Nuclear Theory

Properties of nuclear matter are investigated in the framework of relativistic Brueckner-Hartree-Fock model with the latest high-precision charge-dependent Bonn (pvCD-Bonn) potentials, where the coupling between pion and nucleon is adopted as pseudovector form. These realistic pvCD-Bonn potentials are renormalized to effective nucleon-nucleon ( NN ) interactions, G matrices. They are obtained by solving the Blankenbecler-Sugar (BbS) equation in nuclear medium. Then, the saturation properties of symmetric nuclear matter are calculated with pvCD-Bonn A, B, C potentials. The energies per nucleon are around −10.72 MeV to −16.83 MeV at saturation densities, 0.139 fm −3 to 0.192 fm −3 with these three potentials, respectively. It clearly demonstrates that the pseudovector coupling between pion and nucleon can generate reasonable saturation properties comparing with pseudoscalar coupling. Furthermore, these saturation properties have strong correlations with the tensor components of NN potentials, i.e., the D -state probabilities of deuteron, P D to form a relativistic Coester band. In addition, the charge symmetry breaking (CSB) and charge independence breaking (CIB) effects are also discussed in nuclear matter from the partial wave contributions with these high-precision charge-dependent potentials. In general, the magnitudes of CSB from the differences between nn and pp potentials are about 0.05 MeV, while those of CIB are around 0.35 MeV from the differences between np and pp potentials. Finally, the equations of state of asymmetric nuclear matter are also calculated with different asymmetry parameters. It is found that the effective neutron mass is larger than the proton one in neutron-rich matter.

In this Review we study the nuclear pastas as they are expected to be formed in neutron star cores. We start with a study of the pastas formed in nuclear matter (composed of protons and neutrons), we follow with the role of the electron gas on the formation of pastas, and we then investigate the pastas in neutron star matter (nuclear matter embedded in an electron gas).

We review the properties of the strongly interacting quark-gluon plasma (QGP) at finite temperature T and baryon chemical potential μ B as created in heavy-ion collisions at ultrarelativistic energies. The description of the strongly interacting (non-perturbative) QGP in equilibrium is based on the effective propagators and couplings from the Dynamical QuasiParticle Model (DQPM) that is matched to reproduce the equation-of-state of the partonic system above the deconfinement temperature T C from lattice QCD. Based on a microscopic transport description of heavy-ion collisions we discuss which observables are sensitive to the QGP creation and its properties.

We use covariant density functional theory to obtain the equation of state (EoS) of matter in compact stars at non-zero temperature, including the full baryon octet as well as the Δ(1232) resonance states. Global properties of hot Δ -admixed hypernuclear stars are computed for fixed values of entropy per baryon ( S/A ) and lepton fraction ( Y L ). Universal relations between the moment of inertia, quadrupole moment, tidal deformability, and compactness of compact stars are established for fixed values of S/A and Y L that are analogous to those known for cold catalyzed compact stars. We also verify that the I -Love- Q relations hold at finite temperature for constant values of S/A and Y L .

The isoscalar pn pair is expected to emerge in nuclei having the similar proton and neutron numbers but there is no clear experimental evidence for it. We aim to clarify the correspondence between the pn pairing strength in many-body calculation and the triple differential cross section (TDX) of proton-induced deuteron knockout ( p,pd ) reaction on 16 O. The radial wave function of the isoscalar pn pair with respect to the center of 16 O is calculated with the energy density functional (EDF) approach and is implemented in the distorted wave impulse approximation (DWIA) framework. The pn pairing strength V 0 in the EDF calculation is varied and the corresponding change in the TDX is investigated. A clear V 0 dependence of the TDX is found for the 16 O( p,pd ) 14 N( 1 + 2 ) at 101.3 MeV. The nuclear distortion is found to make the V 0 dependence stronger. Because of the clear V 0 -TDX correspondence, the ( p,pd ) reaction will be a promising probe for the isoscalar pn pair in nuclei. For quantitative discussion, further modification of the description of the reaction process will be necessary.

We study proximity effect of pair correlation in the inner crust of neutron stars by means of the Skyrme-Hartree-Fock-Bogoliubov theory formulated in the coordinate space. We describe a system composed of a nuclear cluster immersed in neutron superfluid, which is confined in a spherical box. Using a density-dependent effective pairing interaction which reproduces both the pair gap of neutron matter obtained in ab initio calculations and that of finite nuclei, we analyze how the pair condensate in neutron superfluid is affected by the presence of the nuclear cluster. It is found that the proximity effect is characterized by the coherence length of neutron superfluid measured from the edge position of the nuclear cluster. The calculation predicts that the proximity effect has a strong density dependence. In the middle layers of the inner crust with baryon density 5× 10 −4 fm −3 < ρ b <2× 10 −2 fm −3 , the proximity effect is well limited in the vicinity of the nuclear cluster, i.e. in a sufficiently smaller area than the Wigner-Seitz cell. On the contrary, the proximity effect is predicted to extend to the whole volume of the Wigner-Seitz cell in shallow layers of the inner crust with ρ b <2× 10 −4 fm −3 , and in deep layers with ρ b >5× 10 −2 fm −3 .

The proxy-SU(3) symmetry has been proposed for spin-orbit like nuclear shells using the asymptotic deformed oscillator basis for the single particle orbitals, in which the restoration of the symmetry of the harmonic oscillator shells is achieved by a change of the number of quanta in the z-direction by one unit for the intruder parity orbitals. The same definition suffices within the cartesian basis of the Elliott SU(3) model. Through a mapping of the cartesian Elliott basis onto the spherical shell model basis, we translate the proxy-SU(3) approximation into spherical coordinates, proving, that in the spherical shell model basis the proxy-SU(3) approximation corresponds to the replacement of the intruder parity orbitals by their de Shalit--Goldhaber partners. Furthermore it is shown, that the proxy-SU(3) approximation in the cartesian Elliott basis is equivalent to a unitary transformation in the z-coordinate, leaving the x-y plane intact, a result which in the asymptotic deformed oscillator coordinates implies, that the z-projections of angular momenta and spin remain unchanged. The present work offers a microscopic justification of the proxy-SU(3) approximation and in addition paves the way, for taking advantage of the proxy-SU(3) symmetry in shell model calculations.

The Dirac Equation is solved approximately for relativistic generalized Woods-Saxon potential including Coulomb-like tensor potential in exact pseudospin and spin symmetry limits. The bound states energy eigenvalues are found by using wavefunction boundary conditions, and corresponding radial wavefunctions are obtained in terms of hypergeometric function. Some numerical examples are given for the dependence of bound states energy eigenvalues on quantum numbers and potential parameters.

A reflection-asymmetric triaxial particle rotor model with three quasiparticles and a reflection-asymmetric triaxial rotor is developed, and applied to investigate the observed multiple chiral doublets (M\c{hi}D) candidates with octupole correlations in 131Ba, i.e., two pairs of positive-parity bands D3-D4 and D5-D6, as well as one pair of negative-parity bands D7-D8. The energy spectra, the energy staggering parameters, the B(M1)/B(E2) ratios, and the B(E1)/B(E2) ratios are reproduced well. The chiral geometries for these M\c{hi}D candidates are examined by the azimuthal plots, and the evolution of chiral geometry with spin is clearly demonstrated. The intrinsic structure for the positive-parity bands is analyzed and the possible pseudospin-chiral quartet bands are suggested.

We review the equation of state of QCD matter at finite densities. We discuss the construction of the equation of state with net baryon number, electric charge, and strangeness using the results of lattice QCD simulations and hadron resonance gas models. Its application to the hydrodynamic analyses of relativistic nuclear collisions suggests that the interplay of multiple conserved charges is important in the quantitative understanding of the dense nuclear matter created at lower beam energies. Several different models of the QCD equation of state are discussed for comparison.