Spin-Parity Combinations for Levels inMg24andSi28

Parities of levels in ${\mathrm{Mg}}^{24}$ and ${\mathrm{Si}}^{28}$ have been found from observations on alpha-particle groups emitted in the forward direction following bombardment of ${\mathrm{O}}^{16}$ by ${\mathrm{C}}^{12}$ and ${\mathrm{O}}^{16}$ ions. The interpretation depends only on conservation laws and not on any assumption about the reaction mechanism. Of the lowest seven known states of ${\mathrm{Mg}}^{24}$ [$E_{\mathrm{ex}}=0, 1.37, 4.12, 4.23, \mathrm{}\left(5.22\right), 6.01, 6.43$ MeV] and the lowest five of ${\mathrm{Si}}^{28}$ [$E_{\mathrm{ex}}=0, 1.77, 4.62, 4.98, \mathrm{}\left(6.28\right)\mathrm{}$ MeV] only the two in parentheses have parity ${\mathrm{}(-)\mathrm{}}^{J+1\mathrm{}}$. The spins ($J$) of all these levels are known, and because these two are the only members with $J$ odd, it follows that all 12 levels have positive parity.