Exact solutions and quantum defect theory for van der Waals potentials in ultracold molecular systems.
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| Title: | Exact solutions and quantum defect theory for van der Waals potentials in ultracold molecular systems. |
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| Authors: | Jie, Jianwen1 (AUTHOR), Chen, Shi1 (AUTHOR), Chen, Yue2,3 (AUTHOR) yuechenphy@163.com, Qi, Ran4,5 (AUTHOR) qiran@ruc.edu.cn |
| Source: | Journal of Physics B: Atomic, Molecular & Optical Physics. 9/14/2025, Vol. 58 Issue 17, p1-12. 12p. |
| Subjects: | Ultracold molecules, Quantum defect theory, Schrödinger equation, Intermolecular forces, Resonance, Scattering (Mathematics), Schroedinger, Erwin, 1887-1961, Two-body problem (Physics), Bound states |
| Abstract: | In this paper, we have provided exact two-body solutions to the 2D and 3D Schrödinger equations with isotropic van der Waals potentials of the form ± 1 / r 6 . Based on these solutions, we developed an analytical quantum defect theory (QDT) applicable to both quasi-2D and 3D geometries, and applied it to study the scattering properties and bound-state spectra of ultracold polar molecules confined in these geometries. Interestingly, we find that in the attractive (repulsive) van der Waals potential case, the short-range interaction can be effectively modeled by an infinite square barrier (finite square well), which leads to narrow and dense (broad and sparse) resonance structures in the quantum defect parameter. In the quasi-2D attractive case, shape resonances can appear in an ordered fashion across different partial waves, characterized by sharp phase jumps as the scattering energy is varied. Furthermore, the low-energy analytical expansions derived from QDT show excellent agreement with the exact numerical results, validating the accuracy and usefulness of our analytical approach in describing two-body physics governed by long-range van der Waals interactions. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Physics B: Atomic, Molecular & Optical Physics is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 189106756 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Exact solutions and quantum defect theory for van der Waals potentials in ultracold molecular systems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Jie%2C+Jianwen%22">Jie, Jianwen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Shi%22">Chen, Shi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Yue%22">Chen, Yue</searchLink><relatesTo>2,3</relatesTo> (AUTHOR)<i> yuechenphy@163.com</i><br /><searchLink fieldCode="AR" term="%22Qi%2C+Ran%22">Qi, Ran</searchLink><relatesTo>4,5</relatesTo> (AUTHOR)<i> qiran@ruc.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Physics+B%3A+Atomic%2C+Molecular+%26+Optical+Physics%22">Journal of Physics B: Atomic, Molecular & Optical Physics</searchLink>. 9/14/2025, Vol. 58 Issue 17, p1-12. 12p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Ultracold+molecules%22">Ultracold molecules</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+defect+theory%22">Quantum defect theory</searchLink><br /><searchLink fieldCode="DE" term="%22Schrödinger+equation%22">Schrödinger equation</searchLink><br /><searchLink fieldCode="DE" term="%22Intermolecular+forces%22">Intermolecular forces</searchLink><br /><searchLink fieldCode="DE" term="%22Resonance%22">Resonance</searchLink><br /><searchLink fieldCode="DE" term="%22Scattering+%28Mathematics%29%22">Scattering (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Schroedinger%2C+Erwin%2C+1887-1961%22">Schroedinger, Erwin, 1887-1961</searchLink><br /><searchLink fieldCode="DE" term="%22Two-body+problem+%28Physics%29%22">Two-body problem (Physics)</searchLink><br /><searchLink fieldCode="DE" term="%22Bound+states%22">Bound states</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In this paper, we have provided exact two-body solutions to the 2D and 3D Schrödinger equations with isotropic van der Waals potentials of the form ± 1 / r 6 . Based on these solutions, we developed an analytical quantum defect theory (QDT) applicable to both quasi-2D and 3D geometries, and applied it to study the scattering properties and bound-state spectra of ultracold polar molecules confined in these geometries. Interestingly, we find that in the attractive (repulsive) van der Waals potential case, the short-range interaction can be effectively modeled by an infinite square barrier (finite square well), which leads to narrow and dense (broad and sparse) resonance structures in the quantum defect parameter. In the quasi-2D attractive case, shape resonances can appear in an ordered fashion across different partial waves, characterized by sharp phase jumps as the scattering energy is varied. Furthermore, the low-energy analytical expansions derived from QDT show excellent agreement with the exact numerical results, validating the accuracy and usefulness of our analytical approach in describing two-body physics governed by long-range van der Waals interactions. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Physics B: Atomic, Molecular & Optical Physics is the property of IOP Publishing and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/1361-6455/ae021e Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 12 StartPage: 1 Subjects: – SubjectFull: Ultracold molecules Type: general – SubjectFull: Quantum defect theory Type: general – SubjectFull: Schrödinger equation Type: general – SubjectFull: Intermolecular forces Type: general – SubjectFull: Resonance Type: general – SubjectFull: Scattering (Mathematics) Type: general – SubjectFull: Schroedinger, Erwin, 1887-1961 Type: general – SubjectFull: Two-body problem (Physics) Type: general – SubjectFull: Bound states Type: general Titles: – TitleFull: Exact solutions and quantum defect theory for van der Waals potentials in ultracold molecular systems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Jie, Jianwen – PersonEntity: Name: NameFull: Chen, Shi – PersonEntity: Name: NameFull: Chen, Yue – PersonEntity: Name: NameFull: Qi, Ran IsPartOfRelationships: – BibEntity: Dates: – D: 14 M: 09 Text: 9/14/2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 09534075 Numbering: – Type: volume Value: 58 – Type: issue Value: 17 Titles: – TitleFull: Journal of Physics B: Atomic, Molecular & Optical Physics Type: main |
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