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We investigate the 2 3 S1-2 3 PJ (J = 0, 1, 2) transitions in 6 Li + using the optical Ramsey technique and achieve the most precise values of the hyperfine splittings of the 2 3 S1 and 2 3 PJ states, with smallest uncertainty of about 10 kHz. The present results reduce the uncertainties of previous experiments by a factor of 5 for the 2 3 S1 state and a factor of 50 for the 2 3 PJ states, and are in better agreement with theoretical values. Combining our measured hyperfine intervals of the 2 3 S1 state with the latest quantum electrodynamic (QED) calculations, the improved Zemach radius of the 6 Li nucleus is determined to be 2.44(2) fm, with the uncertainty entirely due to the uncalculated QED effects of order mα 7 . The result is in sharp disagreement with the value 3.71( 16) fm determined from simple models of the nuclear charge and magnetization distribution. We call for a more definitive nuclear physics value of the 6 Li Zemach radius.