${}^{50}$Ti($d$,$p$)${}^{51}$Ti, single neutron energies in the $N=29$ isotones and the $N=32$ subshell closure

Abstract

A measurement of the ${}^{50}$Ti($d$,$p$)${}^{51}$Ti reaction at 16 MeV was performed using a 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 \textit{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 ${}^{51}$Ti confirm the existence of the $N=32$ gap in Ti. These single neutron energies and those from previous measurements in ${}^{49}$Ca, ${}^{53}$Cr and ${}^{55}$Fe are compared to values from a covariant density functional theory calculation.

17 pages, 6 figures