Finite Nuclear Size Corrections on Hyperfine Structure in Muonic Atoms
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913109586739200 |
|---|---|
| author | Yaşar, Doğa Sikora, Bastian |
| author_facet | Yaşar, Doğa Sikora, Bastian |
| contents | Finite nuclear size (FNS) effects on the magnetic-dipole hyperfine splitting in muonic hydrogenlike ions are investigated within a fully relativistic Dirac framework. The FNS contribution is quantified through the correction factor $δ$, defined by $ΔE_{\mathrm{ext}} = ΔE_{\mathrm{point}}(1 - δ)$, where $ΔE_{\mathrm{ext}}$ is evaluated using Dirac wavefunctions computed for an extended nuclear charge distribution.
Two nuclear models are considered: a homogeneously charged sphere and a two-parameter Fermi distribution. Bound-state energies and radial wavefunctions are obtained using a numerical iterative solver, while a semi-analytic matching scheme provides reference values and initial seeds. We present a systematic dataset of $δ$ values for the $1s$, $2s$, and $2p_{1/2}$ states over a wide range of nuclear charge numbers $Z$. Nuclear-model dependence is quantified, including uncertainties induced by the nuclear radius in the uniform-sphere model.
The results show that $δ$ increases monotonically with $Z$ and exhibits clear state dependence, with reduced magnitude for the $2p_{1/2}$ state relative to $s$ states. A pronounced sensitivity to the nuclear charge distribution is observed, highlighting the importance of realistic nuclear modeling in precision hyperfine studies of muonic atoms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09596 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite Nuclear Size Corrections on Hyperfine Structure in Muonic Atoms Yaşar, Doğa Sikora, Bastian Atomic Physics Finite nuclear size (FNS) effects on the magnetic-dipole hyperfine splitting in muonic hydrogenlike ions are investigated within a fully relativistic Dirac framework. The FNS contribution is quantified through the correction factor $δ$, defined by $ΔE_{\mathrm{ext}} = ΔE_{\mathrm{point}}(1 - δ)$, where $ΔE_{\mathrm{ext}}$ is evaluated using Dirac wavefunctions computed for an extended nuclear charge distribution. Two nuclear models are considered: a homogeneously charged sphere and a two-parameter Fermi distribution. Bound-state energies and radial wavefunctions are obtained using a numerical iterative solver, while a semi-analytic matching scheme provides reference values and initial seeds. We present a systematic dataset of $δ$ values for the $1s$, $2s$, and $2p_{1/2}$ states over a wide range of nuclear charge numbers $Z$. Nuclear-model dependence is quantified, including uncertainties induced by the nuclear radius in the uniform-sphere model. The results show that $δ$ increases monotonically with $Z$ and exhibits clear state dependence, with reduced magnitude for the $2p_{1/2}$ state relative to $s$ states. A pronounced sensitivity to the nuclear charge distribution is observed, highlighting the importance of realistic nuclear modeling in precision hyperfine studies of muonic atoms. |
| title | Finite Nuclear Size Corrections on Hyperfine Structure in Muonic Atoms |
| topic | Atomic Physics |
| url | https://arxiv.org/abs/2605.09596 |