We study the liquid-gas phase transition of stellar matter with the inclusion of the finite-size effect from surface and Coulomb energies. The equilibrium conditions for two coexisting phases are determined by minimizing the total free energy including the surface and Coulomb contributions, which are different from the Gibbs conditions used in the bulk calculations. The finite-size effect can significantly reduce the region of the liquid-gas mixed phase. The influence of the symmetry energy on the liquid-gas phase transition is investigated with the inclusion of finite-size effects. It is found that the slope of the symmetry energy plays an important role in determining the boundary and properties of the mixed phase.
We examine how nuclear masses are related to the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculate nuclear masses in a way dependent on the equation of state of asymmetric nuclear matter. We find by comparison with empirical two-proton separation energies that a smaller symmetry energy at subnuclear densities, corresponding to a larger density symmetry coefficient L, is favored. This tendency, which is clearly seen for nuclei that are neutron-rich, nondeformed, and light, can be understood from the property of the surface symmetry energy in a compressibl…
The self-consistent Thomas-Fermi approximation is an essential method for studying the non-uniform nuclear matter with relativistic mean-field theory. In this method, the nucleon distribution in the Wigner-Seitz cell is obtained self-consistently. We make a detailed comparison between the present results and previous calculations in the Thomas-Fermi approximation with a parameterized nucleon distribution that has been adopted in the widely used Shen equation of state.
This article provides a concise review of selected topics in the many-body physics of low density nuclear systems. The discussion includes the condensation of alpha particles in supernova envelopes, formation of three-body bound states and the BEC-BCS crossover in dilute nuclear matter, and neutrino production in $S$-wave paired superfluid neutron matter.
At low energies nucleon-nucleon interactions are resonant and therefore supernova matter at subnuclear densities has many similarities to atomic gases with interactions dominated by a Feshbach resonance. We calculate the rates of neutrino processes involving nucleon-nucleon collisions and show that these are enhanced in mixtures of neutrons and protons at subnuclear densities due to the large scattering lengths. As a result, the rate for neutrino pair bremsstrahlung and absorption is significantly larger below 10^{13} g cm^{-3} compared to rates used in supernova simulations.
We examine how the properties of inhomogeneous nuclear matter at subnuclear densities depend on the density dependence of the symmetry energy. Using a macroscopic nuclear model we calculate the size and shape of nuclei in neutron star matter at zero temperature in a way dependent on the density dependence of the symmetry energy. We find that for smaller symmetry energy at subnuclear densities, corresponding to larger density symmetry coefficient L, the charge number of nuclei is smaller, and the critical density at which matter with nuclei or bubbles becomes uniform is lower. The decrease in t…
We point out similarity of thermodynamic conditions reached in intermediate energy nuclear collisions and in supernova explosions. We show that a statistical approach, which has been previously applied for nuclear multifragmentation reactions, can be very useful for description of electro-neutral stellar matter. Then properties of hot unstable nuclei extracted from analysis of multifragmentation data can be used for construction of a realistic equation of state of supernova matter.
Structure of hot dense matter at subnuclear densities is investigated by quantum molecular dynamics (QMD) simulations. We analyze nucleon distributions and nuclear shapes using two-point correlation functions and Minkowski functionals to determine the phase-separation line and to classify the phase of nuclear matter in terms of the nuclear structure. Obtained phase diagrams show that the density of the phase boundaries between the different nuclear structures decreases with increasing temperature due to the thermal expansion of nuclear matter region. The critical temperature for the phase sepa…
We study the non-uniform nuclear matter using the self-consistent Thomas--Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. At each temperature $T$, proton fraction $Y_p$, and baryon mass density $ρ_B$, we determine the thermodynamically favored state by minimizing the free energy with respect to the radius of the Wigner--Seitz cell, while the nucleon distribution in the cell can be determined self-consistently in the Thomas--Fermi approximation. A detailed comparison is made b…
Structure of cold nuclear matter at subnuclear densities for the proton fraction $x=0.5$, 0.3 and 0.1 is investigated by quantum molecular dynamics (QMD) simulations. We demonstrate that the phases with slablike and rodlike nuclei, etc. can be formed dynamically from hot uniform nuclear matter without any assumptions on nuclear shape, and also systematically analyze the structure of cold matter using two-point correlation functions and Minkowski functionals. In our simulations, we also observe intermediate phases, which has complicated nuclear shapes. It is found out that these phases can be c…
Non uniform structures of the nucleon matter at subnuclear densities are numerically studied by means of the density functional theory with relativistic mean-fields coupled with the electric field. A particular role of the charge screening effects is demonstrated.
Nuclear matter is considered to be inhomogeneous at subnuclear densities that are realized in supernova cores and neutron star crusts, and the structures of nuclear matter change from spheres to cylinders, slabs, cylindrical holes and spherical holes as the density increases. In this letter, we discuss other possible structures, that is, gyroid and double-diamond morphologies, which are periodic bicontinuous structures discovered in a block copolymer. Utilizing the compressible liquid drop model, we evaluate their surface and Coulomb energies and show that there is a chance of gyroid appearanc…
Structure of cold and hot dense matter at subnuclear densities is investigated by quantum molecular dynamics (QMD) simulations. Obtained phase diagrams show that the density of the phase boundaries between the different nuclear structures decreases with increasing temperature due to the thermal expansion of nuclear matter region.
During the collapse of massive stars, and the supernova type-II explosions, stellar matter reaches densities and temperatures which are similar to the ones obtained in intermediate-energy nucleus-nucleus collisions. The nuclear multifragmentation reactions can be used for determination of properties of nuclear matter at subnuclear densities, in the region of the nuclear liquid-gas phase transition. It is demonstrated that the modified properties of hot nuclei (in particular, their symmetry energy) extracted from the multifragmentation data can essentially influence nuclear composition of stell…
Following the basic prescriptions of the relativistic Tsallis' non-extensive thermostatistics, we investigate from a phenomenological point of view the relevance of non-extensive statistical effects on relativistic heavy-ion collisions observable, such as rapidity spectra of net proton production, transverse momentum distributions and transverse momentum fluctuations. Moreover, we study the nuclear and the subnuclear equation of state, investigating the critical densities of a phase transition to a hadron-quark-gluon mixed phase by requiring the Gibbs conditions on the global conservation of t…
The density and temperature dependence of the nuclear symmetry free energy is investigated using microscopic two- and three-body nuclear potentials constructed from chiral effective field theory. The nuclear force models and many-body methods are benchmarked to properties of isospin-symmetric nuclear matter in the vicinity of the saturation density as well as the virial expansion of the neutron matter equation of state at low fugacities. The free energy per particle of isospin-asymmetric nuclear matter is calculated assuming a quadratic dependence of the interaction contributions on the isospi…
We formulate a statistical model for description of nuclear composition and equation of state of stellar matter at subnuclear densities and temperature up to 20 MeV, which are expected during the collapse and explosion of massive stars. The model includes nuclear, electromagnetic and weak interactions between all kinds of particles, under condition of statistical equilibrium. We emphasize importance of realistic description of the nuclear composition for understanding stellar dynamics and nucleosynthesis. It is demonstrated that the experience accumulated in studies of nuclear multifragmentati…
Structure of cold dense stellar matter at subnuclear densities is investigated with quantum molecular dynamics (QMD). We succeeded in showing that the phases with slab-like and rod-like nuclei etc. can be formed dynamically without any assumptions on the nuclear shape. Our result suggests the existence of these kinds of phases in neutron star crusts.
We review our recent works about ``pasta'' structures following the first-order phase transition in dense matter, which correspond to the structured mixed phases with geometrical symmetries. Three kinds of phase transitions at different density ranges are examined as the stages of pasta structures: liquid-gas phase transition at subnuclear density, kaon condensation and hadron-quark phase transition at high density. Charge density as well as particle density is non-uniform there. A consistent treatment of the Coulomb potential and the particle densities is presented and a peculiar role of the …
Correlation effects in nuclear matter at finite temperatures are studied for subnuclear densities ($ρ<ρ_0$) and medium excitation energy, where a nonrelativistic potential approach is possible. A quantum statistical approach is given, where clusters are treated under the influence of a clustered medium treated within a mean field approximation. Spectral functions, in-medium cross sections, and reaction rates are considered as well as the formation of a quantum condensate. In particluar, exploratory calculations are shown with respect to the pseudo gap in the nucleon level density close to the …
Uniform neutron matter is approximated by a cubic box containing a finite number of neutrons, with periodic boundary conditions. We report variational and Green's function Monte Carlo calculations of the ground state of fourteen neutrons in a periodic box using the Argonne $\vep $ two-nucleon interaction at densities up to one and half times the nuclear matter density. The effects of the finite box size are estimated using variational wave functions together with cluster expansion and chain summation techniques. They are small at subnuclear densities. We discuss the expansion of the energy of …
In multifragmentation of hot nuclear matter, properties of fragments embedded in a soup of nucleonic gas and other fragments should be modified as compared with isolated nuclei. Such modifications are studied within a simple model where only nucleons and one kind of heavy nuclei are considered. The interaction between different species is described with a momentum-dependent two-body potential whose parameters are fitted to reproduce properties of cold isolated nuclei. The internal energy of heavy fragments is parametrized according to a liquid-drop model with density and temperature dependent …
We calculate neutrino processes involving two nucleons at subnuclear densities using chiral effective field theory. Shorter-range noncentral forces reduce the neutrino rates significantly compared with the one-pion exchange approximation currently used in supernova simulations. For densities rho < 10^{14} g cm^{-3}, we find that neutrino rates are well constrained by nuclear interactions and nucleon-nucleon scattering data. As an application, we calculate the mean-square energy transfer in scattering of a neutrino from nucleons and find that collision processes and spin-dependent mean-field ef…
We estimate the quantum corrections to the ground state energy in neutron matter (which could be termed as well either shell correction energy or Casimir energy) at subnuclear densities, where various types of inhomogeneities (bubbles, rods, plates) are energetically favorable. We show that the magnitude of these energy corrections are comparable to the energy differences between various types of inhomogeneous phases. We discuss the dependence of these corrections on a number of physical parameters (density, filling factor, temperature, lattice distortions).
Calculations of equilibrium properties of dense matter predict that at subnuclear densities nuclei can be rodlike or slablike. To investigate whether transitions between phases with non-spherical nuclei can occur during the collapse of a star, we perform quantum molecular dynamic simulations of the compression of dense matter. We have succeeded in simulating the transitions between rodlike and slablike nuclei and between slablike nuclei and cylindrical bubbles. Our results strongly suggest that non-spherical nuclei can be formed in the inner cores of collapsing stars.
In this work, masses and radii of neutron stars are considered to investigate the effect of nuclear symmetry energy to the astrophysical observables. A relativistic mean field model with density-dependent meson-baryon coupling constants is employed in describing the equation of state of dense nuclear matter, and the density dependencies of the symmetry energies are quoted from the recent phenomenological formulae obtained from the heavy ion data at subnuclear saturation densities. Since hyperons can take part in the $β$-equilibrium of the dense matter inside neutron stars, we include hyperons …
Structure of cold dense matter at subnuclear densities is investigated by quantum molecular dynamics (QMD) simulations. We succeeded in showing that the phases with slab-like and rod-like nuclei etc. can be formed dynamically from hot uniform nuclear matter without any assumptions on nuclear shape. We also observe intermediate phases, which has complicated nuclear shapes. Geometrical structures of matter are analyzed with Minkowski functionals, and it is found out that intermediate phases can be characterized as ones with negative Euler characteristic. Our result suggests the existence of thes…
Homogeneous neutron matter at subnuclear densities becomes unstable towards the formation of inhomogeneities. Depending on the average value of the neutron density one can observe the appearance of either bubbles, rods, tubes or plates embeded in a neutron gas. We estimate the quantum corrections to the ground state energy (which could be termed either shell correction or Casimir energy) of such phases of neutron matter. The calculations are performed by evaluating the contribution of the shortest periodic orbits in the Gutzwiller trace formula for the density of states. The magnitude of the q…
We compare three different statistical models for the equation of state (EOS) of stellar matter at subnuclear densities and temperatures (0.5-10 MeV) expected to occur during the collapse of massive stars and supernova explosions. The models introduce the distributions of various nuclear species in nuclear statistical equilibrium, but use somewhat different nuclear physics inputs. It is demonstrated that the basic thermodynamical quantities of stellar matter under these conditions are similar, except in the region of high densities and low temperatures. We demonstrate that mass and isotopic di…
An ultraviolet cutoff dependent on the chemical potential as proposed by Casalbuoni {\it et al} is used in the su(3) Nambu-Jona-Lasinio model. The model is applied to the description of stellar quark matter and compact stars. It is shown that with a new cutoff parametrization it is possible to obtain stable hybrid stars with a quark core. A larger cutoff at finite densities leads to a partial chiral symmetry restoration of quark $s$ at lower densities. A direct consequence is the onset of the $s$ quark in stellar matter at lower densities and a softening of the equation of state.
Screening effects of electrons on inhomogeneous nuclear matter, which includes spherical, slablike, and rodlike nuclei as well as spherical and rodlike nuclear bubbles, are investigated in view of possible application to cold neutron star matter and supernova matter at subnuclear densities. Using a compressible liquid-drop model incorporating uncertainties in the surface tension, we find that the energy change due to the screening effects broadens the density region in which bubbles and nonspherical nuclei appear in the phase diagram delineating the energetically favorable shape of inhomogeneo…
Weak-interaction rates, including beta-decay and electron capture, are studied in several odd-A nuclei in the pf-shell region at various densities and temperatures of astrophysical interest. Special attention is paid to the relative contribution to these rates of thermally populated excited states in the decaying nucleus. The nuclear structure involved in the weak processes is studied within a quasiparticle random-phase approximation with residual interactions in both particle-hole and particle-particle channels on top of a deformed Skyrme Hartree-Fock mean field with pairing correlations. In …
We present simulations of neutron-rich matter at subnuclear densities, like supernova matter, with the time-dependent Hartree-Fock approximation at temperatures of several MeV. The initial state consists of $α$ particles randomly distributed in space that have a Maxwell-Boltzmann distribution in momentum space. Adding a neutron background initialized with Fermi distributed plane waves the calculations reflect a reasonable approximation of astrophysical matter. This matter evolves into spherical, rod-like, and slab-like shapes and mixtures thereof. The simulations employ a full Skyrme interacti…
Geometrical structure of matter at subnuclear densities is investigated in the presence of a degenerate gas of neutrinos as encountered in stellar collapse. The crystalline phases with spherical, cylindrical and planar nuclei as well as with spherical and cylindrical nuclear bubbles are considered by using a compressible liquid-drop model. This model allows for uncertainties in the lepton fraction $Y_{\rm L}$ in addition to those in the nuclear surface tension $E_{\rm surf}$ and in the proton chemical potential in bulk neutron matter $μ_{\rm p}^{(0)}$. The phase diagrams obtained at zero tempe…
We investigate the high-temperature effect on the nuclear matter that consists of mixture of nucleons and all nuclei in the dense and hot stellar environment. The individual nuclei are described within the compressible liquid-drop model that is based on Skyrme interactions for bulk energies and that takes into account modifications of the surface and Coulomb energies at finite temperatures and densities. The free-energy density is minimized with respect to the individual equilibrium densities of all heavy nuclei and the nuclear composition. We find that their optimized equilibrium densities be…
The abundance of light nuclei and hyperons, that are produced in stellar environments such as supernova or binary mergers, is calculated within a relativistic mean-field model with density dependent couplings in low-density matter. Five light nuclei are considered, together with three light hyper-nuclei. We show that the presence of hyperons shifts the dissolution of clusters to larger densities, and increases the amount of clusters. This effect is larger the smaller the charge fraction, and the higher the temperature. The abundance of hyperons is also affected by the cluster formation: neutra…
We investigate the mass fractions and in-medium properties of heavy nuclei in stellar matter at characteristic densities and temperatures for supernova (SN) explosions. The individual nuclei are described within the compressible liquid-drop model taking into account modifications of bulk, surface and Coulomb energies. The equilibrium properties of nuclei and the full ensemble of heavy nuclei are calculated self-consistently. It is found that heavy nuclei in the ensemble are either compressed or decompressed depending on the isospin asymmetry of the system. The compression or decompression has …
The effect of strong magnetic fields on the equation of state (EoS) for compact stars described with density-dependent relativistic hadronic models is studied. A comparison with other mean-field relativistic models is done. It is shown that the largest differences between models occur for low densities, and that the magnetic field affects the crust properties of a star, namely its extension.
Properties and microscopic structures of dense stellar matter in RMF models
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University（扬州大学物理科学与技术学院引力与宇宙学中心）；Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能机构先进科学研究中心）
White dwarfs and neutron stars are stellar objects with masses comparable to that of our sun. However, as the endpoint stages of stellar evolution, these objects do not sustain any thermonuclear burning and therefore can no longer support the gravitational load of their own mass by generating thermal pressure. Rather, matter in their interiors is compressed to much higher densities than commonly found in normal stars, and pressure is created by degenerate fermion kinetic energy and particle interactions. As a result, white dwarfs and neutron stars offer unique cosmic laboratories for studying …
