Angular correlation study of the proton decay ofN14states below 11 MeV

Angular correlations of decay protons from 15 unbound ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ states below $E_x=11\mathrm{}$ MeV were measured in the reaction ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}({}_{}{}^3{}_{}{}^{}\mathrm{He},p){}_{}{}^{14}{}_{}{}^{}\mathrm{N}\left(p^{\prime }\right){}_{}{}^{13}{}_{}{}^{}\mathrm{C}_{\mathrm{g}.\mathrm{s}.\mathrm{}}^{}{}_{}{}^{}$. Incident ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ energies of 12.0, 13.5, and 14.0 MeV were used in the various measurements. The decay protons ($p^{\prime }$) were detected in coincidence with reaction protons ($p$) emitted at 0° to the beam direction. The correlations were fitted to a theoretical expression containing adjustable parameters describing the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ substate populations and the angular momentum coupling in the ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}+p$ system. Where two orbital angular momenta were allowed in the decay channel, generally only the lower allowed value was considered. Our results are compared with previous work and are shown to strengthen several existing $J^{\pi }$ assignments. New assignments are: 10.06 MeV, $J^{\pi }=3^{+}$ or $J\ge 4$; 10.81 MeV, $J^{\pi }=5^{+}$. The $\frac{f-}{p}$-wave mixing in the decay of the 9.17-MeV $2^{+}$, $T=1\mathrm{}$ state is consistent with previous ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}(p,\gamma )$ experiments; for the 10.43-MeV second $2^{+}$, $T=1\mathrm{}$ state, ${\Gamma }_{l=3\mathrm{}}<(2.7\mathrm{}\times {10}^{-3\mathrm{}})\Gamma$. The measured magnetic substate parameters are compared with the predictions of a simple direct-interaction model of the (${}_{}{}^3{}_{}{}^{}\mathrm{He},p$) reaction. A recent weak-coupling model calculation of ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ levels is reviewed in the light of the new results.