Divergence in the Relativistic Mean Field Formalism: A Case Study of the Ground State Properties of the Decay Chain of 214,216,218U Isotopes

A new α-emitting has been observed experimentally for neutron deficient 214U which opens the window to theoretically investigate the ground state properties of 214,216,218U isotopes and to examine α-particle clustering around the shell closure. The decay half-lives are calculated within the preformed cluster-decay model (PCM). To obtain the α-daughter interaction potential, the RMF densities are folded with the newly developed R3Y and the well-known M3Y NN potentials for comparison. The alpha preformation probability (Pα) is calculated from the analytic formula of Deng and Zhang. The WKB approximation is employed for the calculation of the transmission probability. The individual binding energies (BE) for the participating nuclei are estimated from the relativistic mean-field (RMF) formalism and those from the finite range droplet model (FRDM) as well as WS3 mass tables. In addition to Z=84, the so-called abnormal enhancement region, i.e., 84≤Z≤90 and N<126, is normalised by an appropriately fitted neck-parameter ΔR. On the other hand, the discrepancy sets in due to the shell effect at (and around) the proton magic number Z=82 and 84, and thus a higher scaling factor ranging from 10−5–10−8 is required. Additionally, in contrast with the experimental binding energy data, large deviations of about 5–10 MeV are evident in the RMF formalism despite the use of different parameter sets. An accurate prediction of α-decay half-lives requires a Q-value that is in proximity with the experimental data. In addition, other microscopic frameworks besides RMF could be more reliable for the mass region under study. α-particle clustering is largely influenced by the shell effect.

Comparison of perturbative and non-perturbative methods in f(R) gravity

In this work, we investigate the structure and properties of neutron stars in $$R^2$$ R 2 gravity using two approaches, viz: the perturbative and non-perturbative methods. For this purpose, we consider NS with several nucleonic, as well as strange EoS generated in the framework of relativistic mean field models. The strange particles in the core of NS are in the form of $$\Lambda $$ Λ hyperons and quarks, in addition to the nucleons and leptons. In both the approaches, we obtain mass–radius relation for a wide range of values of the extra degree of freedom parameter a arising due to modification of gravity at large scales. The mass–radius relation of the chosen equation of states lies well within the observational limit in the case of GR. We identify the changes in the property of neutron star in the background of f(R) gravity, and compare the results in both the methods. We also identify the best suited method to study the modified gravity using the astrophysical observations.

Skyrme–Hartree–Fock–Bogoliubov Calculations of Even and Odd Neutron-Rich Mg Isotopes

Using the Skyrme functional with SIII, SKM*, SLy4, and UNE0 sets of parameters and the Hartree–Fock–Bogoliubov mean-field method; the ground-state properties of even-even and even-odd neutron-rich Mg isotopes have been investigated. The results of calculations of the binding energy per nucleon (B/A), the one- and two-neutron separation energies (Sn and S2n), proton and neutron rms radii, neutron pairing gap, and quadrupole deformation parameter (B2) have been compared with the available experimental data, the results of Hartree–Fock–Bogoliubov calculations based on the D1S Gogny force, and predictions of some nuclear models such as the Finite Range Droplet Model (FRDM) and Relativistic Mean-Field (RMF) model. Our results show good agreements in comparison with the experimental data and the results of the mentioned models.

Cluster decay half-lives in trans-tin and transition metal region using RMF theory

In the present work, we have studied the alpha-like clusters (8Be, 12C, 16O, 20Ne, and 24Mg) decay half-lives in the trans-tin region for (106-116Xe, 108-122Ba, 114-124Ce, and 118-128Nd) and in transition metal region for (156-166Hf, 158-172W, 160-174Os, 166-180Pt, and 170-182Hg) nuclei. These half-lives have been calculated using the shape parametrization model of cluster decay in conjunction with the relativistic mean-field (RMF) model with the NL3* parameter set. Thus calculated cluster decay half-lives are also compared with the half-lives computed using the latest empirical relations, namely Universal decay law (UDL) and the Scaling Law given by Horoi et al.. From the calculated results, it has been observed that in the trans-tin region, the minimum cluster decay half-lives are found at nearly doubly magic or doubly magic daughter 100Sn (Nd = 50, Nd is the neutron number of the daughter nuclei) shell effect at Nd = 50 and in transition metal region, half-lives are minimum at Nd = 82, which is a magic number. Further, the Geiger-Nuttal plots of half-lives showing Q dependence for different alpha-like clusters from various CR emitters that have been plotted are found to vary linearly.

Surface properties for Ne, Na, Mg, Al and Si isotopes in the Coherent Density Fluctuation Model using the relativistic mean field densities

We have systematically studied the surface properties, such as symmetry energy, neutron pressure, and symmetry energy curvature coefficient for Ne, Na, Mg, Al, and Si nuclei from the proton to neutron drip-lines. The Coherent Density Fluctuation Model (CDFM) is used to estimate these quantities taking the relativistic mean-field densities as inputs. The Br ¨uckner energy density functional is taken for the nuclear matter binding energy and local density approximation is applied for its conversion to coordinate space. The symmetry energy again decomposed to the volume and surface components within the liquid drop model formalism to the volume and surface parts separately. Before calculating the surface properties of finite nuclei, the calculated bulk properties are compared with the experimental data, whenever available. The NL3* parameter set with the BCS pairing approach in an axially deformed frame-work is used to take care of the pairing correlation when needed. The deformed density is converted to its spherical equivalent with a two Gaussian fitting, which is used as an input for the calculation of weight function in the CDFM approximation. With the help of the symmetry energy for the recently isotopes ²⁹F, ²⁸Ne, ^29,30Na and ^31,35,36Mg are considered to be within the island of inversion emphasized [Phys. Lett. B 772, 529 (2017)]. Although we get large symmetric energies corresponding to a few neutron numbers for this isotopic chain as expected, an irregular trend appears for all these considered nuclei. The possible reason behind this abnormal behavior of symmetry energy for these lighter mass nuclei is also included in the discussion, which gives a direction for future analysis.

Isotopic shift in magic nuclei within relativistic mean-field formalism

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 304120.

Microscopic study of higher-order deformation effects on the ground states of superheavy nuclei around Hs-270

We study the effects of higher-order deformations βλ (λ = 4,6,8, and 10) on the ground state properties of superheavy nuclei (SHN) near the deformed doubly magic nucleus 270Hs by using the multidimensionally-constrained (MDC) relativistic mean-field (RMF) model with five effective interactions PC-PK1, PK1, NL3∗, DD-ME2, and PKDD. The doubly magic properties of 270Hs are featured by the large energy gaps at N = 162 and Z = 108 in the single-particle spectra. By investigating the binding energies and single-particle levels of270Hs in multidimensional deformation space, we find that the deformation β6 has the greatest impact on the binding energy among these higher-order deformations and influences the shell gaps considerably. Similar conclusions hold for other SHN near 270Hs. Our calculations demonstrate that the deformation β6 must be considered when studying SHN by using MDC-RMF.