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Mass Ratio Dependence of Three-Body Resonance Lifetimes in 1D and 3D
Quantum Physics · Submitted 7 Dec 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We focus on mass ratios in the typical range for mixtures of ultracold atoms and reveal an intriguing dependence of the resonance widths on the mass ratio: as the mass ratio increases, the widths exhibit oscillations on top of an overall decreasing trend.
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The abstract, sentence by sentence
We present a theoretical study of resonance lifetimes in a two-component three-body system, specifically examining the decay of three-body resonances into a deep dimer and an unbound particle. Utilising the Gaussian expansion method together with the complex scaling method, we obtain the widths of these resonances from first principles. We focus on mass ratios in the typical range for mixtures of ultracold atoms and reveal an intriguing dependence of the resonance widths on the mass ratio: as the mass ratio increases, the widths exhibit oscillations on top of an overall decreasing trend. In particular, for some mass ratios the resonance width vanishes, implying that the resonance becomes in fact stable. Notably, near the mass ratio for Caesium-Lithium mixtures, we obtain nearly vanishing widths of the resonances which validates to treat them in the bound-state approximation. In addition, we perform our analysis of the resonance widths in both one and three dimensions and find a qualitatively similar dependence on the mass ratio.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a theoretical study of resonance lifetimes in a two-component three-body system, specifically examining the decay of three-body resonances into a deep dimer and an unbound particle. | contribution 0.98 | 0.93 | 0.04 | asserted 0.92 |
| s1 | Utilising the Gaussian expansion method together with the complex scaling method, we obtain the widths of these resonances from first principles. | method 1.00 | 0.96 | 0.03 | asserted 1.00 |
| s2 | We focus on mass ratios in the typical range for mixtures of ultracold atoms and reveal an intriguing dependence of the resonance widths on the mass ratio: as the mass ratio increases, the widths exhibit oscillations on top of an overall decreasing trend. | result 0.99 | 0.96 | 0.73 | asserted 1.00 |
| s3 | In particular, for some mass ratios the resonance width vanishes, implying that the resonance becomes in fact stable. | result 0.61 | 0.92 | 0.29 | asserted 0.90 |
| s4 | Notably, near the mass ratio for Caesium-Lithium mixtures, we obtain nearly vanishing widths of the resonances which validates to treat them in the bound-state approximation. | interpretation 0.59 | 0.95 | 0.14 | asserted 0.97 |
| s5 | In addition, we perform our analysis of the resonance widths in both one and three dimensions and find a qualitatively similar dependence on the mass ratio. | result 0.86 | 0.97 | 0.09 | asserted 1.00 |
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Original abstract
We present a theoretical study of resonance lifetimes in a two-component three-body system, specifically examining the decay of three-body resonances into a deep dimer and an unbound particle. Utilising the Gaussian expansion method together with the complex scaling method, we obtain the widths of these resonances from first principles. We focus on mass ratios in the typical range for mixtures of ultracold atoms and reveal an intriguing dependence of the resonance widths on the mass ratio: as the mass ratio increases, the widths exhibit oscillations on top of an overall decreasing trend. In particular, for some mass ratios the resonance width vanishes, implying that the resonance becomes in fact stable. Notably, near the mass ratio for Caesium-Lithium mixtures, we obtain nearly vanishing widths of the resonances which validates to treat them in the bound-state approximation. In addition, we perform our analysis of the resonance widths in both one and three dimensions and find a qualitatively similar dependence on the mass ratio.
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References
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3 arXiv papers cite this in 3 sentences
Papers citing it · 1 sentence without a confident label
Uses its method or tool 2 papers
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The combination of the GEM and the CSM has proven to be a powerful tool for investigating few-body resonances [ref] .
Existence of the $DD^*\bar{K}^*$ and $BB^*K^*$ three-body molecular states · Methodology · 0.87
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Meanwhile, the combination of the Gaussian expansion method (GEM) [ref] and the complex scaling method (CSM) [ref] has proven to be a powerful tool for studying few-body resonance systems.
Constraining the $DDD^*$ three-body bound state via the $Z_c(3900)$ pole · Introduction · 0.96
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