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arXiv:2602.18144

The hyperfine interaction as a probe of the microscopic structure of the atomic nucleus

Denis Janković, Jean-Gabriel Hartmann, Johann Bartel, Hervé Molique, Ludovic Bonneau, Paul-Antoine Hervieux

physics.atom-phnucl-thquant-phSubmitted Feb 20, 2026• Announced Feb 23, 2026
v1 · Feb 20, 2026v2 · Feb 24, 2026
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Abstract

The study of highly charged electronic and muonic hydrogen-like ions, provides an intriguing way to probe the internal structure of their atomic nuclei. In this work, we use nuclear structure calculations to accurately calculate the hyperfine splitting of electronic and muonic hydrogen-like ions, focusing in particular on the incorporation of finite-volume corrections, such as Bohr-Weisskopf and Breit-Rosenthal, due to the penetration of the electron and muon wavefunction into the nuclear electric charge and magnetic dipole densities. These corrections are essential for refining our understanding of the nuclear magnetic dipole and electric quadrupole moments. Our simulations use a Skyrme-Hartree-Fock-BCS model known for its effectiveness in modeling well-deformed nuclei such as ${}^{159}\mathrm{Tb}^{64+}$ and ${}^{165}\mathrm{Ho}^{66+}$, with particular emphasis on ${}^{161,163}\mathrm{Dy}^{65+}$ isotopes. It can also be generalised to multi-electron ions by studying the hyperfine anomaly between two isotopes.

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The study of highly charged electronic and muonic hydrogen-like ions, provides an intriguing way to probe the internal structure of their atomic nuclei. In this work, we use nuclear structure calculations to accurately calculate the hyperfine splitting of electronic and muonic hydrogen-like ions, focusing in particular on the incorporation of finite-volume corrections, such as Bohr-Weisskopf and Breit-Rosenthal, due to the penetration of the electron and muon wavefunction into the nuclear electric charge and magnetic dipole densities. These corrections are essential for refining our understanding of the nuclear magnetic dipole and electric quadrupole moments. Our simulations use a Skyrme-Hartree-Fock-BCS model known for its effectiveness in modeling well-deformed nuclei such as 159Tb64+{}^{159}\mathrm{Tb}^{64+}159Tb64+ and 165Ho66+{}^{165}\mathrm{Ho}^{66+}165Ho66+, with particular emphasis on 161,163Dy65+{}^{161,163}\mathrm{Dy}^{65+}161,163Dy65+ isotopes. It can also be generalised to multi-electron ions by studying the hyperfine anomaly between two isotopes.
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Hyperfine interaction potential energy curves between two different ground state isotopic hydrogen atoms (H, D, or T) in the presence of an external magnetic field are constructed. It is found that the interaction between two isotopic hydrogen atoms is noncentral if relativistic effects are included. The eigenfunctions are expressed in terms of the basis set consisting of electronic and nuclear quantum numbers ‖ms1, mIa; mS2, mIb≳. Unlike the zero-field case with degenerate potential curves, there are 24 and 16 distinct curves for the systems H–D (or D–T) and H–T, respectively. Sample results are given for a magnetic field of B = 100 000 G, in particular. Interesting features at the true crossings and the avoided crossings between those potential curves will be described. With these accurately calculated potential curves, the accurate study of inelastic spin-exchange scattering between two different spin-polarized atoms (H↑, D↑, or T↑) can now be carried out.
High-Resolution Spectroscopy of 173^{173}173Yb+^{+}+ Ions
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