Physical Review A

Fate of multiparticle resonances: From Q -balls to He3 droplets

Dam Thanh Son, Mikhail A. Stephanov, Ho-Ung Yee

Published Nov 28, 2022• 9 citations

Abstract

The authors study a system of $N$ nonrelativistic particles which form a near-threshold resonance. They find that some many-body quantum objects, for example, clusters of about 30 ${}^{3}$He atoms, while being metastable, cannot decay through emission of one particle at a time. Rather, they decay via a spontaneous mini-explosion where all the constituent atoms are released at once.

DOI: 10.1103/physreva.106.l050801

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Physical Review A

Fate of multiparticle resonances: From Q -balls to He3 droplets

Dam Thanh Son, Mikhail A. Stephanov, Ho-Ung Yee

Published Nov 28, 2022• 9 citations

Publisher

Abstract

The authors study a system of

N

nonrelativistic particles which form a near-threshold resonance. They find that some many-body quantum objects, for example, clusters of about 30

{}^{3}

He atoms, while being metastable, cannot decay through emission of one particle at a time. Rather, they decay via a spontaneous mini-explosion where all the constituent atoms are released at once.

DOI: 10.1103/physreva.106.l050801

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

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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 $E^{Δ-5/2}$ in the limit when the energy $E$ of the resonance goes to zero, where $Δ$ 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.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 $E^{Δ-5/2}$ in the limit when the energy $E$ of the resonance goes to zero, where $Δ$ 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.

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The authors study a system of

N

nonrelativistic particles which form a near-threshold resonance. They find that some many-body quantum objects, for example, clusters of about 30

{}^{3}

He atoms, while being metastable, cannot decay through emission of one particle at a time. Rather, they decay via a spontaneous mini-explosion where all the constituent atoms are released at once.

Fate of Multiparticle Resonances: From

Q

-Balls to

^3

He Droplets

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^{Δ-5/2}

in the limit when the energy

E

of the resonance goes to zero, where

Δ

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.

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.

In a recent work [Phys. Rev. Lett.94, 143201 (2005)], we reported an accumulation of three-body resonant states attached to

n=2

and higher two-body thresholds. A more careful investigation revealed that there are resonances of the same kind above the

n=1

threshold as well. This suggests that the resonances attached to the thresholds are Efimov resonances.