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

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.

Figures (39)

• Figure 1: Energy (in MeV) of the $^{162}$Dy nucleus as a function of the constrained expectation value of the intrinsic charge quadrupole moment $Q^{(\rm intr)}_{20}$ in units of $e$barn (see \ref{['subsec_r_Q20']} for its definition). The solid curve is an interpolation through the calculated values marked by filled circles.
• Figure 2: Single-particle spectra for the ground state of $^{162}$Dy near the Fermi level obtained from the HFBCS calculations. Each level is twice degenerate because of the time-reversal symmetry. They are both labeled by the same Nilsson quantum numbers, $\Omega^{\pi}[Nn_z\Lambda]$, representing the dominant contribution of either single-particle state. $\Omega > 0$ and $\Lambda$ are the projections onto the symmetry axis of the total and orbital angular momenta, respectively, $n_z$ is the number of oscillator quanta along that axis and $N$ is the total number of oscillator quanta.
• Figure 3: Excitation energies of the first three bandhead states in $^{161}$Dy and $^{163}$Dy isotopes. Experimental data (levels labelled "Exp.") are taken from Reich11_NDS112_Dy161 and Reich10_NDS111_Dy163, respectively. The levels labelled "Th." correspond to the results of the present Skyrme--HF--BCS calculations using the Skyrme SIII parametrisation and the seniority pairing strengths $G_n = -16.2/(11+N)$ MeV and $G_p=-15.1/(11+Z)$ MeV for neutrons and protons, respectively, with $N=96$ and $Z=66$ (see text for details).
• Figure 4: Nucleon density distributions, $\rho(\vec{R})$, ($(p)$ above: protons, $(n)$ below: neutrons) of $^{159}_{65}$Tb (left), $^{161}_{66}$Dy and $^{163}_{66}$Dy (center), and $^{165}_{67}$Ho (right) on logarithmically spaced contour curves. The figures are plotted in signed cylindrical coordinates $(z,\varrho)$, on a planar slice through the $z-$axis. The spatial coordinates are in units of $R_{\rm N}$, the empirical nuclear radius (see text) for each isotope, leading to a density distribution in units of $R_{\rm N}^{-3}$. The contours represent curves of equal density, with numerical values as indicated by the legend above. The dashed curve indicates the value of the spherically-averaged monopole distribution at a distance of $1 \times R_{\rm N}$, representing the outer shell of the nucleus.
• Figure 5: (color online) Two-dimensional color maps of the orthoradial component of the spin current density $j_{q,\varphi}^{(s)}(\varrho,z)$ (top row) and orbital current density $j_{q,\varphi}^{(\ell)}(\varrho,z)/g_{\bar{q}}^{(\ell)}$ (bottom row) for the charge state $q$ identical to the one of the unpaired nucleon in the ground states of the two odd-proton nuclei $^{159}$Tb and $^{165}$Ho and the two odd-neutron nuclei $^{161}$Dy and $^{163}$Dy.