arXiv subjects

A. Dellafiore

Publications and source records attributed to A. Dellafiore.

15 recordsLinked to original sources

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↗

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↗

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↗

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

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↗

arXiv2001

Kinetic-theory description of isoscalar dipole modes

A semiclassical model, based on a solution of the Vlasov equation for finite systems with moving-surface, is employed to study the isoscalar dipole modes in nuclei. It is shown that, by taking into account the surface degree of freedom, it is possible to obtain an exact treatment of the centre of mass motion. It is also shown that a method often used to subtract the spurious strength in RPA calculations does not always give the correct result. An alternative analytical formula for the intrinsic strength function is derived in a simple confined-Fermi-gas model. In this model the intrinsic isoscalar dipole strength displays essentially a two-resonance structure, hence there are two relevant modes. The interaction between nucleons couples these two modes and changes the compressibility of the system. The evolution of the strength profile is then studied as a function of the compressibility of the nuclear fluid. Comparison with available data favours values of the incompressibility parameter of nuclear matter smaller than those suggested by the analysis of the monopole ``breathing'' mode.

nucl-th↗

arXiv2000

Density fluctuations and multifragmentation of nuclear matter

The density fluctuations of nuclear matter are studied within a mean-field model in wich fluctuations are generated by an external stochastic field. The constraints imposed on the random force by the fluctuation-dissipation theorem are analyzed. It is shown that in the proximity of the borders of the spinodal region the assumption of a white-noise stochastic field can be reliably used. The domain distribution of the liquid phase in the spinodal decomposition of nuclear matter is derived. The related distribution of fragment sizes compares favourably with the experimental fragment distribution observed in heavy ion collisions.

nucl-th↗

arXiv1999

Kinetic-theory approach to low-energy collective modes in nuclei

Two different solutions of the linearized Vlasov equation for finite systems, characterized by fixed and moving-surface boundary conditions, are discussed in a unified perspective. A condition determining the eigenfrequencies of collective nuclear oscillations, that can be obtained from the moving-surface solution, is studied for isoscalar vibrations of lowest multipolarity. Analytic expressions for the friction and mass parameters related to the low-enegy surface excitations are derived and their value is compared to values given by other models. Both similarities and differences are found with respect to the other approaches, however the close agreement obtained in many cases with one of the other models suggests that, in spite of some important differences, the two approaches are substantially equivalent. The formalism based on the Vlasov equation is more transparent since it leads to analytical expressions that can be a basis for further improvement of the model.

nucl-th↗

arXiv1999

Semiclassical theory of surface plasmons in spheroidal clusters

A microscopic theory of linear response based on the Vlasov equation is extended to systems having spheroidal equilibrium shape. The solution of the linearized Vlasov equation, which gives a semiclassical version of the random phase approximation, is studied for electrons moving in a deformed equilibrium mean field. The deformed field has been approximated by a cavity of spheroidal shape, both prolate and oblate. Contrary to spherical systems, there is now a coupling among excitations of different multipolarity induced by the interaction among constituents. Explicit calculations are performed for the dipole response of deformed clusters of different size. In all cases studied here the photoabsorption strength for prolate clusters always displays a typical double-peaked structure. For oblate clusters we find that the high--frequency component of the plasmon doublet can get fragmented in the medium size region ($N \sim 250$). This fragmentation is related to the presence of two kinds of three-dimensional electron orbits in oblate cavities. The possible scaling of our semiclassical equations with the valence electron number and density is investigated.

cond-mat.mes-hall↗

arXiv1997

Relativistic Approach to Superfluidity in Nuclear Matter

Pairing correlations in symmetric nuclear matter are studied within a relativistic mean-field approximation based on a field theory of nucleons coupled to neutral ($σ$ and $ω$) and to charged ($\varrho$) mesons. The Hartree-Fock and the pairing fields are calculated in a self-consistent way. The energy gap is the result of a strong cancellation between the scalar and vector components of the pairing field. We find that the pair amplitude vanishes beyond a certain value of momentum of the paired nucleons. This fact determines an effective cutoff in the gap equation. The value of this cutoff gives an energy gap in agreement with the estimates of non relativistic calculations.

nucl-th↗