Abstract
We present the full description of a measurement of the branching ratios for the $\ensuremath{\beta}$ decay of $^{38}\mathrm{Ca}$. This decay includes five allowed ${0}^{+}\ensuremath{\rightarrow}{1}^{+}$ branches and a superallowed ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ one. With our new result for the latter, we determine its $ft$ value to be $3062.3\ifmmode\pm\else\textpm\fi{}6.8$ s, a result whose precision (0.2%) is comparable to the precision of the 13 well-known ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ transitions used up until now for the determination of ${V}_{\text{ud}}$, the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix. The $^{38}\mathrm{Ca}$ superallowed transition thus becomes the first addition to this set of transitions in nearly a decade and the first for which a precise mirror comparison is possible, thus enabling an improved test of the isospin-symmetry-breaking corrections required for the extraction of ${V}_{\text{ud}}$.
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