Three-Body Barrier Dynamics of Double-Alpha Decay in Heavy Nuclei

Abstract

The simultaneous emission of two $α$ particles--double-$α$ decay--represents a long-predicted but unobserved mode of nuclear radioactivity. Here we formulate this process as a genuine three-body problem within the hyperspherical coordinate framework and evaluate decay probabilities by numerically solving the corresponding hyperradial Schrödinger equation, combined with large-scale random sampling of the potential parameters; the latter treatment ensures that the present results are more convincing. Inspired by this, we demonstrate that the penetrability ratio between simultaneous and sequential $α$ emission exhibits a strikingly linear dependence on $ZQ_{αα}^{-1/2}$, extending the barrier penetration dynamics into the correlated few-body regime. The nuclei $^{108}$Xe, $^{218}$Ra, $^{224}$Pu, $^{222}$U, $^{216}$Rn, and $^{220}$Th are suggested as the most promising candidates for the observation of double-$α$ decay, with predicted half-lives potentially accessible within present detection limits. Our results provide a unified framework for multi-$α$ decay and open a pathway to probing nuclear clustering and few-body correlations in heavy nuclei.

Figures (4)

• Figure 1: Schematic diagrams of simultaneous 2$\alpha$ decay (left panel) and sequential $\alpha$ decay (right panel). The right panel actually illustrates two successive $\alpha$ decays of the same nucleus shown in the left panel. In the simultaneous case, the two $\alpha$ particles are emitted without a predetermined order. Note that $s_{ij}, s_{ik}$ and $s_{jk}$ are not the physical distances between the particles, but rather scaled quantities within the hyperspherical formalism.
• Figure 2: Flowchart for the calculation of half-lives of double-$\alpha$ decay and the decay width branching ratio $\mathrm{BR} = \Gamma_{\alpha\alpha}/\Gamma_\alpha$. The terms Para-$\alpha_1$, Para-$\alpha_2$ and Para-$\alpha\alpha$ denote the parameters associated with the sequential emissions of $\alpha_1$ and $\alpha_2$ and simultaneous $2\alpha$ emission, respectively.
• Figure 3: The main panel shows the logarithm of the penetrability ratio $\mathrm{log_{10}(\Gamma_{\alpha\alpha})}$ as a function of $ZQ^{-1/2}$, with the inset (a) displays BR as a function of the same variable. The linear fit in main panel yields a Pearson correlation coefficient of $0.961$, indicating that the half-lives of double-$\alpha$ decay approximately follow a Geiger–Nuttall type relation.
• Figure 4: Logarithm of the simultaneous 2$\alpha$ decay half-life, $\log_{10}(T_{\alpha\alpha})$, for the promising candidate nuclei. Red circles denote the present prediction using the Faddeev-like formalism, with vertical error bars reflecting the statistical uncertainties obtained from the parameter-sampling procedure. Other symbols correspond to theoretical estimates reported in Refs. JPL1985DenisovZhaoSan1Megtbxv-tlbf.