The possibility of branching in the decays of ${\mathrm{Na}}^{21}$, ${\mathrm{Mg}}^{23}$, ${\mathrm{Al}}^{25}$, ${\mathrm{Si}}^{27}$, ${\mathrm{S}}^{31}$, and ${\mathrm{Ca}}^{39}$ has been investigated using NaI(Tl) scintillation detectors. The nuclear gamma rays emitted as a result of branching transitions were detected in coincidence with the accompanying positron annihilation radiation. Branching was found to the first excited states of the daughter nuclei in the decays of ${\mathrm{Na}}^{21}$, ${\mathrm{Mg}}^{23}$, and ${\mathrm{S}}^{31}$, with intensities (compared to the total decay) of 2.2, 9.1, and 1.1%, respectively. The decays of ${\mathrm{Al}}^{25}$, ${\mathrm{Si}}^{27}$, and ${\mathrm{Ca}}^{39}$ were found to have no detectable branching to the lower excited states of the daughter nuclei, and upper limits of less than one percent were placed on the branching ratios for such branches. The lack of branching in the decay of ${\mathrm{Al}}^{25}$ to the 0.98-Mev level of ${\mathrm{Mg}}^{25}$ favors a unified model description for the nuclear states involved.
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