$T=\frac{5}{2}{\hspace{0.5em}}^{27}\mathrm{Na}$ from ${}^{14}\mathrm{C}{+}^{14}\mathrm{C},$ and the $N=16\mathrm{}$ shell gap

For the first time a comprehensive level and decay scheme has been obtained for a $T=\frac{5}{2}$ nucleus in the $s-d$ shell ${(}^{27}\mathrm{Na})$ by using a radioactive beam and target. Particle-$\gamma$ and $p-\gamma -\gamma$ coincidences were measured following the ${}^{14}\mathrm{C}{(}^{14}\mathrm{C},p\gamma {)}^{27}\mathrm{Na}$ reaction at $E_{\mathrm{lab}}=22\mathrm{}\hspace{0.5em}\mathrm{MeV}.$ The results do not support an inversion of the ${2s}_{1/2}$ and ${1d}_{5/2}$ orbitals, as previously proposed for $T_z>~3,$ but they do suggest an increased $N=16\mathrm{}$ gap between the ${2s}_{1/2}$ and ${1d}_{3/2}$ orbitals due to the neutron excess. A consistent interpretation of the level scheme in terms of the $s-d$ shell model using the USD Hamiltonian is possible below 4 MeV, but differences increase at higher excitation energies. Another interpretation is that the influences of both the $p_{1/2}$ and $f_{7/2}$ intruder orbitals increase simultaneously with increasing T, an effect not included in the USD Hamiltonian.