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S. Shlomo

Publications and source records attributed to S. Shlomo.

At least 37 records · Page 2Linked to original sources

Symmetry energy of dilute warm nuclear matter

The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular by the appearance of bound states. A recently developed quantum statistical (QS) approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.

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The shear viscosity to entropy density ratio in finite nuclei

Experiments at the Relativistic Heavy Ion Collider (RHIC) suggest that the state of matter produced in the experiments has a low shear-viscosity to entropy-density ratio. We ask here the question what is this ratio in usual finite nuclei at low temperature. We use the experimental and theoretical results for the widths of giant vibrational states in nuclei in order to calculate the above ratio. We find that the values of this ratio are not very different from the ones found in the RHIC experiments.

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Effect of medium dependent binding energies on inferring the temperatures and freeze-out density of disassembling hot nuclear matter from cluster yields

We explore the abundance of light clusters in asymmetric nuclear matter at subsaturation density. With increasing density, binding energies and wave functions are modified due to medium effects. The method of Albergo, Costa, Costanzo and Rubbino (ACCR) for determining the temperature and free nucleon density of a disassembling hot nuclear source from fragment yields is modified to include, in addition to Coulomb effects and flow, also effects of medium modifications of cluster properties, which become of importance when the nuclear matter density is above 10$^{-3}$ fm$^{-3}$. We show how the analysis of cluster yields, to infer temperature and nucleon densities, is modified if the shifts in binding energies of in medium clusters are included. While, at low densities, the temperature calculated from given yields changes only modestly if medium effects are taken into account, larger discrepancies are observed when the nucleon densities are determined from measured yields.

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Experimental determination of the symmetry energy of a low density nuclear gas

Experimental analyses of moderate temperature nuclear gases produced in the violent collisions of 35 MeV/nucleon$^{64}$Zn projectiles with $^{92}$Mo and $^{197}$Au target nuclei reveal a large degree of alpha particle clustering at low densities. For these gases, temperature and density dependent symmetry energy coefficients have been derived from isoscaling analyses of the yields of nuclei with A $\leq 4$. At densities of 0.01 to 0.05 times the ground state density of symmetric nuclear matter, the temperature and density dependent symmetry energies are 10.7 to 13.5 MeV. These values are much larger than those obtained in mean field calculations. They are in quite good agreement with results of a recently proposed Virial Equation of State calculation.

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Small damping approach in Fermi-liquid theory

The validity of small damping approximation (SDA) for the quasi-classical description of the averaged properties of nuclei at high temperatures is studied within the framework of collisional kinetic theory. The isoscalar collective quadrupole vibrations in hot nuclei are considered. We show that the extension of the SDA, by accounting for the damping of the distribution function $δf$ in the collision integral reduces the rate of variation with temperature of the Fermi surface distortion effects. The damping of the $δf$ in the collision integral increases significantly the collisional width of the giant quadrupole resonance (GQR) for small enough values of the relaxation time. The temperature dependence of the eigenenergy of the GQR becomes much more weaker than in the corresponding SDA case.

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Effects of self-consistency violation in Hartree-Fock RPA calculations for nuclear giant resonances revisited

We provide accurate assessments of the consequences of violations of self-consistency in Hartree-Fock (HF) based random phase approximation (RPA) calculations of the centroid energy $E_{cen}$ of isoscalar and isovector giant resonances of multi-polarities $L=0-3$ in a wide range of nuclei. This is done by carrying out highly accurate HF-RPA calculations neglecting the particle-hole (ph) spin-orbit or Coulomb interaction in the RPA and comparing with the fully self-consistent HF-RPA results. We find that the shifts in the value of $E_{cen}$ due to self-consistency violation associated with the spin-orbit and Coulomb interactions are comparable or larger than the current experimental errors in $E_{cen}$.

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Continuous phase transition and negative specific heat in finite nuclei

The liquid-gas phase transition in finite nuclei is studied in a heated liquid-drop model where the nuclear drop is assumed to be in thermodynamic equilibrium with its own evaporated nucleonic vapor conserving the total baryon number and isospin of the system. It is found that in the liquid-vapor coexistence region the pressure is not a constant on an isotherm indicating that the transition is continuous. At constant pressure, the caloric curve shows some anomalies, namely, the systems studied exhibit negative heat capacity in a small temperature domain. The dependence of this specific feature on the mass and isospin of the nucleus, Coulomb interaction and the chosen pressure is studied. The effects of the presence of clusters in the vapor phase on specific heat have also been explored.

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Determination of the parameters of a Skyrme type effective interaction using the simulated annealing approach

We implement for the first time the simulated annealing method (SAM) to the problem of searching for the global minimum in the hyper-surface of the chi-square function which depends on the values of the parameters of a Skyrme type effective nucleon-nucleon interaction. We undertake a realistic case of fitting the values of the Skyrme parameters to an extensive set of experimental data on the ground state properties of many nuclei ranging from normal to exotic ones. The set of experimental data used in our fitting procedure includes the radii for the valence $1d_{5/2}$ and $1f_{7/2}$ neutron orbits in the $^{17}$O and $^{41}$Ca nuclei, respectively, and the breathing mode energies for several nuclei, in addition to the typically used data on binding energy, charge radii and spin-orbit splitting. We also include in the fit the critical density $ρ_{cr}$ and further constrain the values of the Skyrme parameters by requiring that (i) the quantity $P = 3ρ\frac{dS}{dρ}$, directly related to the slope of the symmetry energy $S$, must be positive for densities up to $3ρ_0$ (ii) the enhancement factor $κ$, associated with the isovector giant dipole resonance, should lie in the range of $0.1 - 0.5$ and (iii) the Landau parameter $G_0^\prime$ is positive at $ρ= ρ_0$. We provide simple but consistent schemes to account for the center of mass corrections to the binding energy and charge radii.

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Critical densities for the Skyrme type effective interactions

We use the stability conditions of the Landau parameters for the symmetric nuclear matter and pure neutron matter to calculate the critical densities for the Skyrme type effective nucleon-nucleon interactions. We find that the critical density can be maximized by adjusting appropriately the values of the enhancement factor $κ$ associated with isovector giant dipole resonance, the quantity $L$ which is directly related to the slope of the symmetry energy and the Landau parameter $G_0^\prime$. However, restricting $κ$, $L$ and $G_0^\prime$ to vary within acceptable limits reduces the maximum value for the critical density $\tildeρ_{cr}$ by $\sim 25%$. We also show that among the various quantities characterizing the symmetric nuclear matter, $\tildeρ_{cr}$ depends strongly on the isoscalar effective mass $m^*/m$ and surface energy coefficient $E_s$. For realistic values of $m^*/m$ and $E_s$ we get $\tildeρ_{cr} = 2ρ_0$ to $ 3ρ_0$ ($ρ_0 = 0.16$fm$^{-3}$).

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Consequences of self-consistency violations in Hartree-Fock random-phase approximation calculations of the nuclear breathing mode energy

We provide for the first time accurate assessments of the consequences of violations of self-consistency in the Hartree-Fock based random phase approximation (RPA) as commonly used to calculate the energy $E_c$ of the nuclear breathing mode. Using several Skyrme interactions we find that the self-consistency violated by ignoring the spin-orbit interaction in the RPA calculation causes a spurious enhancement of the breathing mode energy for spin unsaturated systems. Contrarily, neglecting the Coulomb interaction in the RPA or performing the RPA calculations in the TJ scheme underestimates the breathing mode energy. Surprisingly, our results for the $^{90}$Zr and $^{208}$Pb nuclei for several Skyrme type effective nucleon-nucleon interactions having a wide range of nuclear matter incompressibility ($K_{nm} \sim 215 - 275$ MeV) and symmetry energy ($J \sim 27 - 37$ MeV) indicate that the net uncertainty ($δE_c \sim 0.3$ MeV) is comparable to the experimental one.

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Flow effects on multifragmentation in the canonical model

A prescription to incorporate the effects of nuclear flow on the process of multifragmentation of hot nuclei is proposed in an analytically solvable canonical model. Flow is simulated by the action of an effective negative external pressure. It favors sharpening the signatures of liquid-gas phase transition in finite nuclei with increased multiplicity and a lowered phase transition temperature.

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Shape fluctuations in a Fermi system with nonlinear dissipativity

The contribution of thermal fluctuations to the widths of isoscalar giant multipole resonances (GMR) in heated nuclei is studied. Starting from the collisional kinetic equation, it is shown that an additional contribution to the nuclear friction and the corresponding GMR widths arises due to the nonlinear dissipativity effect. It is also shown that the magnitude of the contributions of the thermal fluctuations to the nuclear friction coefficient and the GMR widths do not exceed 20%.

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Isoscalar giant monopole resonance and its overtone in microscopic and macroscopic models

We calculate the transition density for the overtone of the isosclar giant monopole resonance (ISGMR) from the response to an appropriate external field $\hat{f}_ξ(r)$ obtained using the seemiclassical fluid dynamic approximation and the Hartree-Fock (HF) based random phase approximation (RPA). We determine the mixing parameter $ξ$ by maximizing the ratio of the energy weighted sum for the overtone mode to the total energy weighted sum rule and derive a simple expression for the microscopic transition density associated with the overtone mode. This macroscopic transition density agrees well with that obtained from the HF-RPA calculations. We also point out that the ISGMR and its overtone can be clearly identified by considering the response to the electromagnetic external field $\hat{j}_o(qr)$ .

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Nuclear matter incompressibility coefficient in relativistic and nonrelativistic microscopic models

We systematically analyze the recent claim that nonrelativistic and relativistic mean field (RMF) based random phase approximation (RPA) calculations for the centroid energy E_0 of the isoscalar giant monopole resonance yield for the nuclear matter incompressibility coefficient, K_{nm}, values which differ by about 20%. For an appropriate comparison with the RMF based RPA calculations, we obtain the parameters for the Skyrme force used in the nonrelativistic model by adopting the same procedure as employed in the determination of the NL3 parameter set of an effective Lagrangian used in the RMF model. Our investigation suggest that the discrepancy between the values of K_{nm} predicted by the relativistic and nonrelativistic models is significantly less than 20%.

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Self-Consistent Hartree-Fock Based Random Phase Approximation And The Spurious State Mixing

We use a fully self-consistent Hartree$-$Fock (HF) based continuum random phase approximation (CRPA) to calculate strength functions $S(E)$ and transition densities $ρ_t(r)$ for isoscalar giant resonances with multipolarities $L = 0$, 1 and 2 in $^{80}Zr$ nucleus. In particular, we consider the effects of spurious state mixing (SSM) in the isoscalar giant dipole resonance (ISGDR) and extend the projection method to determine the mixing amplitude of spurious state so that properly normalized $S(E)$ and $ρ_t(r)$ having no contribution due to SSM can be obtained. For the calculation to be highly accurate we use a very fine radial mesh (0.04 fm) and zero smearing width in HF$-$CRPA calculations. We first use our most accurate results as a basis to establish the credibility of the projection method, employed to eliminate the SSM, and then to investigate the consequences of the common violation of self-consistency, in actual implementation of HF based CRPA and discretized RPA (DRPA), as often encountered in the published literature. The HF$-$DRPA calculations are carried out using a typical box size of 12 fm and a very large box of 72 fm, for different values of particle-hole energy cutoff ranging from 50 to 600 MeV.

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Liquid-gas phase transition and its order in finite nuclei

The liquid-gas phase transition in finite nuclei is studied in a heated liquid-drop model where the drop is assumed to be in thermodynamic equilibrium with the vapour emanated from it. Changing pressure along the liquid-gas coexistence line of the systems, symmetric or asymmetric, suggests that the phase transition is a continuous one. This is further corroborated from the study of the thermal evolution of the entropy at constant pressure.

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Has Nucleonic Matter at the Critical Point Been Produced in Recent Multifragmentation Experiments?

For nuclei in five different mass regions the critical temperatures, at which the surface tension vanishes, are derived from information on the liquid branch of the coexistence curve. These critical temperatures increase with increasing mass and, for higher masses are well above recently reported critical temperatures obtained from Fisher Droplet model and percolation model analyses. However, for the lowest mass region nuclei, with 30<A<60, this analysis indicates that nucleonic matter has been produced essentially at the critical point, characterized by Tc and rho_c.

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Caloric Curves and Nuclear Expansion

Nuclear caloric curves have been analyzed using an expanding Fermi gas hypothesis to extract average nuclear densities. In this approach the observed flattening of the caloric curves reflects progressively increasing expansion with increasing excitation energy. This expansion results in a corresponding decrease in the density and Fermi energy of the excited system. For nuclei of medium to heavy mass apparent densities ~ 0.4 rho_0 are reached at the higher excitation energies.

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