Single particle strengths and mirror states in ${}^{15}\mathrm{N}-{}^{15}\mathrm{O}$ below 12.0 MeV

New ${}^{14}\mathrm{N}(d,p)$ angular distribution data were taken at a deuteron bombarding energy of 16 MeV to locate all narrow peaks up to 15 MeV in excitation. A new shell model calculation is able to reproduce all levels in ${}^{15}\mathrm{N}$ up to 11.5 MeV and is used to characterize a narrow level at 11.236 MeV and to provide a map of single particle strengths. The known levels in ${}^{15}\mathrm{N}$ are then used to suggest mirrors in the lesser known nucleus ${}^{15}\mathrm{O}$. Neutron spectroscopic factors obtained from the present work and proton spectroscopic factors previously published in a ${}^{14}\mathrm{N}({}^3\mathrm{He},d)$ study were used to determine the $2s_{1/2}$ and $1d_{5/2}$ single particle energies for the ${}^{15}\mathrm{N}-{}^{15}\mathrm{O}$ mirror pairs as ${}^{15}\mathrm{N}\left({2s}_{1/2}\right)=7.64$ MeV, ${}^{15}\mathrm{O}\left({2s}_{1/2}\right)=7.11$ MeV, ${}^{15}\mathrm{N}\left({1d}_{5/2}\right)=7.26$ MeV, and ${}^{15}\mathrm{O}\left({1d}_{5/2}\right)=6.98$ MeV. These results confirm the degeneracy of these orbitals and that the ${}^{15}\mathrm{N}-{}^{15}\mathrm{O}$ nuclei are where the transition of the $2s_{1/2}$ orbital transitions from lying below the $1d_{5/2}$ to above it. The $1d_{3/2}$ single particle strength is estimated to be centered around 14 MeV in these nuclei.

Figure 1

Typical spectra from the present work for the ${}^{14}\mathrm{N}{(d,p)}^{15}\mathrm{N}$ and ${}^{12}\mathrm{C}{(d,p)}^{13}\mathrm{C}$ reactions at ${10}^{\circ }$, taken at a beam energy of 16 MeV, each having an energy resolution of 55 keV. The ${}^{12}\mathrm{C}(d,p)$ spectrum was channel shifted and then magnitude shifted to match the peak height of the 3.854 MeV state in ${}^{13}\mathrm{C}$ to be able to compare matching peaks. Known particle separation energies have also been added to each spectrum. The dotted line at 15.4 MeV is where one of the strongest peaks in three-particle transfer [6, 7] would appear. The line at 14.5 MeV is roughly the centroid of possible $1d_{3/2}$ strength.

Figure 2

Energy differences between theoretically calculated and experimental excitation energies in ${}^{15}\mathrm{N}$ as a function of spin and parity. These differences are also given in Table 1.

Figure 3

Angular distributions for states in ${}^{15}\mathrm{N}$ which were determined to be $\ell =0$ dominant.

Figure 4

Angular distributions for states in ${}^{15}\mathrm{N}$ which were determined to be $\ell =1$ dominant.

Figure 5

Angular distributions for states in ${}^{15}\mathrm{N}$ which were determined to be $\ell =2$ dominant.

Figure 6

Plot of the theoretical calculations showing where the dominant $2s_{1/2}, 1d_{5/2}$, and $1d_{3/2}$ strength is located in relation to the excitation energy in ${}^{15}\mathrm{N}$.

Figure 7

Suggested mirror states between ${}^{15}\mathrm{N}$ and ${}^{15}\mathrm{O}$, with the theoretical result for ${}^{15}\mathrm{N}$.