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.

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.

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.

Structural properties of nuclei with semi-magic number N(Z) = 40

In this paper, various ground state properties are explored for full isotonic(isotopic) chain of neutron number N [Formula: see text]proton number [Formula: see text] using different families of Relativistic Mean-Field theory. Several properties, such as nucleon separation energies, pairing energies, deformation, radii and nucleon density distributions, are evaluated and compared with the experimental data as well as those from other microscopic and macroscopic models. [Formula: see text] isotonic chain presents ample of support for the neutron magicity and articulates double magicity in recently discovered [Formula: see text]Ca and [Formula: see text]Ni. Our results are in close conformity with the recently measured value of charge radius of [Formula: see text]Ni [S. Kaufmann et al., Phys. Rev. Lett. 124 (2020) 132502] which supports the [Formula: see text] magicity. Contrarily, Zr isotopes ([Formula: see text]) display variety of shapes leading to the phenomenon of shape transitions and shape co-existence. The role of 3s[Formula: see text] state, which leads to central depletion if unoccupied, is also investigated. [Formula: see text]S and [Formula: see text]Zr are found to be doubly bubble nuclei.