Toward extracting scattering phase shift from integrated correlation functions IV: Coulomb corrections
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913923431661568 |
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| author | Guo, Peng Lee, Frank X. |
| author_facet | Guo, Peng Lee, Frank X. |
| contents | The formalism developed in Refs.~\cite{Guo:2023ecc,Guo:2024zal,Guo:2024pvt} that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral is further extended to include Coulomb interaction between charged particles. The original formalism cannot be applied due to different divergent asymptotic behavior resulting from the long-range nature of the Coulomb force. We show that a modified formula in which the difference of integrated correlation functions between particles interacting with Coulomb plus short-range interaction and with Coulomb interaction alone is free of divergence, and has rapid approach to its infinite volume limit. Using an exactly solvable model, we demonstrate that the short-range potential scattering phase shifts can be reliably extracted from the formula in the presence of Coulomb interaction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_01768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Toward extracting scattering phase shift from integrated correlation functions IV: Coulomb corrections Guo, Peng Lee, Frank X. High Energy Physics - Lattice Other Condensed Matter Quantum Gases High Energy Physics - Phenomenology Nuclear Theory The formalism developed in Refs.~\cite{Guo:2023ecc,Guo:2024zal,Guo:2024pvt} that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral is further extended to include Coulomb interaction between charged particles. The original formalism cannot be applied due to different divergent asymptotic behavior resulting from the long-range nature of the Coulomb force. We show that a modified formula in which the difference of integrated correlation functions between particles interacting with Coulomb plus short-range interaction and with Coulomb interaction alone is free of divergence, and has rapid approach to its infinite volume limit. Using an exactly solvable model, we demonstrate that the short-range potential scattering phase shifts can be reliably extracted from the formula in the presence of Coulomb interaction. |
| title | Toward extracting scattering phase shift from integrated correlation functions IV: Coulomb corrections |
| topic | High Energy Physics - Lattice Other Condensed Matter Quantum Gases High Energy Physics - Phenomenology Nuclear Theory |
| url | https://arxiv.org/abs/2506.01768 |