${}^{54}$Fe($d$,$p$)${}^{55}$Fe and the evolution of single neutron energies in the $N=29$ isotones

A measurement of the ${}^{54}$Fe($d$,$p$)${}^{55}$Fe reaction at 16 MeV was performed using the Florida State University Super-Enge Split-Pole Spectrograph to determine single-neutron energies for the $2p_{3\mathrm{/}2}$, $2p_{1\mathrm{/}2}$, $1f_{5\mathrm{/}2}$, $1g_{9\mathrm{/}2}$ and $2d_{5\mathrm{/}2}$ orbits. Two states were observed that had not been observed in previous (d, p) measurements. In addition, we made angular momentum transfer, $\mathit{\text{L}}$, assignments to four states and changed $\mathit{\text{L}}$ assignments from previous ($d$, $p$) measurements for nine more states. The spin-orbit splitting between the $2p_{3\mathrm{/}2}$ and $2p_{1\mathrm{/}2}$ orbits is similar to that in the other $N=29$ isotones and not close to zero as a previous measurement suggested. While the $1f_{5\mathrm{/}2}$ single neutron energy is significantly lower in ${}^{55}$Fe than in ${}^{51}$Ti, as predicted by a covariant density functional theory calculation, the single-neutron energy for this orbit in ${}^{55}$Fe is more than 1 MeV higher than the calculation suggests, although it is only 400 keV above the $2p_{1\mathrm{/}2}$ orbit. The summed spectroscopic strength we observed for the $1g_{9\mathrm{/}2}$ orbit up to the single-neutron separation energy of 9.3 MeV is only 0.3. This is surprising because the $1g_{9\mathrm{/}2}$ orbit is predicted by Togashi $\mathit{\text{et}}\mathit{\text{al.}}$ to be located only 5.5 MeV above the $2p_{3\mathrm{/}2}$ orbit.