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arXiv:2407.03102 · Physical Review A

Droplets of bosons at a narrow resonance

Ke Wang, Thimo Preis, Dam Thanh Son

Published Jun 26, 2025• 0 citations
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Abstract

We consider bosons interacting through a narrow $s$-wave resonance. Such a resonance is characterized by an infinite scattering length and a large and negative effective range $r_0$. We argue that any number $N\ge3$ of bosons can form a self-bound cluster with the binding energy per particle increasing as $N^2$ for $1\ll N\ll (-r_0/a_\text{bg})^{1/2}$, where $a_\text{bg}$ is the background scattering length (between atoms and molecules). In the opposite limit $N\gg (-r_0/a_\text{bg})^{1/2}$, bosons form droplets with binding energy per particle saturating to a constant value independent of the particle number. The stability of clusters and droplets when the interaction is detuned from the resonance is also studied.

DOI
10.1103/zx28-gxlt

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We consider a system of NNN 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 NNN particles. We show that the decay width of the resonance scales as EΔ−5/2E^{Δ-5/2}EΔ−5/2 in the limit when the energy EEE of the resonance goes to zero, where ΔΔΔ is the ground state energy of a system of NNN particles in a spherical harmonic trap with unit frequency. The formula remains valid when some pairs of final particles have zero-energy sss-wave resonance, but the Efimov effect is not present. In the limit of large NNN, 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 3^33He 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.
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