Lifetime of Near-Threshold Multiparticle Resonances: From Q-balls to helium-3 droplets

We consider a system of N nonrelativistic particles which form a near-threshold resonance. Assuming no subset of these particles forms a bound state, the resonance can decay only to N particles. We show that the decay width of the resonance scales as E^Δ-5/2 where ∆ is the ground state energy of a system of N particles in a spherical harmonic trap with unit frequency. The formula remains to be valid when some of the final particles have resonant s-wave interaction with each other, provided that the Efimov effect is not present. In the limit of large N, we show that the spectrum of final particles is the Maxwell-Bolzmann distribution in the case of bosons, and follows a semicircle-like law in the case of fermions. We argue that metastable ³He droplets exist with the lifetime varying over many orders of magnitudes ranging from a fraction of a nanosecond to values much larger than the age of the Universe.