Ti 50 ( d , p ) Ti 51 : Single-neutron energies in the N = 29 isotones, and the N = 32 subshell closure

A measurement of the $^{50}\mathrm{Ti}(d,p)^{51}\mathrm{Ti}$ reaction at 16 MeV was performed using the Super Enge Split-Pole Spectrograph to measure the magnitude of the $N=32$ subshell gap in Ti. Seven states were observed that had not been observed in previous $(d,p)$ measurements, and the $L$ transfer values for six previously measured states were either changed or measured for the first time. The results were used to determine single neutron energies for the ${p}_{3/2}$, ${p}_{1/2}$, and ${f}_{5/2}$ orbitals. The resulting single neutron energies in $^{51}\mathrm{Ti}$ confirm the existence of the $N=32$ gap in Ti. These single neutron energies and those from previous measurements in $^{49}\mathrm{Ca}$, $^{53}\mathrm{Cr}$, and $^{55}\mathrm{Fe}$ are compared to values from a covariant density functional theory calculation.