Universality and threshold laws for collision lifetimes at ultralow temperatures
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| Format: | Preprint |
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2024
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| _version_ | 1866916524538724352 |
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| author | Hermsmeier, Rebekah Tscherbul, Timur V. |
| author_facet | Hermsmeier, Rebekah Tscherbul, Timur V. |
| contents | While collision lifetimes are a fundamental property of few-body scattering events, their behavior at ultralow temperatures is not completely understood. We derive a general expression for the Smith lifetime Q-matrix using multichannel quantum defect theory, which allows us to obtain the average time delay in the incident $s$-wave collision channel in the limit of zero collision energy $E$, $Q_{11}=A/\sqrt{E} + B$, where $A$ and $B$ are constants. We show that the time delay is dominated by elastic scattering, and contains an additional multichannel contribution independent of the two-body scattering length. We also obtain the expressions for the collision lifetime using the universal model of Idziaszek and Julienne [Phys. Rev. Lett. 104, 113202 (2010)]. The lifetime acquires an imaginary part in the presence of inelastic loss due to the lack of unitarity of the S-matrix, and shortens with increasing the short-range loss parameter $y$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_12438 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universality and threshold laws for collision lifetimes at ultralow temperatures Hermsmeier, Rebekah Tscherbul, Timur V. Chemical Physics Atomic Physics While collision lifetimes are a fundamental property of few-body scattering events, their behavior at ultralow temperatures is not completely understood. We derive a general expression for the Smith lifetime Q-matrix using multichannel quantum defect theory, which allows us to obtain the average time delay in the incident $s$-wave collision channel in the limit of zero collision energy $E$, $Q_{11}=A/\sqrt{E} + B$, where $A$ and $B$ are constants. We show that the time delay is dominated by elastic scattering, and contains an additional multichannel contribution independent of the two-body scattering length. We also obtain the expressions for the collision lifetime using the universal model of Idziaszek and Julienne [Phys. Rev. Lett. 104, 113202 (2010)]. The lifetime acquires an imaginary part in the presence of inelastic loss due to the lack of unitarity of the S-matrix, and shortens with increasing the short-range loss parameter $y$. |
| title | Universality and threshold laws for collision lifetimes at ultralow temperatures |
| topic | Chemical Physics Atomic Physics |
| url | https://arxiv.org/abs/2409.12438 |