The simultaneous emission of two $\alpha$ particles—double-$\alpha$ 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. Inspired by this, we demonstrate that the decay width ratio between simultaneous and sequential $\alpha$ emission exhibits a strikingly linear dependence on $Z{Q}_{\alpha \alpha }^{-1/2}$, extending the barrier penetration dynamics into the correlated few-body regime. The nuclei ${}^{108}\mathrm{Xe}$, ${}^{218}\mathrm{Ra}$, ${}^{224}\mathrm{Pu}$, ${}^{222}\mathrm{U}$, ${}^{216}\mathrm{Rn}$, and ${}^{220}\mathrm{Th}$ are suggested as the most promising candidates for the observation of double-$\alpha$ decay, with predicted half-lives potentially accessible within present detection limits. Our results provide a unified framework for multi-$\alpha$ decay and open a pathway to probing nuclear clustering and few-body correlations in heavy nuclei.

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• Alpha decay
• Nuclear structure & decays
• Nuclear many-body theory