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We investigated the effect of the degree of freedom of neutron transfer on the cross section of heavy-ion fusion reactions, using the relativistic mean-field formalism within the coupled channel approach (CCFULL). We obtain the microscopic nuclear interaction potential in terms of the density distributions for the targets and projectiles with the NL3$^*$ parameter set and corresponding R3Y nucleon-nucleon potential. The present analysis includes the $^{18}$O-induced reactions, for which experimental fusion cross-section is available around the Coulomb barrier. It is evident from the results that including vibrational and/or rotational degrees of freedom enhances the fusion cross-section at energies below the barrier. However, fusion hindrance persists in this energy region. To address this, we incorporated the two-neutron $(2n)$ transfer channels in the Coupled Channel calculation. A comparison with the Woods-Saxon potential (WS) shows that the R3Y nucleon-nucleon (NN) potential, with intrinsic degrees of freedom, is superior to it, especially at energies below the barrier. This superiority can be attributed to the observed higher barrier heights and lower cross-section of the WS potential compared to the relativistic R3Y NN potential for the considered reaction systems. Consequently, we employed the relativistic mean-field formalism to estimate fusion characteristics for the unknown $^{18}$O-induced reactions, namely $^{18}$O + $^{62}${Ni}, $^{18}$O + $^{70,72,76}${Ge}, $^{18}$O + $^{144,150}${Nd}, and $^{18}$O + $^{144,148,152,154}${Sm}. Our analysis highlights the significant role of positive $Q$-value neutron transfer in enhancing the sub-barrier fusion cross-section for the $^{18}$O + $^{148}${Nd} reaction with the R3Y NN potential. However, the effect of this transfer channel for the other considered reactions is comparatively less pronounced.

The analytical expression of the density-dependent binding energy per nucleon for the relativistic mean field (RMF), also known as the relativistic energy density functional (Relativistic-EDF), is used to obtain the isospin-dependent symmetry energy and its components for the isotopic chain of Sc, Ti, V, and Cr nuclei. The procedure of the coherent density fluctuation model is employed to formulate the Relativistic-EDF and Brueckner energy density functional (Brueckner-EDF) at local density. A few signatures of shell and/or sub-shell closure are observed in the symmetry energy and its components, i.e., surface and volume symmetry energy, far from the beta-stable region for odd-A Sc and V, and even-even Ti and Cr nuclei with non-linear NL3 and G3 parameter sets. A comparison is made with the results obtained from Relativistic-EDF and Brueckner-EDF with both NL3 and G3 for the considered isotopic chains. We find Relativistic-EDF outperforms the Brueckner-EDF in predicting the shell and/or sub-shell closure of neutron-rich isotopes at N = 50 for these atomic nuclei. Moreover, a relative comparison has been made for the results obtained with the non-linear NL3 and G3 parameter sets., Comment: 18 pages, 4 figures

Nuclear shape and orientation degrees of freedom are incorporated into the calculation of the double-folding nuclear potential within the relativistic mean-field (RMF) formalism. The quadrupole deformations ($\beta_2$), nuclear densities and the effective nucleon-nucleon (NN) interaction potential are obtained using the RMF approach for the Hybrid, NL3$^*$ and NL3 parameterizations. The calculated quadrupole deformations are included in the target densities through the nuclear radius. The deformation and orientation-dependent microscopic nuclear potentials are further employed to obtain fusion barrier characteristics and cross-sections for 12 even-even heavy-ion reactions with doubly magic spherical $^{16}$O and $^{48}$Ca as projectiles along with deformed targets from different mass regions. The results obtained for the relativistic R3Y NN potential are compared with those of the Reid version of the non-relativistic M3Y NN potential as well as with the available experimental data. A decrease in the barrier height and increase in the cross-section is observed upon the inclusion of target quadrupole deformations in the nuclear density distributions at the target orientation angles, $\theta_2\le58^\circ$ for the R3Y NN potential and at $\theta_2\le60^\circ$ for the M3Y NN potential. On comparing the $\theta_2$-integrated cross-section calculated using M3Y and R3Y NN potentials with spherical and deformed densities, one observes that the deformed densities and the relativistic R3Y NN potential obtained for the Hybrid parameter set provide better agreement with the available experimental data for all the considered reactions. Moreover, the modifications in the characteristics of the fusion barrier and hence in the cross-section with the inclusion of nuclear shape degrees of freedom and orientations are found to become more prominent in reactions forming heavier compound nuclei.

A sufficiently precise measurement of black hole spin is required to carry out quantitative tests of the Kerr metric and to understand several phenomena related to astrophysical black holes. After 24 years, XTE J2012+381 again underwent an outburst in December 2022. In this work, we focused on the measurement of spin and mass of black hole candidate XTE J2012+381 using broadband spectral analysis of X-ray data from \emph{Swift/XRT} and \emph{NuSTAR}. By using the relxillCp model, the spin and inclination of the source were found to be $0.883_{-0.061}^{+0.033}$ and $46.2_{-2.0}^{+3.7}$ degrees, respectively for high disk density ($i.e.\;10^{20}\;\mathrm{cm}^{-3}$). We further test our results for lamp post geometry using the relxilllpCp model. The spin and inclination of the source were found to be $0.892_{-0.044}^{+0.020}$ and $43.1_{-1.2}^{+1.4}$ degrees, respectively. Then "continuum-fitting" method was used for the soft state to estimate the mass of BH and found to be $7.95_{-3.25}^{+7.65}\;\mathrm{M}_{\odot}$ and $7.48_{-2.75}^{+5.80}\;\mathrm{M}_{\odot}$ for the spin and inclination estimated from the relxillCp and relxilllpCp model respectively. We used a distance of 5.4 kpc as measured by Gaia using the parallax method. This study also addresses the issue of supersolar iron abundance in XTE J2012+381 by using \texttt{reflionx} based reflection model and found high disk density for the source., Comment: Accepted for publication in MNRAS; 9 pages

The fusion mechanism of reactions involving even-even $^{112-124}$Sn, doubly magic $^{132}$Sn, $^{208}$Pb as targets, and $^{64}$Ni as the projectile is explored within the relativistic mean field (RMF) formalism. The main aim of choosing these nuclei is to explore the correlation between the nuclear incompressibility and the fusion cross-section. The nucleus-nucleus interaction potential is calculated by folding the axially deformed nuclear densities and the relativistic R3Y nucleon-nucleon (NN) potential obtained for the nonlinear sets of NL3$^*$, hybrid, and NL1, which yield different values for various characteristics of nuclear matter at saturation. The fusion barrier characteristics obtained for different RMF parameterizations are further used to calculate the cross-section within the $\ell$-summed Wong model. We found a decrease in the barrier height and consequently, an increase in the cross-section with a decrease in the incompressibility for all sets of parameters considered. The calculated cross section is satisfactorily consistent with the available experimental data for $^{64}$Ni+$^{208}$Pb system. In contrast, the nuclear potentials obtained for NL3$^*$ and the hybrid parameter sets underestimate the cross-section at below-barrier energies for $^{64}$Ni+$^{112-124,132}$Sn reactions. This discrepancy between the experimental data and the theoretical results for $^{64}$Ni+$^{112-124,132}$Sn reactions can be correlated with the soft behaviour of the Sn isotopes. The compressible nature of Sn-isotopes is inferred to lower the barrier height, which further leads to enhancement of the experimental fusion and/or capture cross-section at below-barrier energies. Thus, the NL1 parameter set with a comparatively soft equation of state (EoS) is observed to be a better choice to describe the sub-barrier nuclear fusion dynamics of reactions involving the Sn-isotopes.

The $\alpha$-decay half-lives of superheavy nuclei with $100 \leq Z \leq 120$ are comprehensively analyzed using the axially deformed relativistic mean field (RMF) formalism for the NL3$^*$ parameter set. We employ RMF binding energies to determine the $\alpha$-decay energies and make a comparison with both the available experimental data and the theoretical results obtained from the global nuclear mass model WS4. The four distinct formulae, specifically the modified scaling law Brown, modified Viola-Seaborg, Yibin {\it et al.} formula, and its modified form are used to calculate the decay half-lives and examine the numerical correlation between the half-life ($T_{1/2}$) for each $\alpha$-decay energy. We notice that $T_{1/2}$ is significantly dependent on the decay formula in terms of isospin asymmetry and decay energy. We also noticed that modified scaling law Brown formula estimates of half-lives agreed comparatively better with the experiment as compared to others. Moreover, the present investigation provides significant information on the stability of the superheavy island considered for ongoing and/or future experiments.

In the present work, we have incorporated the microscopic relativistic nuclear potential obtained from recently developed relativistic R3Y NN potential in the coupled channels code CCFULL to study the fusion dynamics. The R3Y NN-potential and the densities of interacting nuclei are obtained for the relativistic mean-field approach for the NL3$^*$ parameter set. It is to be noted that the R3Y NN potential can be expressed in terms of masses of the mesons and their couplings by considering the meson degrees of freedom within the relativistic mean field, which has a form similar to the widely used M3Y potential. We focused on the fusion cross-sections for $Oxygen$-based reactions with targets from different mass regions of the periodic table i.e. $^{16}$O + $^{24}$Mg, $^{18}$O + $^{24}$Mg, $^{16}$O + $^{148}$Sm, $^{16}$O + $^{176}$Hf, $^{16}$O + $^{176}$Yb, $^{16}$O + $^{182}$W, and $^{16}$O + $^{186}$W. A comparison is also made with the ones calculated using the nuclear potential obtained from the traditional Woods-Saxon potential and the widely used M3Y NN potential within CCFULL. The coupled channel calculations are performed with shape and rotational degrees of freedom to examine the fusion enhancement at below-barrier energies. It is observed from the calculations that the fusion cross-sections obtained using R3Y NN potential with rotational degrees of freedom are found to be more consistent with the experimental data than those for the M3Y and Woods-Saxon potentials mainly at below barrier energies.

In this theoretical study, we have derived a simplified analytical expression for the binding energy per nucleon as a function of density and isospin asymmetry within the relativistic mean-field model. We have generated a new parameterization for the density-dependent DD-ME2 parameter set using the Relativistic-Hartree-Bogoliubov approach. Moreover, this work attempts to revisit the prior polynomial fitting in [Phy. Rev. C 103, 024305 (2021)] for the non-linear NL3 force parameter to provide a simplified set of equations for the energy density functional which is used for calculating the surface properties of finite nuclei. The current study improves the existing fitting procedure by effectively proposing a simpler model that provides comparably precise results while lowering the computational expense. To study the surface properties of finite nuclei with these parameterizations, we have adopted the coherent density fluctuation model, which effectively translates the quantities of nuclear matter from momentum space to coordinate space at local density. The isospin properties, such as symmetry energy and its surface and volume components, slope parameter, finite nuclear incompressibility, and surface incompressibility for even-even nuclei, are calculated for different mass regions. Moreover, we have studied the effect of density, weight function, and choice of relativistic force parameters on the surface properties. The consequence of this work will help to determine the properties of nuclei along the nuclear landscape and can facilitate an improved understanding of the island of stability, heavy-ion collision, and nucleosynthesis, among others.