We study a system of $N$ nonrelativistic particles which form a near-threshold resonance. Assuming no subset of these particles can form a bound state, the resonance can only decay through an “explosion” into $N$ particles. We find that the decay width of the resonance scales as $E^{\mathrm{\Delta }-5/2}$ in the limit when the energy $E$ of the resonance goes to zero, where $\mathrm{\Delta }$ is the ground-state energy of a system of $N$ particles in a spherical harmonic trap with unit frequency. The formula remains valid when some pairs of final particles have zero-energy $s$-wave resonance, but the Efimov effect is not present. In the limit of large $N$, we show that the final particles follow a Maxwell-Boltzmann distribution if they are bosons and a semicirclelike law if they are fermions. We expect our general result to be applicable to various systems that exist in nature. In particular, we argue that metastable ${}^3\mathrm{He}$ droplets exist with the lifetime varying over many orders of magnitude ranging from a fraction of a nanosecond to values greatly exceeding the age of the Universe.

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• Atomic & molecular clusters
• Bound states
• Classical solutions in field theory
• Lifetimes & widths
• Stability of clusters
• Clusters
• Ultracold gases
• Nuclear structure & decays