucl-th↗

arXiv2003

Effects of surface vibrations on quadrupole response of nuclei

The effect of quadrupole-type surface vibrations on the quadrupole response function of heavy nuclei is studied by using a model based on the solution of the linearized Vlasov equation with moving-surface boundary conditions. By using a separable approximation for the residual interaction, an analytical expression is obtained for the moving-surface response function. Comparison of the fixed- and moving-surface strength functions shows that surface vibrations are essential in order to achieve a unified description of the two characteristic features of the quadrupole response: the giant resonance and the low-lying states. Calculations performed by setting the surface tension equal to zero shows that the low-lying strength is strongly affected by the surface tension.

nucl-th↗

arXiv2003

Spinodal decomposition of expanding nuclear matter and multifragmentation

Density fluctuations of expanding nuclear matter are studied within a mean-field model in which fluctuations are generated by an external stochastic field. Fluctuations develop about a mean one-body phase-space density corresponding to a hydrodinamic motion that describes a slow expansion of the system. A fluctuation-dissipation relation suitable for a uniformly expanding medium is obtained and used to constrain the strength of the stochastic field. The distribution of the liquid domains in the spinodal decomposition is derived. Comparison of the related distribution of the fragment size with experimental data on the nuclear multifragmentation is quite satisfactory.

nucl-th↗

arXiv2002

Collective modes of asymmetric nuclear matter in Quantum HadroDynamics

We discuss a fully relativistic Landau Fermi liquid theory based on the Quantum Hadro-Dynamics ($QHD$) effective field picture of Nuclear Matter ({\it NM}). From the linearized kinetic equations we get the dispersion relations of the propagating collective modes. We focus our attention on the dynamical effects of the interplay between scalar and vector channel contributions. A beautiful ``mirror'' structure in the form of the dynamical response in the isoscalar/isovector degree of freedom is revealed, with a complete parallelism in the role respectively played by the compressibility and the symmetry energy. All that strongly supports the introduction of an explicit coupling to the scalar-isovector channel of the nucleon-nucleon interaction. In particular we study the influence of this coupling (to a $δ$-meson-like effective field) on the collective response of asymmetric nuclear matter ($ANM$). Interesting contributions are found on the propagation of isovector-like modes at normal density and on an expected smooth transition to isoscalar-like oscillations at high baryon density. Important ``chemical'' effects on the neutron-proton structure of the mode are shown. For dilute $ANM$ we have the isospin distillation mechanism of the unstable isoscalar-like oscillations, while at high baryon density we predict an almost pure neutron wave structure of the propagating sounds.

nucl-th↗

arXiv2002

Oscillations in finite Fermi systems

A semiclassical linear response theory based on the Vlasov equation is reviewed. The approach discussed here differs from the classical one of Vlasov and Landau for the fact that the finite size of the system is explicitly taken into account. The non-trivial problem of deciding which boundary conditions are more appropriate for the fluctuations of the phase-space density has been circumvented by studying solutions corresponding to different boundary conditions (fixed and moving surface). The fixed-surface theory has been applied to systems having both spherical and spheroidal equilibrium shapes. The moving-surface theory is related to the liquid-drop model of the nucleus and from it one can obtain a kinetic-theory description of surface and compression modes in nuclei. Quantum corrections to the semiclassical theory are also briefly discussed.

nucl-th↗