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

Abstract

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.

Preformation probability and kinematics of cluster emission yielding Pb-daughters*

“…where denotes the radius of the parent nucleus and represents the kinetic energy of the emitted cluster. The -values are estimated from the ground state binding energies from the RMF, AME2016 [37], and WS3 [36] mass tables using the expression…”

“…Figure 4 shows the variation of as a function of the neutron number of isotopes at different neck-lengths ( R). It is worth mentioning that the Q-value ( ) used here is calculated from the experimental binding energy data [37] only for the sake of accuracy. In several studies, the minima in were used to indicate the most probable decay channels; here, variations are made in order to decide on the most appropriate neck length, especially for the recently developed R3Y interaction.…”

“…The Q-values are calculated using the binding energies from experimental data [37]. Columns ( 8)-( 13) are exclusively devoted to the cluster preformation and emission details from the proposed Eqs.…”

“…The RMF theory is apt for handling the ground and excited-state properties of the atomic nuclei [33][34][35]. The -values are also calculated from the RMF (NL ) and are compared with the macroscopic-microscopic WS3 [36] and those obtained from the experimental binding energy data [37]. The WKB approximation is used to estimate the penetration probability P. The remainder of this paper is organized as follows: Sec.…”

“…5 (upper panel) shows the variation of the recoil energy of the daughter nuclei w.r.t. the corresponding neutron number for different Q-values calculated from the RMF and (dashed line with blue star), in comparison with the binding energies of Wang et al [37] denoted as (solid line with black square), as well as the WS3 given by Liu et al [36] ted line with red circle). The profile shows a regular pattern for the three sets of Q-values, which directly influences their magnitude.…”