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

TL;DR

This study maps single particle states in $^{15}$N and $^{15}$O using new experimental data and shell model calculations, revealing mirror symmetry and the energy transition point between specific orbitals.

Contribution

It provides new experimental data and shell model analysis to characterize single particle states and their mirror counterparts in $^{15}$N and $^{15}$O.

Findings

Identified all narrow single particle neutron states up to 15 MeV in $^{15}$N.

Determined the centroid energies of key orbitals in $^{15}$N and $^{15}$O.

Confirmed the degeneracy and transition point of the 2s$_{1/2}$ and 1d$_{5/2}$ orbitals.

Abstract

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.