Search Results (67 total)

Experimental analyses of moderate-temperature nuclear gases produced in the violent collisions of 35 MeV/nucleon ⁶⁴Zn projectiles with ⁹²Mo and ¹⁹⁷Au target nuclei reveal a large degree of α 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≤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 range from 9.03 to 13.6 MeV. This is much larger than those obtained in mean-field calculations and reflects the clusterization of low-density nuclear matter. The results are in quite reasonable agreement with calculated values obtained with a recently proposed virial equation of state calculation.

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 multipolarities L=0-3 in a wide range of nuclei. This is done by carrying out highly accurate HF-RPA calculations neglecting the particle-hole (p-h) 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 because of self-consistency violation associated with the spin-orbit and Coulomb interactions are comparable or larger than the current experimental errors in E_cen.

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.

The well-known splitting of the isovector giant dipole resonance is traditionally explained as a phenomenon of the nuclear isospin asymmetry (isospin splitting model) or the nuclear deformation. We suggest a new mechanism of the splitting of the giant multipole resonances in spherical neutron-rich nuclei resulting from the interplay of the isovector and isoscalar sounds with different velocities. Our approach is based on the collisional Landau kinetic theory and can be used for description of the splitting phenomena for both the isoscalar and the isovector modes in a wide region of nuclear masses A~40-240. For the isovector dipole modes, the evaluated values of the splitting energy, the relative strength of the main and satellite resonance peaks, and the contribution to the energy-weighted sum rule are in agreement with experimental data.

We implement for the first time the simulated annealing method to the problem of searching for the global minimum in the hypersurface of the χ² 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 ¹⁷O and ⁴¹Ca 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(dS/dρ), directly related to the slope of the symmetry energy S, must be positive for densities up to 3ρ₀; (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 G₀^' is positive at ρ=ρ₀. We provide simple but consistent schemes to account for the center-of-mass corrections to the binding energy and charge radii.

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 appropriately adjusting 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 G₀^′. However, restricting κ,  L, and G₀^′ to vary within acceptable limits reduces the maximum value for the critical density ρ̃_cr by ∼25%. We also show that among the various quantities characterizing the symmetric nuclear matter, ρ̃_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 ρ̃_cr=2ρ₀ to 3ρ₀ (ρ₀=0.16  fm⁻³).

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 ⁹⁰Zr and ²⁰⁸Pb nuclei for several Skyrme type effective nucleon-nucleon interactions having a wide range of nuclear matter incompressibility (K_nm∼215–275  MeV) and symmetry energy (J∼27–37  MeV) indicate that the net uncertainty (δE_c∼0.3  MeV) is comparable to the experimental one.

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.

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%.

The liquid-gas phase transition in infinite asymmetric nuclear matter is studied with the SkM^* interaction. In its light, the said transition is investigated in finite nuclei in a heated liquid-drop model where the drop is assumed to be in thermodynamic equilibrium with the vapor emanated from it. Results for caloric curve, isospin fractionation, heat capacity, and entropy are presented. The results of the calculations in this model are suggestive of a continuous phase transition.

We calculate the transition density for the overtone of the isoscalar giant monopole resonance (ISGMR) from the response to an appropriate external field ∼f̂_ξ(r) obtained using the semiclassical 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 macroscopic 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 ∼j₀(qr).

We systematically analyze the recent claim that nonrelativistic and relativistic mean field (RMF) based random phase approximation (RPA) calculations for the centroid energy E₀ 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 of the Skyrme force used in the nonrelativistic model by adopting the same procedure as employed in the determination of the NL3 parameter set of the effective Lagrangian used in the RMF model. Our investigation suggests that the discrepancy between the values of K_nm predicted by the relativistic and nonrelativistic models is significantly less than 20%.

We study the conditions for the generation and the dynamical evolution of embryonic overcritical vapor bubbles in an overheated asymmetric nuclear matter. We show that the Fermi-surface distortion and memory effects significantly hinder the growth of the bubbles. Moreover, the growth of the bubble is accompanied by characteristic oscillations of its radius R. The characteristic energy E, the damping parameter Γ, and the instability growth rate parameter ζ, depend on the relaxation time τ. The characteristic oscillations disappear in the short relaxation time limit τ→0. Our approach ignores the fluctuations of the particle numbers in the bubble region and the finite diffuse layer of the bubble. The minimum size of the critical radius R^* for which our approach applies is determined by the condition a/R^*≪1, where a=0.5–1 fm is the temperature-dependent surface thickness of the bubble.

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 ⁸⁰Zr nucleus. In particular, we consider the effects of spurious state mixing (SSM) in the isoscalar giant dipole resonance and extend the projection method to determine the mixing amplitude of the 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 use our most accurate results as a basis to (i) establish the credibility of the projection method, employed to eliminate the SSM, and (ii) to assess the consequences of the common violations of self-consistency, often encountered in actual implementation of HF based CRPA and discretized RPA (DRPA) published in the literature, on the values of S(E) and ρ_t(r). This is achieved by varying the radial mesh size, the particle-hole interaction, the smearing parameter, and the particle-hole energy cutoff used in the HF-RPA calculations.

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 ∼0.4ρ₀ are reached at the higher excitation energies.

We present results of microscopic calculations of the strength function S(E) and α-particle excitation cross sections σ(E) for the isoscalar giant dipole resonance (ISGDR). An accurate and general method to eliminate the contributions of spurious state mixing is presented and used in the calculations. Our results provide a resolution to the long standing problem that the nuclear matter incompressibility coefficient K deduced from σ(E) data for the ISGDR is significantly smaller than that deduced from data for the isoscalar giant monopole resonance.

Non-Markovian transport equations for nuclear large amplitude motion are derived from the collisional kinetic equation. The memory effects are caused by Fermi surface distortions and depend on the relaxation time. It is shown that nuclear collective motion and nuclear fission are influenced strongly by memory effects at the relaxation time τ>~5×10^-23 s. In particular, the descent of the nucleus from the fission barrier is accompanied by characteristic shape oscillations. The eigenfrequency and the damping of the shape oscillations depend on the contribution of the memory integral in the equations of motion. The shape oscillations disappear at the short relaxation time regime at τ→0, which corresponds to the usual Markovian motion in the presence of friction forces. We show that the elastic forces produced by the memory integral lead to a significant delay for the descent of the nucleus from the barrier. Numerical calculations for the nucleus ²³⁶U show that due to the memory effect the saddle-to-scission time grows by a factor of about 3 with respect to the corresponding saddle-to-scission time obtained in liquid drop model calculations with friction forces.

The propagation of the isoscalar and isovector sound modes in a hot nuclear matter is considered. The approach is based on the collisional kinetic theory and takes into account the temperature and memory effects. It is shown that the sound velocity and the attenuation coefficient are significantly influenced by the Fermi surface distortion (FSD). The corresponding influence is much stronger for the isoscalar mode than for the isovector one. The memory effects cause a nonmonotonous behavior of the attenuation coefficient as a function of the relaxation time leading to a zero-to-first sound transition with increasing temperature. The mixing of both the isoscalar and the isovector sound modes in an asymmetric nuclear matter is evaluated. The condition for the bulk instability and the instability growth rate in the presence of the memory effects is studied. It is shown that both the FSD and the relaxation processes lead to a shift of the maximum of the instability growth rate to the longer-wavelength region.

The structure of the three-dimension pressure-temperature-asymmetry surface of equilibrium of the asymmetric nuclear matter is studied within the thermal Thomas-Fermi approximation. Special attention is paid to the difference of the asymmetry parameter between the boiling sheet and that of the condensation sheet of the surface of equilibrium. We derive the condition of existence of the regime of retrograde condensation at the boiling of the asymmetric nuclear matter. We have performed calculations of the caloric curves in the case of isobaric heating. We have shown the presence of the plateau region in caloric curves at the isobaric heating of the asymmetric nuclear matter. The shape of the caloric curve depends on the pressure and is sensitive to the value of the asymmetry parameter. We point out that the experimental value of the plateau temperature T≈7 MeV corresponds to the pressure P=10^-2 MeV/fm³ at the isobaric boiling.

We calculate the Coulomb displacement energies (CDEs) of mirror nuclei using the recent parameter set (NL3) in the relativistic mean-field (RMF) model which includes self-coupling of the scalar meson. The results obtained are compared with the available ones calculated in the nonrelativistic Skyrme-Hartree-Fock (SHF) approach that have the best fit to the experimental data. When adjusted to reproduce the charge root-mean-square (rms) radius r_c and the rms radii of the valence orbits, the results of the RMF model for the CDEs agree with those of the SHF model within ∼1%. Our investigation also shows that, although the RMF with the NL3 parameter set reproduces the kink in the isotope variation of r_c, the values obtained for CDEs are too small to account for the experimental values without the addition of the contribution due to long-range correlation effects.

The strength function and partial widths for the direct nucleon decay of the isoscalar giant monopole and dipole resonances are analyzed within an extended continuum-random-phase-approximation approach. Calculations are performed for several medium and heavy mass nuclei with the use of a phenomenological nuclear mean field, the Landau-Migdal particle-hole interaction, and some partial self-consistency conditions. Calculation results are compared with available experimental data.

We study the nuclear isoscalar monopole and dipole compression modes in nuclei within the fluid dynamic approach (FDA) with and without the effect of relaxation. For a wide region of the medium and heavy nuclei, the FDA predicts that the isoscalar giant monopole resonance (ISGMR) and the isoscalar giant dipole resonance (ISGDR) exhaust about 90% of the corresponding model-independent sum rules. In the case of neglecting the effect of relaxation, the FDA, when adjusted to reproduce the centroid energy E0 of the ISGMR, results with centroid energy E1 of the ISGDR which is in agreement with the predictions of the self-consistent Hartree-Fock random-phase approximation calculations and the scaling model but significantly larger than the experimental value. We also show that the FDA leads to the correct hydrodynamic limit for the ratio (E1/E0)_FDA. We find that the ratio (E1/E0)_FDA depends on the relaxation time and approaches the preliminary experimental value (E1/E0)_exp=1.5±0.1 in a short relaxation time limit.

A microscopic description of the excitation of isoscalar giant monopole resonance (ISGMR) and quadrupole resonance (ISGQR) in ²⁸Si, ⁴⁰Ca, ⁵⁸Ni, and ¹¹⁶Sn by 240 MeV bombarding energy α particles is provided based on self-consistent Hartree-Fock– (HF-) random-phase-approximation (RPA) approach and the distorted-wave Born approximation (DWBA). The folding model is used to obtain optical potentials from the HF ground-state density and a density dependent Gaussian nucleon-α interaction (V_αn). The parameters of V_αn are determined by fitting experimentally measured angular distributions for the case of elastic scattering. Angular distributions of inelastically scattered α particles for ISGMR and ISGQR excitations of the target nucleus are obtained using the folding model DWBA and both microscopic (RPA) and hydrodynamical (collective model) transition densities (found from HF ground state densities). A possible overestimation of the energy weighted sum rules and shifts of centroid energies due to the collective-model-based DWBA reaction description is reported.

The instability of a Fermi-liquid drop with respect to bulk density distortions is considered. It is shown that the presence of the surface strongly reduces the growth rate of the bulk instability of the finite Fermi-liquid drop because of the anomalous dispersion term in the dispersion relation. The instability growth rate is reduced due to the Fermi-surface distortions and the relaxation processes. The dependence of the bulk instability on the multipolarity of the particle density fluctuations is demonstrated for two nuclei ⁴⁰Ca and ²⁰⁸Pb. It is shown that the formation of the decay modes (fission or multifragmentation) of an unstable Fermi-liquid drop depends on the location of the radial wave number q on the slopes of the instability growth rate Γ(q) and is different for both nuclei ⁴⁰Ca and ²⁰⁸Pb.

We study the important effects of Fermi surface distortion on the isoscalar giant monopole resonance (ISGMR), within a Fermi-liquid drop model, by considering consistently the effects on nuclear incompressibility coefficients and the boundary conditions needed to determine the energy of the ISGMR. There is a significant difference between the static nuclear incompressibility K, derived as a stiffness coefficient with respect to an adiabatic change in the bulk density, and the dynamic one K^′ associated with the zero sound velocity. We show that the enhancement in the energy of the ISGMR, the lowest breathing mode, which is due to the renormalization of K into K^′ is strongly suppressed by the effects of the Fermi surface distortion on the boundary condition. This is not the case for higher breathing modes such as the overtone. We also discuss, in particular, the effects of the Fermi surface distortion on energy weighted sums for the monopole mode and on the constrained and the scaling incompressibility coefficients and their relation to the liquid drop one.