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We report a fourfold improvement in the determination of nuclear magneticmoments for neutron-deficient isotopes of francium-207--213, reducing theuncertainties from 2% for most isotopes to 0.5%. These are found by comparingour high-precision calculations of hyperfine structure constants for the groundstates with experimental values. In particular, we show the importance of acareful modeling of the Bohr-Weisskopf effect, which arises due to the finitenuclear magnetization distribution. This effect is particularly large in Fr anduntil now has not been modeled with sufficiently high accuracy. An improvedunderstanding of the nuclear magnetic moments and Bohr-Weisskopf effect arecrucial for benchmarking the atomic theory required in precision tests of thestandard model, in particular atomic parity violation studies, that areunderway in francium.

Nuclear magnetic moments of francium 207-213 from precision hyperfine comparisons