Academic Journal
Non-relativistic perturbative hydrogenic Lamb shifts and radiative decay rates – a so(4, 2)-based algebraic approach.
| Τίτλος: | Non-relativistic perturbative hydrogenic Lamb shifts and radiative decay rates – a so(4, 2)-based algebraic approach. |
|---|---|
| Συγγραφείς: | Alber, Gernot |
| Πηγή: | Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences; Sep2026, Vol. 81 Issue 9, p761-780, 20p |
| Θεματικοί όροι: | Perturbation theory, Lie algebras, Atomic hydrogen, Approximation error, Radiative transitions, Fine-structure constant, Symbolic computation, Radiation |
| Περίληψη: | It is shown that algebraic techniques based on the Lie algebra so(4, 2) provide efficient tools for evaluating Lamb shifts and radiative decay rates for hydrogenic energy eigenstates as they systematically exploit the intrinsic symmetry of the hydrogenic Hamiltonian. As a main result in lowest order perturbation theory with respect to the fine-structure constant integral representations are derived for the complex-valued energy shifts of hydrogen-like ions from which Lamb shifts and radiative decay rates can be evaluated in a unified way, thus generalizing a recently discussed algebraic approach of Maclay ("Dynamical symmetries of the H atom, one of the most important tools of modern physics: SO(4) to SO(4, 2), background, theory and use in calculating radiative shifts," Symmetry, vol. 12, no. 1323, pp. 1–66, 2020). In order to exemplify the usefulness of this algebraic approach numerical results are presented for Lamb shifts and radiative decay rates which transcend the dipole approximation and contain the dipole approximation as a limiting case. [ABSTRACT FROM AUTHOR] |
| Copyright of Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences is the property of De Gruyter 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.) | |
| Βάση Δεδομένων: | Complementary Index |
| FullText | Text: Availability: 0 |
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| Header | DbId: edb DbLabel: Complementary Index An: 196850720 RelevancyScore: 1082 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1082.42749023438 |
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| Items | – Name: Title Label: Title Group: Ti Data: Non-relativistic perturbative hydrogenic Lamb shifts and radiative decay rates – a so(4, 2)-based algebraic approach. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Alber%2C+Gernot%22">Alber, Gernot</searchLink> – Name: TitleSource Label: Source Group: Src Data: Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences; Sep2026, Vol. 81 Issue 9, p761-780, 20p – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Perturbation+theory%22">Perturbation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Lie+algebras%22">Lie algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Atomic+hydrogen%22">Atomic hydrogen</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Radiative+transitions%22">Radiative transitions</searchLink><br /><searchLink fieldCode="DE" term="%22Fine-structure+constant%22">Fine-structure constant</searchLink><br /><searchLink fieldCode="DE" term="%22Symbolic+computation%22">Symbolic computation</searchLink><br /><searchLink fieldCode="DE" term="%22Radiation%22">Radiation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: It is shown that algebraic techniques based on the Lie algebra so(4, 2) provide efficient tools for evaluating Lamb shifts and radiative decay rates for hydrogenic energy eigenstates as they systematically exploit the intrinsic symmetry of the hydrogenic Hamiltonian. As a main result in lowest order perturbation theory with respect to the fine-structure constant integral representations are derived for the complex-valued energy shifts of hydrogen-like ions from which Lamb shifts and radiative decay rates can be evaluated in a unified way, thus generalizing a recently discussed algebraic approach of Maclay ("Dynamical symmetries of the H atom, one of the most important tools of modern physics: SO(4) to SO(4, 2), background, theory and use in calculating radiative shifts," Symmetry, vol. 12, no. 1323, pp. 1–66, 2020). In order to exemplify the usefulness of this algebraic approach numerical results are presented for Lamb shifts and radiative decay rates which transcend the dipole approximation and contain the dipole approximation as a limiting case. [ABSTRACT FROM AUTHOR] – Name: Abstract Label: Group: Ab Data: <i>Copyright of Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences is the property of De Gruyter 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: 10.1515/zna-2026-0121 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 761 Subjects: – SubjectFull: Perturbation theory Type: general – SubjectFull: Lie algebras Type: general – SubjectFull: Atomic hydrogen Type: general – SubjectFull: Approximation error Type: general – SubjectFull: Radiative transitions Type: general – SubjectFull: Fine-structure constant Type: general – SubjectFull: Symbolic computation Type: general – SubjectFull: Radiation Type: general Titles: – TitleFull: Non-relativistic perturbative hydrogenic Lamb shifts and radiative decay rates – a so(4, 2)-based algebraic approach. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Alber, Gernot IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 09 Text: Sep2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 09320784 Numbering: – Type: volume Value: 81 – Type: issue Value: 9 Titles: – TitleFull: Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences Type: main |
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