Quest for a universal cluster preformation formula: A new paradigm for estimating the cluster formation energy

¹ Institute of Engineering Mathematics, Universiti Malaysia Perlis - Arau, 02600, Perlis, Malaysia
² School of Physics and Materials Science, Thapar Institute of Engineering and Technology - Patiala, Punjab 147004, India
³ Center for Theoretical and Computational Physics, Department of Physics, Faculty of Science, University of Malaya - Kuala Lumpur 50603, Malaysia

^(a) E-mail: bunuphy@um.edu.my (corresponding author)

Received: 17 April 2023
Accepted: 5 July 2023

Abstract

This study presents a holistic picture of the preformation of nuclear clusters with credence to the kinematics of their emissions. Besides the fitting of the preformation formula to reproduce the experimental half-lives, we have investigated the interrelationship between the parameters involved in the cluster decay process for medium, heavy and superheavy nuclei. Based on the established conceptual findings, we propose a new cluster preformation probability (P₀) formula that incorporates all influential parameters of the cluster radioactivity and thus has an edge over the existing formulae in the literature. Further, we hypothesize that a fraction of the decay energy is needed for cluster formation within the parent nucleus. The proposed formula opens a new paradigm to separately estimate the energy contributed during the cluster formation from its emission and thus shows that the contribution of the Q-value splits into three major parts accounting for the energy contributed during the cluster preformation, its emission and recoil of the daughter nucleus. Moreover, the expression P₀ is adept at accommodating the theorized concept of heavy particle radioactivity (HPR). The result reveals that, like α-decay, a proper estimation of the P₀- and Q-value in the cluster studies is enriched with qualitative information about the nuclear structure. However, from the analysis, the Geiger-Nuttall law is not the best compromise in the clustering due to the non-linearity between log₁₀ T_1/2 and , unlike in α-decay. We have demonstrated that with the inclusion of the proposed formula, the half-life predictions from both microscopic R3Y and phenomenological M3Y NN potentials closely agree with the available experimental data and that the slight variation can be traced to their peculiar barrier characteristics.