Abstract
The 'island of inversion' around $^{32}$Mg is one of the most important paradigm for studying the disappearance of the stabilizing 'magic' of a shell closure. We present the first Penning-trap mass measurements of the exotic nuclides $^{29-31}$Na and $^{30-34}$Mg, which allow a precise determination of the empirical shell gap for $^{32}$Mg. The new value of 1.10(3) MeV is the lowest observed shell gap for any nuclide with a canonical magic number.
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