Abstract
The ground-state masses of $^{9}\mathrm{C}$, $^{13}\mathrm{O}$, and $^{21}\mathrm{Mg}$ have been determined through measurement of the $Q$ values of the $^{12}\mathrm{C}$($^{3}\mathrm{He}$, $^{6}\mathrm{He}$)$^{9}\mathrm{C}$, $^{16}\mathrm{O}$($^{3}\mathrm{He}$, $^{6}\mathrm{He}$)$^{13}\mathrm{O}$, and $^{24}\mathrm{Mg}$($^{3}\mathrm{He}$, $^{6}\mathrm{He}$)$^{21}\mathrm{Mg}$ reactions. The measurements were made with 68-70-MeV $^{3}\mathrm{He}$ beams using a split-pole magnetic spectrograph. A new method for obtaining a precise calibration for the beam analyzer and magnetic spectrograph at these high bombarding energies is presented.The mass excess of $^{9}\mathrm{C}$ has been measured as 28.911 \ifmmode\pm\else\textpm\fi{} 0.009 MeV, that of $^{13}\mathrm{O}$ as 23.103 \ifmmode\pm\else\textpm\fi{} 0.014 MeV, and that of $^{21}\mathrm{Mg}$ as 10.912 \ifmmode\pm\else\textpm\fi{} 0.018 MeV. These nuclei represent the ${T}_{z}=\ensuremath{-}\frac{3}{2}$ members of the $T=\frac{3}{2}$ quartets for $A=9, 13, \mathrm{and} 21$, respectively.The present results show excellent agreement with a quadratic isobaric-multiplet mass equation for $A=13$ and $A=21$, but there is some indication that a small cubic term is required for the $A=9$ multiplet.
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