Recent studies have completed the $A=16$ isospin quintets for states with $J^{\pi }=0^{+}$ and $2^{+}$. The dependence of their masses as a function of isospin projection shows evidence for deviations from quadratic behavior indicating isospin violation beyond the expectation from two-body forces. The deviation is most pronounced for the $2^{+}$ states. Predictions from the shell model embedded in the continuum allow us to explain that this isospin violation is associated with a modification of the nuclear structure due to the open-quantum-system nature of the proton-rich members of the quintet. In particular, the $0^{+}$ and $2^{+}$ states in ${}^{16}\mathrm{Ne}$ and the $2^{+}$ state in ${}^{16}\mathrm{F}$ are threshold resonances located just above a proton-decay threshold where $s$-wave coupling to the continuum is expected. The measured deviations of these threshold states from the quadratic behavior of the remaining members of the multiplets makes it possible to obtain information on the magnitude and the energy dependence of the continuum-coupling energy correction. Continuum coupling is also indicated for the ground state of ${}^8\mathrm{C}$, but this time through $p$-wave coupling.

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• Coulomb energies & analogue states
• Energy levels
• Nuclear spin & parity
• Nuclear structure & decays
• Proton emission
• Unstable nuclei induced nuclear reactions