The ground-state properties such as binding energy, root-mean-square radius, pairing energy, nucleons density distribution, symmetry energy, and single-particle energies are calculated for the isotopic chain of Ca, Sn, Pb, and Z = 120 nuclei. The recently developed G3 and IOPB-I forces along with the DD-ME1 and DD-ME2 sets are used in the analysis employing the relativistic mean-field approximation. To locate the magic numbers in the superheavy region and to explain the observed kink at neutron number N = 82 for Sn isotopes, a three-point formula is used to see the shift of the observable and other nuclear properties in the isotopic chain. Unlike the electronic configuration, due to strong spin-orbit interaction, the higher spin orbitals are occupied earlier than the lower spin, causing the possible kink at the neutron magic numbers. We find peaks at the known neutron magic number with the confirmation of sub-shell, shell closure respectively at N = 40, 184 for Ca and ³⁰⁴ 120.

We systematically investigate f-mode oscillations (ℓ = 2) in quarkyonic neutron stars with dark matter, employing the Cowling approximation within the framework of linearized general relativity. The relativistic mean-field approach is used to compute various macroscopic properties of neutron stars. The analysis focuses on three key free parameters in the model: transition density, QCD confinement scale, and dark matter (DM) Fermi momentum, all of which significantly affect the properties of f-mode oscillations. The inclusion of dark matter in quarkyonic equations of state leads to notable variations in f-mode frequencies. Despite these changes, several universal relations among the oscillation properties are found to hold, demonstrating their robustness in the presence of dark matter. Motivation: our model is distinct in that it incorporates quarkyonic matter composed of up and down quarks, which exists in beta equilibrium with neutron star matter, i.e., this model is a combination of the quarkyonic degrees of freedom, the E-RMF framework, and the inclusion of the Fermionic dark matter. To our knowledge, no such unique model exists in the literature. Please note that the development of the model is recently published in JCAP [1], and the present work is an application to f-mode calculations of neutron stars. Understanding the oscillation properties within such a composition provides crucial insights into the possible existence and behavior of quarkyonic matter in neutron stars. This model is a viable alternative to explain the mysterious secondary object present in the recent GW190814 multi-messenger event [2].

The newly derived relativistic energy density functional [ Phys. Rev. C 103, 024305 (2021)], which stems from the effective field theory motivated relativistic mean field (E-RMF), is employed to establish the appearance of peaks and/or kinks in the symmetry energy over the isotopic chain of Pb nuclei. The coherent density fluctuation model parametrization procedure for finite nuclei is adopted here to obtain the relativistic energy density functional at local density. The relativistic energy density functional from relativistic mean-field theory takes precedence over the Brückner energy density functional as it accurately predicts the empirical saturation density and binding energy per nucleon $E/A$, so-called coester band problem. Interestingly, using the relativistic energy density functional, it is possible to predict the peak at $N=126$ for recently developed G3 and widely used NL3 parameter sets, which is not observed for Brückener's functional in spite of using the relativistic mean-field density. From the present analysis, the newly fitted energy density functional is found to be minutely sensitive to the choice of the parameter sets employed.

The formulation of quarkyonic matter consists of treating both quarks and nucleons as quasi-particles, where a cross-over transition occurs between the two phases. This work is based on some of the early ideas of quark matter (QM). It has satisfied the different observational constraints on the neutron star (NS), such as its maximum mass and the canonical radius. In addition, we put an extra component inside the NS, known as Dark Matter (DM) because it is trapped due to its immense gravitational potential. In this work, we explore the impact of fermionic DM on the structure of the NS. The equation of state (EOS) is derived for the NS with the quarkyonic matter by assuming that nucleons and quarks are in equilibrium, followed by the relativistic mean-field (RMF) formalism. The recently modeled two parameterizations, such as G3 and IOPB-I, are taken to calculate the various macroscopic properties of the NS. The three unknown parameters such as the transition density (n_t ), the QCD confinement scale (Λ_cs), and the DM Fermi momentum (k _f ^DM) are varied to obtain the NS properties. The quarkyonic matter stiffens the EOS while DM softens it. The mutual combination provides good theoretical descriptions for the magnitude of macroscopic properties consistent with the different observational results. Also, one can estimate the parameters of the DM admixed quarkyonic star with different statistical analyses, which can be further used to explore the other properties of the quarkyonic star.

The anisotropy of pressure arises due to the various complex phenomena that happen inside the neutron star (NS). In this study, we calculate the degree of anisotropy inside the NS using the scalar pressure anisotropy model. Macroscopic properties such as mass, radius, compactness, redshift, tidal deformability, the moment of inertia, and surface curvature (SC) are computed for the anisotropic NS with the equation of states spanning from relativistic to nonrelativistic cases. The variation of SC as the functions of the above-mentioned quantities are computed by changing the degree of anisotropy. Pressure anisotropy has significant effects on the magnitude of SC. The relations between the canonical $\mathrm{SC}-\mathrm{\Lambda }$ and $\mathrm{SC}-\overline{I}$ are studied. From the GW170817 tidal deformability data, we constraints the magnitude of SC are found to be ${\mathrm{SC}}_{1.4}({10}^{14})={3.44}_{-1.0}^{+0.4},{2.85}_{-1.20}^{+0.62},{2.52}_{-1.02}^{+0.61}$ for ${\lambda }_{\mathrm{BL}}=0.0$, 1.0, and 2.0, respectively.