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

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.