Single Particle Strengths and Mirror States in $^{15}$N$-^{15}$O below 12.0 MeV

New $^{14}$N(d,p) angular distribution data were taken at a deuteron bombarding energy of 16 MeV to locate all narrow single particle neutron states up to 15 MeV in excitation. A new shell model calculation is able to reproduce all levels in $^{15}$N up to 11.5 MeV and is used to characterize a narrow single particle level at 11.236 MeV and to provide a map of the single particle strengths. The known levels in $^{15}$N are then used to determine their mirrors in the lesser known nucleus $^{15}$O. The 2s$_{1/2}$ and 1d$_{5/2}$ single particle centroid energies are determined for the $^{15}$N$-^{15}$O mirror pair as: $^{15}$N $(\text{2s}_{1/2}) = 8.08$ MeV, $^{15}$O $(\text{2s}_{1/2}) = 7.43$ MeV, $^{15}$N $(\text{1d}_{5/2}) = 7.97$ MeV, and $^{15}$O $(\text{1d}_{5/2}) = 7.47$ MeV. These results confirm the degeneracy of these orbits and that the $^{15}$N$-^{15}$O nuclei are where the transition between the $\text{2s}_{1/2}$ lying below the $\text{1d}_{5/2}$ to lying above it, takes place. The $\text{1d}_{3/2}$ single particle strength is estimated to be centered around 13 MeV in these nuclei.
Comment: 9 pages, 7 figures, submitted to Physical Review C for publication