Quest for a Universal Cluster Preformation Formula: A new paradigm for estimating the cluster formation energy

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 ($P_0$) 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 $P_0$ is adept at accommodating the theorized concept of heavy particle radioactivity (HPR). The result reveals that, like $\alpha$-decay, a proper estimation of the $P_0$ and $Q$-value in the cluster studies are 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 ${\log }_{10}{T}_{1/2}$ and $\sqrt{Q}$, unlike in $\alpha$-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.

arXiv comment7 pages, 3 figures, Journal

References in corpus (8)

• Relativistic Mean-Field Hadronic Models under Nuclear Matter Constraints
• The effective force NL3 revisited
• Microscopic Theory of Nuclear Fission: A Review
• Heavy particle radioactivities of superheavy nuclei
• Universal decay rule for reduced widths
• A new semiempirical formula for exotic cluster decays of nuclei
• Internal stucture of clusters in ${}^{112-122}$Ba nuclei within relativistic mean field theory
• Limitations of the Geiger-Nuttall Law in heavy cluster decay