Short-Range Hard-Sphere Potential and Coulomb Interaction: Deser-Trueman Formula for Rydberg States of Exotic Atomic Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915489642446848 |
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| author | Adkins, G. S. Jentschura, U. D. |
| author_facet | Adkins, G. S. Jentschura, U. D. |
| contents | 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 treated on the basis of Wigner-Brioullin perturbation theory. Recently, high-angular-momentum Rydberg states of exotic atomic systems with hadronic constituents have been identified as promising candidates for the search of New Physics in the low-energy sector of the Standard Model. In order to render this endeavor feasible, it is necessary to estimate the strong-interaction correction to the atomic energy levels. 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~$\ell$, and find that the energy shift is given by the formula delta E = 2 alpha_{n, L} beta_L (a_h/a_0)^(2 L + 1) E_h/n^3, where alpha_{n,0} = 1, alpha_{n,L} is the product from s=1 to s=L of the expression (s^(-2) - n^(-2)), beta_L = (2 L + 1)/[(2 L + 1)!!]^2, where E_h is the Hartree energy, a_h is the hadronic radius and a_0 is the generalized Bohr radius. The square of the double factorial, [(2\ell + 1)!!]^2, in the denominator implies a drastic suppression of the effect for higher angular momenta. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_15973 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Short-Range Hard-Sphere Potential and Coulomb Interaction: Deser-Trueman Formula for Rydberg States of Exotic Atomic Systems Adkins, G. S. Jentschura, U. D. Atomic Physics 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 treated on the basis of Wigner-Brioullin perturbation theory. Recently, high-angular-momentum Rydberg states of exotic atomic systems with hadronic constituents have been identified as promising candidates for the search of New Physics in the low-energy sector of the Standard Model. In order to render this endeavor feasible, it is necessary to estimate the strong-interaction correction to the atomic energy levels. 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~$\ell$, and find that the energy shift is given by the formula delta E = 2 alpha_{n, L} beta_L (a_h/a_0)^(2 L + 1) E_h/n^3, where alpha_{n,0} = 1, alpha_{n,L} is the product from s=1 to s=L of the expression (s^(-2) - n^(-2)), beta_L = (2 L + 1)/[(2 L + 1)!!]^2, where E_h is the Hartree energy, a_h is the hadronic radius and a_0 is the generalized Bohr radius. The square of the double factorial, [(2\ell + 1)!!]^2, in the denominator implies a drastic suppression of the effect for higher angular momenta. |
| title | Short-Range Hard-Sphere Potential and Coulomb Interaction: Deser-Trueman Formula for Rydberg States of Exotic Atomic Systems |
| topic | Atomic Physics |
| url | https://arxiv.org/abs/2506.15973 |