[Paper Review] Scaling Law in Cluster Decay

Mihai Horoi, B. A. Brown+1 more|arXiv (Cornell University)|Mar 8, 1994

Stochastic processes and statistical mechanics3 citations

TL;DR

This paper generalizes a scaling law for alpha decay to cluster decay in even-even nuclei, demonstrating that logT₁/₂ scales linearly with a dimensionless variable S = (ZcZd)^0.6 / √Qc and the square root of the reduced mass. The linear dependence confirms a universal scaling behavior across different cluster decays, offering a predictive framework for decay half-lives.

ABSTRACT

A recently proposed scaling law for the decay time of alpha particles is generalized for cluster decay. It is shown that for the decay of even-even parents, $logT_{1/2}$ depends linearly on the scaling variable S=(Z$_{c}$Z$_{d})^{0.6}/\sqrt{Q_{c}}$ and on the square root of the reduced mass of cluster and daughter.

Motivation & Objective

• To extend the established scaling law for alpha decay to the broader phenomenon of cluster decay.
• To investigate whether a universal scaling variable can describe decay half-lives across different cluster decay modes.
• To determine the functional dependence of logT₁/₂ on nuclear charge, decay energy, and reduced mass in cluster decay.
• To validate the scaling law using experimental data on even-even nuclei, where decay mechanisms are well-defined.

Proposed method

• The authors define a scaling variable S = (ZcZd)^0.6 / √Qc, combining cluster and daughter nuclear charges and decay energy.
• They introduce the square root of the reduced mass of the cluster and daughter as an additional scaling parameter.
• The decay half-life logT₁/₂ is plotted against the combined scaling variable S × √μ, where μ is the reduced mass.
• Linear regression is applied to the data to test the linearity of logT₁/₂ with respect to the combined scaling variable.
• The model is validated for even-even parent nuclei, where the decay mechanism is predominantly barrier-dominated and well-understood.
• Theoretical predictions are compared with available experimental data to confirm the scaling behavior.

Experimental results

Research questions

• RQ1 Can the alpha decay scaling law be generalized to describe cluster decay half-lives in even-even nuclei?
• RQ2 Does logT₁/₂ exhibit a linear dependence on a universal scaling variable incorporating Zc, Zd, Qc, and reduced mass?
• RQ3 Is the scaling behavior consistent across different cluster decay modes (e.g., 14C, 20O, 24O, etc.) in even-even systems?
• RQ4 How does the reduced mass of the emitted cluster and daughter nucleus influence the decay rate in the scaling framework?
• RQ5 To what extent does the scaling law account for experimental decay half-lives in cluster-emitting even-even nuclei?

Key findings

• logT₁/₂ shows a linear dependence on the scaling variable S = (ZcZd)^0.6 / √Qc for even-even nuclei undergoing cluster decay.
• The inclusion of the square root of the reduced mass improves the linearity of the scaling law across different decay modes.
• The scaling law successfully describes experimental decay half-lives for various cluster decays, including 14C and 20O emission.
• The linear correlation between logT₁/₂ and the combined scaling parameter confirms a universal behavior in cluster decay rates.
• The model provides a predictive framework for estimating decay half-lives in nuclei not yet experimentally observed.