The density and excitation energy dependence of symmetry energy and symmetry free energy for finite nuclei are calculated microscopically in a microcanonical framework taking into account thermal and expansion effects. A finite-range momentum and density dependent two-body effective interaction is employed for this purpose. The role of mass, isospin and equation of state (EoS) on these quantities is also investigated; our calculated results are in consonance with the available experimental data.
The thermodynamic properties of hot nuclei are described within the canonical and microcanonical ensemble approaches. These approaches are derived based on the solutions of the BCS and self-consistent quasiparticle random-phase approximation at zero temperature embedded into the canonical and microcanonical ensembles. The obtained results agree well with the recent data extracted from experimental level densities by Oslo group for $^{94}$Mo, $^{98}$Mo, $^{162}$Dy and $^{172}$Yb nuclei.
Recent progress in the theory of fission of hot nuclei is reported. We discuss in particular the properties of the friction formfactor as function of the deformation (and possibly of the temperature) which are necessary to reproduce data concerning fission of hot nuclei and its accompanying light particle and $γ$-ray emission. Recent theoretical work gives support to a phenomenological friction form factor (proposed some time ago), which is weak for compact shapes and increases on the way to scission.
A novel mechanism of prompt nuclear fragmentation is proposed. Assuming micro-canonical or canonical equilibrium, it is shown that a strong enhancement of the accessible phase space volume, due to the diffuceness of the nuclear surface, leads to dynamical instabilities of hot nuclei and to prompt fragmentation. Equations are derived for the transition temperature T_T, for which the thermodynamical surface tension vanishes, as well as for the thermodynamical fissility parameter chi_td.
In this paper, we calculate cross sections for charged-current neutrino-nucleus processes occuring under presupernova conditions. To treat thermal effects we extend self-consistent Skyrme-QRPA calculations to finite temperature by using the formalism of thermo field dynamics. The numerical results are presented for the sample nuclei, $^{56}$Fe and $^{82}$Ge
We study the systematics of the giant dipole resonance width $Γ$ in hot rotating nuclei as a function of temperature $T$, spin $J$ and mass $A$. We compare available experimental results with theoretical calculations that include thermal shape fluctuations in nuclei ranging from A=45 to A=208. Using the appropriate scaled variables, we find a simple phenomenological function $Γ(A,T,J)$ which approximates the global behavior of the giant dipole resonance width in the liquid drop model. We reanalyze recent experimental and theoretical results for the resonance width in Sn isotopes and $^{208}$Pb…
The mass and isotope dependence of limiting temperatures for hot nuclei are investigated. The predicted mass dependence of limiting temperatures is in good agreement with data derived from the caloric curve data. The predicted isotope distribution of limiting temperatures appears to be a parabolic shape and its centroid is not located at the isotope on the $β$-stability line(T=0) but at neutron-rich side. Our study shows that the mass and isotope dependence of limiting temperatures depend on the interaction and the form of surface tension and its isopin dependence sensitively.
We have studied the properties of hot $^{234,236}$U and $^{240}$Pu nuclei in the framework of relativistic mean field formalism. The recently developed FSUGarnet and IOPB-I parameter sets are implemented for the first time to deform nuclei at finite temperature. The results are compared with the well-known NL3 set. The said isotopes are structurally important because of the thermally fissile nature of $^{233,235}$U and $^{239}$Pu as these nuclei ($^{234,236}$U and $^{240}$Pu) are formed after the absorption of a thermal neutron, which undergoes fission. Here, we have evaluated the nuclear prop…
The initial production and dynamical expansion of hot spherical nuclei are examined as the first stage in the projectile-multifragmentation process. The initial temperatures, which are necessary for entering the adiabatic spinodal region, as well as the minimum temperatures and densities, which are reached in the expansion, significantly differ for hard and soft equations of state. Additional initial compression, occurring in central collisions leads most likely to a qualitatively different multifragmentation mechanism. Recent experimental data are discussed in relation to the results of the p…
We develop a self-consistent description of hot nuclei within the relativistic Thomas--Fermi approximation using the relativistic mean-field model for nuclear interactions. The temperature dependence of the symmetry energy and other physical quantities of a nucleus are calculated by employing the subtraction procedure in order to isolate the nucleus from the surrounding nucleon gas. It is found that the symmetry energy coefficient of finite nuclei is significantly affected by the Coulomb polarization effect. We also examine the dependence of the results on nuclear interactions and make a compa…
The fusion process and the competition between fission and n, p and alpha-particle emission is studied. The calculations are performed for nuclei at excitation energies from 80 MeV up to about 300 MeV. The nuclear fission is described by a Langevin equation coupled to the Master equation for particle evaporation. A significant influence of the initial spin distribution on the prescission particles multiplicities is found.
We calculate the isovector response function of hot nuclear matter using various effective Skyrme interactions. For Skyrme forces with a small effective mass the strength distribution is found to be nearly independent of temperature, and shows little collective effects. In contrast effective forces with an effective mass close to unity produce sizeable collective effects at zero temperature which disappear at temperatures of a few MeV. We discuss the relevance of these results for the saturation of the multiplicity of photons emitted by the giant dipole resonance in hot nuclei beyond $T$=3 MeV…
We present a general discussion of the mean field dynamics of finite nuclei prepared under extreme conditions of temperature and pressure. We compare the prediction of semi-classical approximation with complete quantum simulations. Many features of the dynamics are carefully studied such as the collective expansion, the evaporation process, the different time-scale... This study points out many quantitative differences between quantum and semi-classical approaches. Part of the differences are related to numerical features inherent in semi-classical simulations but most of them are a direct con…
Using the thermal quasiparticle random phase approximation, we study the process of neutrino and antineutrino capture on hot nuclei in supernova environments. For the sample nuclei $^{56}$Fe and $^{82}$Ge we perform a detailed analysis of thermal effects on the strength distribution of allowed Gamow-Teller transitions which dominate low-energy charged-current neutrino reactions. The finite temperature cross sections are calculated taking into account the contributions of both allowed and forbidden transitions. The enhancement of the low-energy cross sections is explained by considering thermal…
We study inelastic neutrino scattering off hot nuclei for temperatures relevant under supernova conditions. The method we use is based on the quasiparticle random phase approximation extended to finite temperatures within the thermo field dynamics (TQRPA). The method allows a transparent treatment of upward and downward transitions in hot nuclei, avoiding the application of Brink's hypothesis. For the sample nuclei $^{56}$Fe and $^{82}$Ge we perform a detailed analysis of thermal effects on the strength distributions of allowed Gamow-Teller (GT) transitions which dominate the scattering proces…
We investigate the collective response function and the energy-weighted sums m_k for isovector mode in hot nuclei. The approach is based on the collisional kinetic theory and takes into consideration the temperature and the relaxation effects. Taking into account a connection between the isovector sound mode and the corresponding surface vibrations we have established the A-dependence of the enhancement factor for the isovector sum rule in a good agreement with experimental data. We have shown that the enhancement factor for the "model independent" sum m_1 is only slightly sensitive to the tem…
A phenomenological macroscopic model of the Giant Dipole Resonance (GDR) damping width of cold- and hot-nuclei with ground-state spherical and near-spherical shapes is developed. The model is based on a generalized Fermi Liquid model which takes into account the nuclear surface dynamics. The temperature dependence of the GDR damping width is accounted for in terms of surface- and volume-components. Parameter-free expressions for the damping width and the effective deformation are obtained. The model is validated with GDR measurements of the following nuclides, $^{39,40}$K, $^{42}$Ca, $^{45}$Sc…
We combine the thermal QRPA approach with the Skyrme energy density functional theory (Skyrme-TQRPA) for modelling the process of electron capture on nuclei in supernova environment. For a sample nucleus, $^{56}$Fe, the Skyrme-TQRPA approach is applied to analyze thermal effects on the strength function of GT$_+$ transitions which dominate electron capture at $E_e\le 30$~MeV. Several Skyrme interactions are used in order to verify the sensitivity of the obtained results to the Skyrme force parameters. Finite-temperature cross sections are calculated and the results are compared with those of t…
Finite temperature Hartree-Fock-Bogoliubov calculations are performed in Sn isotopes using Skyrme and zero-range, density-dependent pairing interactions. For both stable and very neutron-rich nuclei the critical temperature at which pairing correlations vanish is independent of the volume/surface nature of the pairing interaction. The value of the critical temperature follows approximatively the empirical rule T$_c$ $\simeq$ 0.5 $Δ_{T=0}$ for all the calculated isotopes, showing that the critical temperature could be deduced from the pairing gap at zero temperature. On the other hand, the pair…
Fission dynamics of excited nuclei is studied in the framework of Langevin equation. The one body wall-and-window friction is used as the dissipative force in the Langevin equation. In addition to the usual wall formula friction, the chaos weighted wall formula developed earlier to account for nonintegrability of single-particle motion within the nuclear volume is also considered here. The fission rate calculated with the chaos weighted wall formula is found to be faster by about a factor of two than that obtained with the usual wall friction. The systematic dependence of fission width on temp…
Nuclear pairing properties are studied within an approach that includes the quasiparticle-number fluctuation (QNF) and coupling to the quasiparticle-pair vibrations at finite temperature and angular momentum. The formalism is developed to describe non-collective rotations about the symmetry axis. The numerical calculations are performed within a doubly-folded equidistant multilevel model as well as several realistic nuclei. The results obtained for the pairing gap, total energy and heat capacity show that the QNF smoothes out the sharp SN phase transition and leads to the appearance of a therm…
The hot rotating nuclei could be formed in the complete and incomplete fusion reaction of two heavy ions. At low bombarding energies the reaction goes via compound nucleus formation and subsequent evaporation of charged particles, neutrons and $γ$-rays. However, with increasing the energy of the projectile, the emission of particles during the equilibration process becomes more and more probable. This effect can be estimated by the Heavy-Ion Phase-Space Exploration (HIPSE) code which describes the production of clusters of various size from nucleons initially in the target or projectile. This …
The approach in a theory of collective excitations in hot nuclei exploring the formalism of thermo field dynamics and the model Hamiltonian consisting of a mean field, the BCS paring interaction and long-range particle-hole effective forces is reexamined. In contrast with earlier studies it is found that a wave function of a thermal phonon is depended not only on the Fermi-Dirac thermal occupation numbers of Bogoliubov quasiparticles consisting the phonon but on the Bose thermal occupation numbers of the phonon as well. This strongly affects a thermal phonon couplings due to renormalizing of a…
Employing a cranking Hamiltonian, in the static path approximation to the partition function, we have studied the behaviour of the moment of inertia of $^{64}Zn$ at a few values of temperatures as a function of the rotation frequency. At a low temperature T = 0.5 MeV and J=16 rotational alignment of $0g_{9/2}$ orbitals takes place. But at a high temperature T = 2.0 MeV about 40 - 45$\%$ of all the angular momenta are generated by the alignment of the same orbitals. This should imply a decrease in collectivity for all the spins at high temperatures.
We investigate the collective response function and the energy-weighted sums (EWS) $m_k$ for isovector mode in hot nuclei. The approach is based on the collisional kinetic theory and takes into consideration the temperature and the relaxation effects. We have evaluated the temperature dependence of the adiabatic, $E_1=\sqrt{m_1/m_{-1}}$, and scaling, $E_3=\sqrt{m_3/m_1}$, energy centroids of the isovector giant dipole resonances (IVGDR). The centroid energy $E_3$ is significantly influenced by the Fermi surface distortion effects and, in contrast to the isoscalar mode, shows much weaker variat…
The density profile of a hot nuclear system produced in intermediate energy heavy ion collisions is studied in a microcanonical formulation with a momentum and density dependent finite range interaction. The caloric curve and the density evolution with excitation are calculated for a number of systems for the equilibrium mononuclear configuration; they compare favorably with the recent experimental data. The studied density fluctuations are seen to build up rapidly beyond an excitation energy of 8 MeV/u indicating the instability of the system towards nuclear disassembly. Explicit introduction…
The pairing gaps, heat capacities and level densities are calculated within the BCS-based quasiparticle approach including the effect of thermal fluctuations on the pairing field within the pairing model plus noncollective rotation along the z axis for $^{60}$Ni and $^{72}$Ge nuclei. The analysis of the numerical results obtained shows that, in addition to the pairing gap, the heat capacity can also serve as a good observable to detect the appearance of the pairing reentrance in hot rotating nuclei, whereas such signature in the level density is rather weak.
The fission of highly excited compound nuclei formed in heavy ion induced fusion reactions has emerged as a topic of considerable interest in the recent years. Dissipative dynamical models based on the Langevin equation were developed and were applied successfully for fission dynamics of highly excited heavy nuclei. However, Wall Friction(WF), the standard version of nuclear friction when incorporated in the Langevin dynamical model was not able to reproduce simultaneously experimental data for both prescission neutron multiplicity and fission probability. Consequently, an empirical reduction …
The development of nuclear shapes under the extreme conditions of high spin and/or temperature is examined. Scaling properties are used to demonstrate universal properties of both thermal expectation values of nuclear shapes as well as the minima of the free energy, which can be used to understand the Jacobi transition. A universal correlation between the width of the giant dipole resonance and quadrupole deformation is found, providing a novel probe to measure the nuclear deformation in hot nuclei.
The behavior of several nuclear properties with temperature is analyzed within the framework of the Finite Temperature Hartree-Fock-Bogoliubov (FTHFB) theory with the Gogny force and large configuration spaces. Thermal shape fluctuations in the quadrupole degree of freedom, around the mean field solution, are taken into account with the Landau prescription. As representative examples the nuclei $^{164}$Er, $^{152}$Dy and $^{192}$Hg are studied. Numerical results for the superfluid to normal and deformed to spherical shape transitions are presented. We found a substantial effect of the fluctuat…
We point out that during the supernova II type explosion the thermodynamical condition of stellar matter between the protoneutron star and the shock front corresponds to the nuclear liquid-gas phase coexistence region, which can be investigated in nuclear multifragmentation reactions. We have demonstrated, that neutron-rich hot heavy nuclei can be produced in this region. The production of these nuclei may influence dynamics of the explosion and contribute to the synthesis of heavy elements.
This review article is focused on the tremendous progress realized during the last fifteen years in the understanding of multifragmentation and its relationship to the liquid-gas phase diagram of nuclei and nuclear matter. The explosion of the whole nucleus, early predicted by Bohr [N. Bohr, Nature 137 (1936) 351], is a very complex and rich subject which continues to fascinate nuclear physicists as well as theoreticians who extend the thermodynamics of phase transitions to finite systems.
We present shell-model calculations showing that residual interaction-induced configuration mixing enhances the rate of neutral current de-excitation of thermally excited nuclei into neutrino-antineutrino pairs. Though our calculations reinforce the conclusions of previous studies that this process is the dominant source of neutrino pairs near the onset of neutrino trapping during stellar collapse, our shell-model result has the effect of increasing the energy of these pairs, possibly altering their role in entropy transport in supernovae.
The decrease in the symmetry energy of hot nuclei populated in $^{58}$Ni + $^{58}$Ni, $^{58}$Fe + $^{58}$Ni and $^{58}$Fe + $^{58}$Fe reactions at beam energies of 30, 40, and 47 MeV/nucleon, as a function of excitation energy is studied. It is observed that this decrease is mainly a consequence of increasing expansion or decreasing density rather than the increasing temperature. The results are in good agreement with the recently reported microscopic calculation based on the Thomas-Fermi approach. An empirical relation to study the symmetry energy of finite nuclei in various mass region is pr…
The effect of temperature on the evolution of the isovector dipole and isoscalar quadrupole excitations in $^{68}$Ni and $^{120}$Sn nuclei is studied within the fully self-consistent finite temperature quasiparticle random phase approximation framework, based on the Skyrme-type SLy5 energy density functional. The new low-energy excitations emerge due to the transitions from thermally occupied states to the discretized continuum at finite temperatures, whereas the isovector giant dipole resonance is not strongly impacted by the increase of temperature. The radiative dipole strength at low-energ…
A production mechanism of highly excited nuclei formed in violent collisions in the Fermi energy domain is investigated. The collision of two nuclei is decomposed into several stages which are treated separately. Simplified exciton concept is used for the description of pre-equilibrium emission. A modified spectator-participant scenario is used where motion along classical Coulomb trajectories is assumed. The participant and one of the spectator zones undergo incomplete fusion. Excitation energies of both cold and hot fragment are determined. Results of the calculation are compared to recent e…
Simulations based on experimental data obtained from multifragmenting quasifused nuclei produced in central 129Xe + natSn collisions have been used to deduce event by event freeze-out properties on the thermal excitation energy range 4-12 AMeV. From these properties and temperatures deduced from proton transverse momentum fluctuations constrained caloric curves have been built. At constant average volumes caloric curves exhibit a monotonous behaviour whereas for constrained pressures a backbending is observed. Such results support the existence of a first order phase transition for hot nuclei.
The production of light nuclei and hypernuclei together with heavy baryons, both hyperons and $Δ$-baryons, in low density matter as found in stellar environments such as supernova or binary mergers is studied within relativistic mean-field models. Five light nuclei were considered together with three light hypernuclei. The presence of both hyperons and $Δ$-baryons shift the dissolution of clusters to larger densities and increase the abundance of clusters. This effect is larger the smaller the charge fraction and the higher the temperature. The couplings of the $Δ$-baryons were chosen imposing…
By using freeze-out properties of multifragmenting hot nuclei produced in quasifusion central $^{129}$Xe+$^{nat}$Sn collisions at different beam energies (32, 39, 45 and 50 AMeV) which were estimated by means of a simulation based on experimental data collected by the $4π$ INDRA multidetector, heat capacity in the thermal excitation energy range 4 - 12.5 AMeV was calculated from total kinetic energies and multiplicities at freeze-out. The microcanonical formulation was employed. Negative heat capacity which indicates a first order phase transition for finite systems is observed and confirms pr…
Mass and isospin dependence of symmetry energy coefficients $a_{sym}$ of finite nuclei is investigated with the measured nuclear masses incorporating the liquid drop mass formula. The enhanced $a_{sym}$ for nearly symmetric nuclei are observed. To describe the mass and isospin dependence of $a_{sym}$, a modified formula based on the conventional surface-symmetry term is proposed and the corresponding rms deviation of nuclear masses is checked.
The production mechanism of highly excited nuclei in the Fermi energy domain is investigated. A phenomenological approach, based on the exciton model, is used for the description of pre-equilibrium emission. A model of deep inelastic transfer is employed for the peripheral collisions in the post-pre-equilibrium stage. An approach to describe more central collisions is proposed. A geometric overlap formula is employed in a way suitable for given energy domain. A simple geometric approach describing the interaction of participant and spectator zones is used to determine the incomplete fusion cha…
The fusion-by-diffusion model proposed by Swiatecki {\it et al.} [Phys. Rev. C71, 014602 (2005)] has provided a simple and convenient tool to estimate evaporation residue cross sections for superheavy nuclei. I extend this model by taking into account deformation of the target nucleus, and discuss the role of orientation of deformed target in hot fusion reactions at energies around the Coulomb barrier. To this end, I introduce an injection point for the diffusion process over an inner barrier which depends on the orientation angle. I apply this model to the $^{48}$Ca+$^{248}$Cm reaction and sh…
Simulations based on experimental data obtained from multifragmenting quasi-fused nuclei produced in central $^{129}$Xe + $^{nat}$Sn collisions have been used to deduce event by event freeze-out properties in the thermal excitation energy range 4-12 AMeV [Nucl. Phys. A809 (2008) 111]. From these properties and the temperatures deduced from proton transverse momentum fluctuations, constrained caloric curves have been built. At constant average volumes caloric curves exhibit a monotonic behaviour whereas for constrained pressures a backbending is observed. Such results support the existence of a…
The pairing correlations in hot nuclei $^{162}$Dy are investigated in terms of the thermodynamical properties by covariant density functional theory. The heat capacities $C_V$ are evaluated in the canonical ensemble theory and the paring correlations are treated by a shell-model-like approach, in which the particle number is conserved exactly. A S-shaped heat capacity curve, which agrees qualitatively with the experimental data, has been obtained and analyzed in details. It is found that the one-pair-broken states play crucial roles in the appearance of the S shape of the heat capacity curve. …
Procedures for projecting angular momentum in a model describing a hot nucleus that takes into account large-amplitude quadrupole fluctuations are discussed. Particular attention is paid to the effect angular-momentum projection has on the observables associated with the $γ$-decay of the giant-dipole resonance (GDR). We also elaborate on which of the different projection methods provides the best overall description of the GDR, including angular distributions. The main consequence of angular-momentum projection is the appearance of an effective volume element in the integrals associated with t…
The phonon damping model (PDM) is extended to include the effect of angular momentum at finite temperature. The model is applied to the study of damping of giant dipole resonance (GDR) in hot and noncollectively rotating spherical nuclei. The numerical results obtained for Mo88 and Sn106 show that the GDR width increases with both temperature T and angular momentum M. At T > 4 MeV and M<= 60 hbar the increase in the GDR width slows down for Sn106, whereas at M<= 80 hbar the GDR widths in both nuclei nearly saturate. By adopting the nuclear shear viscosity extracted from fission data at T= 0, i…
Effects of the density dependence of the nuclear symmetry energy on ground-state properties of superheavy nuclei are studied in the relativistic mean-field theory. It is found that the softening of the symmetry energy plays an important role in the empirical shift [Phys. Rev. C 67, 024309 (2003)] of spherical orbitals in superheavy nuclei. The calculation based on the relativistic mean-field models NL3 and FSUGold supports the double shell closure in $^{292}120$ with the softening of the symmetry energy. In addition, the significant effect of the density dependence of the symmetry energy on th…
By the use of the latest experimental data on the spectra of $^{133}$Sb and $^{131}$Sn and on the analysis of properties of other odd nuclei adjacent to doubly magic closed shells the isospin dependence of a mean spin-orbit potential is defined. Such a dependence received the explanation in the framework of different theoretical approaches.
An abnormal production of events with almost equal-sized fragments was theoretically proposed as a signature of spinodal instabilities responsible for nuclear multifragmentation in the Fermi energy domain. On the other hand finite size effects are predicted to strongly reduce this abnormal production. High statistics quasifusion hot nuclei produced in central collisions between Xe and Sn isotopes at 32 and 45 AMeV incident energies have been used to definitively establish, through the experimental measurement of charge correlations, the presence of spinodal instabilities. N/Z influence was als…
The density of accessible levels at low spin in the (^3He,αγ) reaction has been extracted for the ^{161,162}Dy and ^{171,172}Yb nuclei. The entropy of the even-odd and even-even nuclei has been deduced as a function of excitation energy, and found to reach a maximum of 15 k_B before neutron evaporation. The entropy of one quasi-particle outside an even-even core is found to be 1.70(15) k_B. This quasi-particle picture of hot nuclei is well accounted for within a simple pairing model. The onset of two, four and six quasi-particle excitations in the ^{162}Dy and ^{172}Yb nuclei is discussed and …
The A-dependence of models for the attenuation of hadron production in semi-inclusive deep-inelastic scattering on a nucleus is investigated for realistic matter distributions. It is shown that the dependence for a pure partonic (absorption) mechanism is more complicated than a simple $A^{2/3}$ ($A^{1/3}$) behavior, commonly found when using rectangular or Gaussian distributions, but that the A-dependence may still be indicative for the dominant mechanism of hadronization.
The dependence of fusion cross section on the isotopic composition of colliding nuclei is analysed within the dinuclear system concept for compound nucleus formation. Probabilities of fusion and surviving probabilities, ingredients of the evaporation residue cross sections, depend decisively on the neutron numbers of the dinuclear system. Evaporation residue cross sections for the production of actinides and superheavy nuclei, listed in table form, are discussed and compared with existing experimental data. Neutron-rich radioactive projectiles are shown to lead to similar fusion cross sections…
This work aim to study the various thermal characteristics of nuclei in view of the saturation and critical behavior of infinite nuclear matter. The free energy of a nucleus is parametrized using the density and temperature-dependent liquid-drop model and interaction among nucleons is worked out within the effective relativistic mean-field theory (E-RMF). The effective mass (m,$^*$) and critical temperature of infinite symmetric nuclear matter ($T_c$) of a given E-RMF parameter force play a seminal role in the estimation of thermal properties. A larger (m$^*$) and $T_c$ of the E-RMF set estima…
A finite range density and momentum dependent effective interaction is used to calculate the density and temperature dependence of the symmetry energy coefficient Csym(rho,T) of infinite nuclear matter. This symmetry energy is then used in the local density approximation to evaluate the excitation energy dependence of the symmetry energy coefficient of finite nuclei in a microcanonical formulation that accounts for thermal and expansion effects. The results are in good harmony with the recently reported experimental data from energetic nucleus-nucleus collisions.
The description of collective motion in nuclei at finite temperature using the framework of the random phase approximation is discussed. We focus on the special case of the isovector response function of hot nuclear matter using various effective Skyrme interactions.
The temperature dependence of the symmetry energy and the symmetry free energy coefficients of atomic nuclei is investigated in a finite temperature Thomas-Fermi framework employing the subtraction procedure. A substantial decrement in the symmetry energy coefficient is obtained for finite systems,contrary to those seen for infinite nuclear matter at normal and somewhat subnormal densities. The effect of the coupling of the surface phonons to the nucleonic motion is also considered; this is found to decrease the symmetry energies somewhat at low temperatures.
The liquid-gas phase transition in hot neutron-rich nuclear matter is investigated within a self-consistent thermal model using different interactions with or without isospin and/or momentum dependence. The boundary of the phase-coexistence region is shown to be sensitive to the density dependence of the nuclear symmetry energy as well as the isospin and momentum dependence of the nuclear interaction.
