Fate of Multiparticle Resonances: From $Q$-Balls to ${}^3$He Droplets

Abstract

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.

6 pages, 1 figure

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• Scaling Laws Governing the Collapse of a Bose-Einstein Condensate
• Universal spectrum of isolated three-body resonances