Study of the Isobaric Triplet ${\mathrm{Mg}}^{28}$—${\mathrm{Al}}^{28}$—${\mathrm{Si}}^{28}$

The nuclide ${\mathrm{Mg}}^{28}$ has been produced by betatron irradiation and cyclotron bombardments in the following reactions: ${\mathrm{Si}}^{30}(\gamma , 2p){\mathrm{Mg}}^{28}$ and ${\mathrm{Mg}}^{26}(\alpha , 2p){\mathrm{Mg}}^{28}$. It is a 21.3±0.2 hour ${\beta }^{-}$ emitter ($E_{max}=0.418\mathrm{}\pm 0.01$ Mev, $logft=4.30\mathrm{}$). ${\mathrm{Mg}}^{28}$ decays to ${\mathrm{Al}}^{28}$ with which it is in secular equilibrium. Milking experiments indicate that the ${\mathrm{Al}}^{28}$ daughter has a 2.3-min half-life, and confirm the mass assignment of ${\mathrm{Mg}}^{28}$. Gamma-ray spectra of the ${\mathrm{Mg}}^{28}$—${\mathrm{Al}}^{28}$ secular equilibrium mixture indicate gamma rays of the following energies in Mev (intensities in parentheses): 1.769±0.01 (0.98), 1.346±0.01 (0.70), 0.949±0.01 (0.29), 0.400±0.01 (0.31), 0.0319±0.001 (0.96). The 1.769-Mev gamma results from the decay of ${\mathrm{Al}}^{28}$. Coincidence measurements show that the 1.346-, the 0.949-, and the 0.400-Mev gammas are each in coincidence with the 0.0319-Mev gamma, and that the 0.949- and 0.400-Mev gammas are in coincidence with each other. Delay coincidence measurements between the 1.346-Mev gamma and the 0.0319-Mev gamma indicate that the half-life of the latter is <2×${10}^{-9\mathrm{}}$ sec. This information together with the ${{\alpha }^K}_{\exp }=0.032\mathrm{}\pm 0.066$ indicates that the 0.0319-Mev gamma is an $M1\mathrm{}$ transition as predicted if the ground-state doublet of ${\mathrm{Al}}^{28}$ is a $j-j$ doublet. A complete decay scheme for the isobaric triplet, ${\mathrm{Mg}}^{28}$—${\mathrm{Al}}^{28}$—${\mathrm{Si}}^{28}$, is proposed. All spins and parities of ground and excited states are assigned. Assuming a mass of 27.985818±0.000043 amu for ${\mathrm{Si}}^{28}$, the mass of ${\mathrm{Al}}^{28}$ is 27.990809±0.000045 and the mass of ${\mathrm{Mg}}^{28}$ is 27.992738±0.000047. On the basis of an empirical scheme of nuclear systematics the energy available for decay and the half-lives of the following nuclei are discussed: ${\mathrm{Si}}^{32}$, ${\mathrm{Ne}}^{24}$, ${\mathrm{O}}^{20}$. A test for $j-j$ doublets is proposed. This test indicates that the ground state doublets of ${\mathrm{Al}}^{28}$ and ${\mathrm{P}}^{32}$ are true $j-j$ doublets, whereas the first excited state doublet of ${\mathrm{Al}}^{28}$ is not.