  We consider 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 show that the decay width of the resonance scales as
$E^{\Delta-5/2}$ in the limit when the energy $E$ of the resonance goes to
zero, where $\Delta$ 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
semicircle-like law if they are fermions. We argue that metastable $^3$He
droplets exist with the lifetime varying over many orders of magnitudes ranging
from a fraction of a nanosecond to values greatly exceeding the age of the
Universe.
