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By combining RMF models and equivparticle models with density-dependent quark masses, we construct explicitly ``a quark Fermi Sea'' and ``a baryonic Fermi surface'' to model the quarkyonic phase, where baryons with momentums ranging from zero to Fermi momentums are included. The properties of nuclear matter, quark matter, and quarkyonic matter are then investigated in a unified manner, where quarkyonic matter is more stable and energy minimization is still applicable to obtain the microscopic properties of dense matter. Three different covariant density functionals TW99, PKDD, and DD-ME2 are adopted in our work, where TW99 gives satisfactory predictions for the properties of nuclear matter both in neutron stars and heavy-ion collisions and quarkyonic transition is unfavorable. Nevertheless, if PKDD with larger slope of symmetry energy $L$ or DD-ME2 with larger skewness coefficient $J$ are adopted, the corresponding EOSs are too stiff according to both experimental and astrophysical constraints. The situation is improved if quarkyonic transition takes place, where the EOSs become softer and can accommodate various experimental and astrophysical constraints.

The possible exotic nuclear properties in the neutron-rich Ca, Ni, Zr, and Sn isotopes are explored with the continuum Skyrme Hartree-Fock-Bogoliubov theory formulated with the Green's function method. The available experimental two-neutron separation energies $S_{\rm 2n}$ and one-neutron separation energies $S_{\rm n}$ are well reproduced. Much shorter drip lines predicted by $S_{\rm n}$ are obtained compared with those by $S_{\rm 2n}$. The systematic studies of the neutron pairing energies $-E_{\rm pair}$ shown that values of the odd-$A$ nuclei are much smaller in comparison with those of the neighboring even-even nuclei due to the absent contribution of pairing energy by the unpaired odd neutron. By investigating the single-particle structures, the rms radii and the density distributions, the possible halo structures in the neutron-rich Ca, Ni, and Sn isotopes are predicted, in which the sharp increases of rms radii with significant deviations from the traditional $r\varpropto A^{1/3}$ rule and very diffuse spatial distributions in densities are observed. By analyzing the contributions of different partial waves to the total neutron density $\rho_{lj}(r)/\rho(r)$, the orbitals locating around the Fermi surface especially those with low angular momenta are found the main reason causing the extended nuclear density and large rms radii. Finally, the numbers of the neutrons $N_{\lambda}$~($N_0$) occupied above the Fermi surface $\lambda_n$~(in the continuum) are discussed, the behaviors of which are basically consistent with those of pairing energy, supporting the key role of the pairing correlations in the halo phenomena., Comment: 10 figures

We investigate systematically the possible deconfinement phase transition from nuclear matter to quark matter in compact stars. The properties of nuclear matter are fixed by expanding its binding energy to the order of $\rho^3$, while those of quark matter are predicted by an equivparticle model. The Maxwell construction is then applied for the quark-hadron mixed phase. By confronting compact star structures with pulsar observations, we obtain several EOSs that are compatible with the latest observations while supporting quark cores inside the most massive stars. It is found that the quark core is rather small and does not emerge for compact stars with $M\lesssim 2M_\odot$. The in-medium quark condensate of the stellar matter in those stars are then extracted within the framework of an equivparticle model, which decreases nonlinearly with density. At larger densities with pure quark matter, the quark condensate is still large and does not necessary decrease with density, indicating significant nonperturbative contributions within the density regions covered by compact stars.

The relativistic mean field theory with the Green's function method is taken to study the single-particle resonant states. Different from our previous work [Phys.Rev.C 90,054321(2014)], the resonant states are identified by searching for the poles of Green's function or the extremes of the density of states. This new approach is very effective for all kinds of resonant states, no matter it is broad or narrow. The dependence on the space size for the resonant energies, widths, and the density distributions in the coordinate space has been checked and it is found very stable. Taking $^{120}$Sn as an example, four new broad resonant states $2g_{7/2}$, $2g_{9/2}$, $2h_{11/2}$ and $1j_{13/2}$ are observed, and also the accuracy for the width of the very narrow resonant state $1h_{9/2}$ is highly improved to be $1\times 10^{-8}$ MeV. Besides, our results are very close to those by the complex momentum representation method and the complex scaling method., Comment: 5 figures and 2 tables

We explore the effects of strangeness and $��$ resonance in baryonic matter and compact stars within the relativistic-mean-field (RMF) models. The covariant density functional PKDD is adopted for $N$-$N$ interaction, parameters fixed based on finite hypernuclei and neutron stars are taken for the hyperon-meson couplings, and the universal baryon-meson coupling scheme is adopted for the $��$-meson couplings. In light of the recent observations of GW170817 with the dimensionless combined tidal deformability $197 \leq \bar��\leq 720$, we find it is essential to include the $��$ resonances in compact stars, and small $��$-$��$ coupling $g_{����}$ is favored if the mass $2.27{}_{-0.15}^{+0.17}\ M_\odot$ of PSR J2215+5135 is confirmed.

The relativistic mean-field theory with Green's function method is extended to study $��$ hypernuclei. Taking hypernucleus $^{61}_��$Ca as an example, the single-particle resonant states for $��$ hyperons are investigated by analyzing density of states and the corresponding energies and widths are given. Different behaviors are observed for the resonant states, i.e., the distributions of the very narrow $1f_{5/2}$ and $1f_{7/2}$ states are very similar as bound states while that of the wide $1g_{7/2}$ and $1g_{9/2}$ states are like scattering states. Besides, the impurity effect of $��$ hyperons on the single-neutron resonant states are investigated. For most of the resonant states, both the energies and widths decrease with adding more $��$ hyperons due to the attractive $��N$ interaction. Finally, the energy level structure of $��$ hyperons in the Ca hypernucleus isotopes with mass number $A=53-73$ are studied, obvious shell structure and small spin-orbit splitting are found for the single-$��$ spectrum., 10pages, 6 figures,2 tables

Based on relativistic mean field (RMF) models, we study finite $��$-hypernuclei and massive neutron stars. The effective $N$-$N$ interactions PK1 and TM1 are adopted, while the $N$-$��$ interactions are constrained by reproducing the binding energy of $��$-hyperon at $1s$ orbit of $^{40}_��$Ca. It is found that the $��$-meson couplings follow a simple relation, indicating a fixed $��$ potential well for symmetric nuclear matter at saturation densities, i.e., around $V_�� = -29.786$ MeV. With those interactions, a large mass range of $��$-hypernuclei can be well described. Furthermore, the masses of PSR J1614-2230 and PSR J0348+0432 can be attained adopting the $��$-meson couplings $g_{����}/g_{��N}\gtrsim 0.73$, $g_{����}/g_{��N}\gtrsim 0.80$ for PK1 and $g_{����}/g_{��N}\gtrsim 0.81$, $g_{����}/g_{��N}\gtrsim 0.90$ for TM1, respectively. This resolves the Hyperon Puzzle without introducing any additional degrees of freedom., 5 figures, 1 table, to be published in Chinese Physics C