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

Tolulope Majekodunmi Joshua,Mrutunjaya Bhuyan,Nooraihan Abdullah,Khairul Anwar,Raj Kumar,Nishu Jain

doi:10.3390/foundations2010004

Abstract

A new α-emitting 214U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even–even neutron deficient 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 10−8–10−5 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.

Highlights

A careful evaluation of Figure 6, which portrays the relationship between the preformation probability P0 and the penetrability P, where both parameters are shown as a function of the mass number, reveals that lower P0 values correspond to a higher P and vice versa, such that their products P0 P are near to the same order for all the decay chains under study
The relativistic mean-field (RMF) framework is employed for the calculation of the ground-state properties of the newly measured 214 U and remeasured 216,218 U together with the decay product in their respective α-decay chains and compared with those from the finite range droplet model (FRDM) and WS3 mass tables
The FRDM data with the new R3Y NN potential are found to be in close agreement with the experimental half-lives

Summary

Introduction

The authors [15] reported that an abnormal enhancement was observed in the reduced width of other remeasured light even-even 216,218 U isotopes around the proton closed-shell 84 ≤ Z ≤ 90 and neutron closed-shell N < 126 This constitutes our motivation to theoretically examine this phenomenon in the α-decay chain of these lighter uranium isotopes using the PCM within the RMF framework [41,42,43], which is cognate with the energy density functional formalism and gives an accurate description of both ground and excited-state properties across the entire nuclear landscape [44].

Theoretical Framework

Calculations and Discussions

Summary and Conclusions