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.
The separation between single particle levels in nuclei plays the dominant role in determining the location of the neutron drip line. The separation also provides a test of current crossed shell model interactions if the experimental data is such tha
t multiple shells are involved. The present work uses the $^{14}$N(d, p)$^{15}$N reaction to extract the 2s$_{1/2}$, and 1d$_{5/2}$ total neutron single particle strengths and then compares these results with a shell model calculation using a p-sd crossed shell interaction to identify the J$^pi$ of all levels in $^{15}$N up to 12.8 MeV in excitation.
