Abstract
Using a 33 MeV proton beam with our Enge split-pole spectrograph, we measured the ${Q}_{0}$ values of the $^{24}\mathrm{Mg}(p,t)^{22}\mathrm{Mg}$ and $^{28}\mathrm{Si}(p,t)^{26}\mathrm{Si}$ reactions relative to that of the $^{16}\mathrm{O}(p,t)^{14}\mathrm{O}$ reaction. Data were obtained at scattering angles of ${15}^{\ifmmode^\circ\else\textdegree\fi{}}$ and ${25}^{\ifmmode^\circ\else\textdegree\fi{}}$. Based on the masses of $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{16}\mathrm{O}$, ${}^{14}O,p$, and t, we determined the mass excesses of $^{22}\mathrm{Mg}$ and $^{26}\mathrm{Si}$ to be \ensuremath{-}400.5(1.0) and \ensuremath{-}7139.5(1.0) keV, respectively. Our result for the mass of $^{22}\mathrm{Mg}$ is in excellent agreement with recent high-precision measurements.
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