We have performed precision laser spectroscopy on individual 6He (t1/2 = 0.8 s) atoms confined and cooled in a magneto-optical trap, and measured the isotope shift between 6He and 4He to be 43,194.772 +/- 0.056 MHz for the 2 3S1 - 3 3P2 transition. Based on this measurement and atomic theory, the nuclear charge radius of 6He is determined, for the first time in a method independent of nuclear models, to be 2.054 +/- 0.014 fm. The result is compared with the values predicted by a number of nuclear structure calculations, and tests their ability to characterize this loosely bound, halo nucleus.
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