Effective numbers of charge carriers in doped graphene: The generalized Fermi liquid approach

The single-band current-dipole Kubo formula for the dynamical conductivity of heavily doped graphene from Kup\v{c}i\'{c} [Phys. Rev. B 91, 205428 (2015)] is extended to a two-band model for conduction $\pi$ electrons in lightly doped graphene. Using a posteriori relaxation-time approximation in the two-band quantum transport equations, with two different relaxation rates and one quasi-particle lifetime, we explain a seemingly inconsistent dependence of the dc conductivity $\sigma^{\rm dc}_{\alpha \alpha}$ of ultraclean and dirty lightly doped graphene samples on electron doping, in a way consistent with the charge continuity equation. It is also shown that the intraband contribution to the effective number of conduction electrons in $\sigma^{\rm dc}_{\alpha \alpha}$ vanishes at $T=0$ K in the ultraclean regime, but it remains finite in the dirty regime. The present model is shown to be consistent with a picture in which the intraband and interband contributions to $\sigma^{\rm dc}_{\alpha \alpha}$ are characterized by two different mobilities of conduction electrons, the values of which are well below the widely accepted value of mobility in ultraclean graphene. The dispersions of Dirac and $\pi$ plasmon resonances are reexamined to show that the present, relatively simple expression for the dynamical conductivity tensor can be used to study simultaneously single-particle excitations in the dc and optical conductivity and collective excitations in energy loss spectroscopy experiments.Comment: 13 pages, 11 figure

Relativistic Energy Density Functional Description of Shape Transition in Superheavy Nuclei

Relativistic energy density functionals (REDF) provide a complete and accurate, global description of nuclear structure phenomena. A modern semi-empirical functional, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, is applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison of calculated masses, quadrupole deformations, and potential energy barriers to available data on actinide isotopes. Self-consistent mean-field calculations predict a variety of spherical, axial and triaxial shapes of long-lived superheavy nuclei, and their alpha-decay energies and half-lives are compared to data. A microscopic, REDF-based, quadrupole collective Hamiltonian model is used to study the effect of explicit treatment of collective correlations in the calculation of Q{\alpha} values and half-lives.Comment: 23 pages, 10 figure

New relativistic mean-field interaction with density-dependent meson-nucleon couplings

We adjust a new improved relativistic mean-field effective interaction with explicit density dependence of the meson-nucleon couplings. The effective interaction DD-ME2 is tested in relativistic Hartree-Bogoliubov and quasiparticle random-phase approximation (QRPA) calculations of nuclear ground states and properties of excited states, in calculation of masses, and it is applied to the analysis of very recent data on superheavy nuclei

Localization and clustering in the nuclear Fermi liquid

Using the framework of nuclear energy density functionals we examine the conditions for single-nucleon localization and formation of cluster structures in finite nuclei. We propose to characterize localization by the ratio of the dispersion of single-nucleon wave functions to the average inter-nucleon distance. This parameter generally increases with mass and describes the gradual transition from a hybrid phase in light nuclei, characterized by the spatial localization of individual nucleon states that leads to the formation of cluster structures, toward the Fermi liquid phase in heavier nuclei. Values of the localization parameter that correspond to a crystal phase cannot occur in finite nuclei. Typical length and energy scales in nuclei allow the formation of liquid drops, clusters, and halo structures.Comment: 6 pages, 3 figure

Constraints on the inner edge of neutron star crusts from relativistic nuclear energy density functionals

The transition density nt and pressure Pt at the inner edge between the liquid core and the solid crust of a neutron star are analyzed using the thermodynamical method and the framework of relativistic nuclear energy density functionals. Starting from a functional that has been carefully adjusted to experimental binding energies of finite nuclei, and varying the density dependence of the corresponding symmetry energy within the limits determined by isovector properties of finite nuclei, we estimate the constraints on the core-crust transition density and pressure of neutron stars: 0.086 fm-3⩽nt<0.090 fm-3 and 0.3  MeV fm-3

A microscopic estimate of the nuclear matter compressibility and symmetry energy in relativistic mean-field models

The relativistic mean-field plus RPA calculations, based on effective Lagrangians with density-dependent meson-nucleon vertex functions, are employed in a microscopic analysis of the nuclear matter compressibility and symmetry energy. We compute the isoscalar monopole and the isovector dipole response of $^{208}$Pb, as well as the differences between the neutron and proton radii for $^{208}$Pb and several Sn isotopes. The comparison of the calculated excitation energies with the experimental data on the giant monopole resonance in $^{208}$Pb, restricts the nuclear matter compression modulus of structure models based on the relativistic mean-field approximation to $K_{\rm nm}\approx 250 - 270$ MeV. The isovector giant dipole resonance in $^{208}$Pb, and the available data on differences between neutron and proton radii, limit the range of the nuclear matter symmetry energy at saturation (volume asymmetry) to 32 MeV $\leq a_4 \leq$ 36 MeV.Comment: 16 pages, 6 figure

Superallowed Fermi transitions in RPA with a relativistic point-coupling energy functional

The self-consistent random phase approximation (RPA) approach with the residual interaction derived from a relativistic point-coupling energy functional is applied to evaluate the isospin symmetry-breaking corrections {\delta}c for the 0+\to0+ superallowed Fermi transitions. With these {\delta}c values, together with the available experimental ft values and the improved radiative corrections, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is examined. Even with the consideration of uncertainty, the sum of squared top-row elements has been shown to deviate from the unitarity condition by 0.1% for all the employed relativistic energy functionals.Comment: 13 pages,2 figure

Microscopic analysis of nuclear quantum phase transitions in the N~90 region

The analysis of shape transitions in Nd isotopes, based on the framework of relativistic energy-density functionals and restricted to axially symmetric shapes in T. Nikšić, D. Vretenar, G. A. Lalazissis, and P. Ring [Phys. Rev. Lett. 99, 092502 (2007)], is extended to the region Z=60, 62, 64 with N[approximate]90 and includes both beta and gamma deformations. Collective excitation spectra and transition probabilities are calculated starting from a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The results reproduce available data and show that there is an abrupt change of structure at N=90 that can be approximately characterized by the X(5) analytic solution at the critical point of the first-order quantum phase transition between spherical and axially deformed shapes