States in ${\mathrm{Si}}^{28}$ with $12.7<\mathrm{}{E}_x<13.7\mathrm{}$ MeV by ($\alpha ,\gamma$) and ($\alpha ,\alpha$) Reactions on ${\mathrm{Mg}}^{24}$

The radiative capture and elastic scattering of alpha particles by ${\mathrm{Mg}}^{24}$ have been studied for alpha-particle energies between 3.2 and 4.5 MeV. The yield and angular distributions of the gamma radiation in combination with a dispersion analysis of the ${\mathrm{Mg}}^{24}(\alpha ,\alpha ){\mathrm{Mg}}^{24}$ data gave information on the resonance energies, angular momenta, parities, and some partial widths of states in ${\mathrm{Si}}^{28}$. The excitation energies and the corresponding spins and parities of the ${\mathrm{Si}}^{28}$ levels considered were: 12.74 MeV, $2^{+}$; 12.82 MeV, [$0^{+}$ or $3^{-}$]; 12.83 MeV, $1^{-}$; 12.87 MeV, $4^{+}$; 12.92 MeV, $2^{+}$; 12.99 MeV, $1^{-}$ and $0^{+}$ (two levels); 13.06 MeV, $0^{+}$; 13.12 MeV, $2^{+}$; 13.19 MeV, [?]; 13.25 MeV, $0^{+}$; 13.27 MeV, [$1^{-}$]; 13.38 MeV, [?]; and 13.71 MeV, $2^{+}$.