Abstract
In exotic atomic systems with hadronic constituent particles, it is notoriously difficult to estimate the strong-interaction correction to energy levels. It is well known that, due to the strength of the nuclear interaction, the problem cannot be solved using Wigner–Brillouin perturbation theory alone. Recently, high-angular-momentum Rydberg states of exotic atomic systems with hadronic constituents have been identified as promising candidates in the search for new physics in the low-energy sector of the Standard Model. We thus derive a generalized Deser–Trueman formula for the induced energy shift for a general hydrogenic bound state with principal quantum number n and orbital angular momentum quantum number ℓ, and we find that the energy shift is given by the formula (Formula presented.), where (Formula presented.), (Formula presented.), (Formula presented.), (Formula presented.) is the Hartree energy, (Formula presented.) is the hadronic radius and (Formula presented.) is the generalized Bohr radius. The square of the double factorial, (Formula presented.), in the denominator implies a drastic suppression of the effect for higher angular momenta.
Recommended Citation
G. S. Adkins and U. D. Jentschura, "Short–Range Hard–Sphere Potential and Coulomb Interaction: Deser–Trueman Formula for Rydberg States of Exotic Atomic Systems," Atoms, vol. 13, no. 9, article no. 81, MDPI, Sep 2025.
The definitive version is available at https://doi.org/10.3390/atoms13090081
Department(s)
Physics
Publication Status
Open Access
Keywords and Phrases
exotic atoms; hadronic atoms; quantum defect theory; radius perturbation theory
International Standard Serial Number (ISSN)
2218-2004
Document Type
Article - Journal
Document Version
Final Version
File Type
text
Language(s)
English
Rights
© 2025 The Authors, All rights reserved.
Creative Commons Licensing
This work is licensed under a Creative Commons Attribution 4.0 License.
Publication Date
01 Sep 2025
Comments
National Science Foundation, Grant PHY-2308792