$^{48}$Ca, the lightest double beta decay candidate, is the only one simple enough to be treated exactly in the nuclear shell model. Thus, the $betabeta(2 u)$ half-life measurement, reported here, provides a unique test of the nuclear physics involved in the $betabeta$ matrix element calculation. Enriched $^{48}$Ca sources of two different thicknesses have been exposed in a time projection chamber, and yield T$_{1/2}^{2 u} = (4.3^{+2.4}_{-1.1} [{rm stat.}] pm 1.4 [{rm syst.}]) times 10^{19}$ years, compatible with the shell model calculations.
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