Low-density Nuclear Matter Research Articles

Molecular dynamics for dense matter

We review a molecular dynamics method for nucleon many-body systems called the quantum molecular dynamics (QMD) and our studies using this method. These studies address the structure and the dynamics of nuclear matter relevant to the neutron star crusts, supernova cores, and heavy-ion collisions. A key advantage of QMD is that we can study dynamical processes of nucleon many-body systems without any assumptions on the nuclear structure. First we focus on the inhomogeneous structures of low-density nuclear matter consisting not only of spherical nuclei but also of nuclear "pasta", i.e., rod-like and slab-like nuclei. We show that the pasta phases can appear in the ground and equilibrium states of nuclear matter without assuming nuclear shape. Next we show our simulation of compression of nuclear matter which corresponds to the collapsing stage of supernovae. With increase of density, a crystalline solid of spherical nuclei change to a triangular lattice of rods by connecting neighboring nuclei. Finally, we discuss the fragment formation in expanding nuclear matter. Our results suggest that a generally accepted scenario based on the liquid-gas phase transition is not plausible at lower temperatures.

Nuclear collective excitations in a two-phase coexistence region

The relation between collective modes and the phase transition in low density nuclear matter is examined. The dispersion relations for collective modes in a linear approach are evaluated within a Landau-Fermi liquid scheme by assuming coexisting phases in thermodynamical equilibrium. Temperature and isospin composition are taken as relevant parameters. The in-medium nuclear interaction is taken from a recently proposed density functional model. We found significative modifications in the energy spectrum, within certain range of temperatures and isospin asymmetry, due to the separation of matter into independent phases. We conclude that detailed calculations should not neglect this effect.

Low density nuclear matter in effective field theory

The two- and three-nucleon interaction derived in chiral effective field theory is used to obtain the binding energy of nuclear matter for small densities at next-to-leading (NLO) and next-to-next-to-leading orders (N 2 LO). The order N 2 LO is not yet suffi cient to push the range of validity of the expansion beyond the empirical Fermi momentum of nuclear matter. A phenomenological extension of the interaction suggests that both effective three- and four-nucleon interactions are required for a description of the bulk properties of nuclear mater.

Charge correlations and isotopic distributions of projectile fragmentation events inXe124+Sn112atE/A=50MeV

Ternary breakup of an excited projectile-like fragment produced in mid-peripheral collisions of $^{124}\mathrm{Xe}$ projectiles with $^{112}\mathrm{Sn}$ nuclei at $E/A=50$ MeV is examined. Charge correlations reveal that symmetric breakups occur with significant probability. By selecting on the parallel velocity of the heaviest fragment we minimize the entrance channel dynamics. Calculations with the statistical decay code GEMINI failed to reproduce the experimental charge correlations for any suitable combination of excitation energy and spin considered. A statistical multifragmentation model (SMM) in which breakup of low-density nuclear matter is assumed was able to reproduce the observed charge correlations. The $\ensuremath{\langle}N\ensuremath{\rangle}/Z$ and isotope distributions of fragments were compared to the results of the SMM calculations. Describing the $\ensuremath{\langle}N\ensuremath{\rangle}/Z$ of heavy fragments ($Z>6$) within SMM suggests that a reduction of the symmetry energy parameter from $\ensuremath{\gamma}=25$ to $14$ MeV is necessary. We observe that the yield of neutron-rich isotopes of heavy fragments is particularly sensitive to the symmetry energy.

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 Zn-64 projectiles with Mo-92 and Au-197 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 <= 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.

Clustering and Symmetry Energy in a Low Density Nuclear Gas

Temperature and density dependent symmetry energy coefficients have been derived from isoscaling analyses of the yields of nuclei with A ⩽ 4 in the reactions of 35AMeV 64 Zn projectiles with 92 Mo and 197 Au target nuclei. The symmetry energies at low density are larger than those obtained in mean field calculations, reflecting the clustering of low density nuclear matter. They are in quite good agreement with results of a recently proposed Virial Equation of State calculation.

Cluster formation and the virial equation of state of low-density nuclear matter

We present the virial equation of state of low-density nuclear matter composed of neutrons, protons and alpha particles. The virial equation of state is model-independent, and therefore sets a benchmark for all nuclear equations of state at low densities. We calculate the second virial coefficients for nucleon–nucleon, nucleon–alpha and alpha–alpha interactions directly from the relevant binding energies and scattering phase shifts. The virial approach systematically takes into account contributions from bound nuclei and the resonant continuum, and consequently provides a framework to include strong-interaction corrections to nuclear statistical equilibrium models. The virial coefficients are used to make model-independent predictions for a variety of properties of nuclear matter over a range of densities, temperatures and compositions. Our results provide constraints on the physics of the neutrinosphere in supernovae. The resulting alpha particle concentration differs from all equations of state currently used in supernova simulations. Finally, the virial equation of state greatly improves our conceptual understanding of low-density nuclear matter.

Precritical Pair Fluctuations and Formation of a Pseudogap in Low-Density Nuclear Matter

Low-density nuclear matter at finite temperature is considered representing the strong coupling situation of a highly correlated fermion system. One-particle self-energies and the density of states in the vicinity of the pairing transition point are presented. Within the Green function approach, model calculations are performed using the thermodynamic $T$ matrix in ladder approximation. As a main result the formation of a pseudogap in the level density near the critical temperature of the pairing phase transition has been found. It is shown that compared to mean-field approaches the scenario of the onset of the pairing transition is essentially changed if correlations are taken into account.

Two-nucleon correlations and the nucleon spectral function in nuclear matter at finite temperature: low-density region

The nucleon spectral function is calculated in low-density nuclear matter at finite temperature. Using Matsubara Green's functions the nucleon selfenergy is evaluated in the ladder approximation for the thermodynamic two-particle T-matrix. In addition to the contribution from the continuum part of the T-matrix special attention is paid to its pole contribution reflecting the two-particle bound state (deuteron) in the medium. The consequences of the formation of two-particle bound states for the selfenergy and the one-particle spectral function are shown.

A new metastable phase in low density nuclear matter and the anomalon problem

On the basis of a nuclear matter model calculation at finite temperature it is shown that at densities of about 1/15 of normal nuclear mattor density a new metastable phase exists which is determined by cluster formation effects. The existence of a low density isomer might be related to the recently observed anomalous short reaction mean free paths from 2 GeV/N heavy ion collisions.

Confinement of quarks in nuclear matter

The transition from low density nuclear matter to high density quark matter can, it is argued, take place in two steps: first, a percolation transition at (subnuclear densities, if the radius of the nucleon is ⪅1 fm) in which the quarks become deconfined but still remain localized, followed by an unbinding transition at higher density, in which the matter becomes a uniform quark Fermi liquid.

Ground state properties of alpha matter

The ground state of a uniform, extended system of alpha particles at zero temperature is studied by a variational method. The alpha particles are treated as elementary bosons and are assumed to interact through two-body potentials fitting the alpha-alpha elastic scattering data. A cluster development is used to evaluate the expectation value of the energy for a trial ground state wave function of Jastrow form. The conventional Bose cluster expansion is modified to cope with the rather strong angular-momentum dependence of the best phenomenological alpha-alpha potentials. Numerical calculations of the two- and three-body cluster contributions to the energy have been performed over a wide range of densities and variational parameters. Some estimates of the four-body terms have also been made. The convergence of the cluster expansions, for the optimally determined variational parameters, appears quite satisfactory. The resulting equations of state for zero-temperature alpha-matter are of interest in relation to the theory of low-density nuclear matter and, more specifically, the problems of nucleon clustering in the nuclear surface.