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

TL;DR

This study measured single neutron energies in $^{51}$Ti to confirm the $N=32$ subshell gap, revealing new nuclear states and refining orbital energy values, supporting the existence of this shell closure.

Contribution

The paper provides new experimental data on single neutron energies in $^{51}$Ti, confirming the $N=32$ subshell closure and comparing results with theoretical models.

Findings

Seven new nuclear states observed.

Refined transfer values for six states.

Confirmation of the $N=32$ gap in Ti.

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.