Precision calculation of hyperfine structure and the Zemach radii of $^{6,7}$Li$^+$ ions

The hyperfine structures of the 2(3)S(1) states of the Li-6(+) and Li-7(+) ions are investigated theoretically to extract the Zemach radii of the Li-6 and Li-7 nuclei by comparing with precision measurements. The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki [Phys. Rev. Lett. 111, 243001(2013)] and disagree with them by about 1.5 and 2.2 standard deviations for Li-6 and Li-7, respectively. Furthermore, our Zemach radius of Li-6 differs significantly from the nuclear physics value, derived from the nuclear charge and magnetic radii [Phys. Rev. A 78, 012513 (2008)] by more than 6 sigma, indicating an anomalous nuclear structure for Li-6. The conclusion that the Zemach radius of Li-7 is about 40% larger than that of Li-6 is confirmed. The obtained Zemach radii are used to calculate the hyperfine splittings of the 2(3)P(J) states of L-6.7(+), where an order of magnitude improvement over the previous theory has been achieved for Li-7(+).