Precision spectroscopy and nuclear structure information of Li⁺ ions

Abstract

Precision spectroscopy of lithium ions offers a unique research platform for exploring bound state quantum electrodynamics and investigating the structure of atomic nuclei. This article provides an overview of our recent efforts, which focus on the precision theoretical calculations and experimental measurements of the hyperfine splittings of ^6,7Li⁺ ions in the 2³<i>S</i>₁ and 2³<i>P</i>_<i>J</i> states. In our theoretical framework, we apply bound state quantum electrodynamics to calculate the hyperfine splitting of the 2³<i>S</i>₁ and 2³<i>P</i>_<i>J</i> states with remarkable precision, achieving an accuracy on the order of <i>mα</i>⁶. Using Hylleraas basis sets, we first solve the non-relativistic Hamiltonian of the three-body system to derive highprecision energies and wave functions. Subsequently, we consider various orders of relativity and QED corrections using the perturbation method, leading to a final calculated accuracy of the hyperfine splitting on the order of tens of kHz. In our experimental efforts, we have developed a low-energy metastable lithium-ion source that provides a stable and continuous ion beam in the 2³<i>S</i>₁ state. Using this ion beam, we employed saturated fluorescence spectroscopy to enhance the precision of hyperfine structure splittings of ⁷Li⁺ in the 2³<i>S</i>₁ and 2³<i>P</i>_<i>J</i> states to about 100 kHz. Furthermore, by utilizing the optical Ramsey method, we obtained the most precise values of the hyperfine splittings of ⁶Li⁺, with the smallest uncertainty of about 10 kHz. By combining theoretical calculations and experimental measurements, our team derived the Zemach radii of the ^6,7Li nuclei, revealing a significant deviation between the Zemach radius of ⁶Li and the values predicted by the nuclear model. These findings illuminate the distinct attributes of the ⁶Li nucleus, catalyzing further investigations in atomic nucleus and propelling advancements in precision spectroscopy of few-electron atoms and molecules.