High-isospin multiplets in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mo>=</mml:mo> <mml:mn>15</mml:mn> </mml:mrow> </mml:math> and 16 nuclei

Isospin quartets ($T=3/2$) and quintets ($T=2$) have been investigated for $A=15$ and $A=16$ nuclei, respectively. Data from an invariant-mass experiment, with a $^{17}\mathrm{Ne}$ beam, were reanalyzed and the $T=3/2$ and $T=2$ states in $^{15}\mathrm{O}$ and $^{16}\mathrm{F}$, associated with $p+^{14}\mathrm{N}$ and $2p+^{14}\mathrm{N}$ exit channels, respectively, were found. In some cases, $\ensuremath{\gamma}$-ray gating was used to tag on events that decay to the excited ${0}^{+}$, $T=1$ state in $^{14}\mathrm{N}$ rather than the ground state. With the new states, the lowest-energy $1/{2}^{+}$ and $5/{2}^{+}$ quartets for $A=15$ and the ${0}^{+}$ and ${2}^{+}$ quintets for $A=16$ are completed. In addition, members of these multiplets in $^{15}\mathrm{F}$ and $^{16}\mathrm{Ne}$ decaying to the $p+^{14}\mathrm{O}$ and $2p+^{14}\mathrm{O}$ channels are reevaluated by gating on events where the $^{14}\mathrm{O}$ fragment recoils perpendicular to beam axis in the parent reference frame. Such transverse-decay events have the best invariant-mass resolution. No evidence for deviations from a quadratic dependence of the mass on the isospin projection was found for the $A=15$ quartets. However for the $A=16\phantom{\rule{0.28em}{0ex}}{0}^{+}$ and ${2}^{+}$ quintets, evidence for deviations were found.