We performed a measurement of the ${}^{51}\mathrm{V}(d,p){}^{52}\mathrm{V}$ reaction at 16 MeV using the Florida State University Super-Enge Split-Pole Spectrograph (SE-SPS) to search for single-neutron transfer strength for the $g_{9/2}$ intruder orbit. Measurements of $\nu g_{9/2}$ strength with ($d,p$) reactions in the $N=29$ isotones ${}^{49}\mathrm{Ca}, {}^{51}\mathrm{Ti}, {}^{53}\mathrm{Cr}$, and ${}^{55}\mathrm{Fe}$ have concluded that much of the expected $\nu g_{9/2}$ strength is “missing”; that is, the summed strength is much smaller than the sum rule. In odd-odd $N=29$ isotones, we expect a significant amount of $\nu g_{9/2}$ strength to be located in the “stretched” $8^{-}$ states with $\pi f_{7/2}^n\nu g_{9/2}$ structure that were systematically observed in the odd-odd $N=29$ isotones via the $(\alpha ,d)$ reaction. ${}^{52}\mathrm{V}$ is the only one of these odd-odd isotones in which a stable target is available for single-neutron transfer reactions. We report on a determination of $\nu g_{9/2}$ strength for the stretched $8^{-}$ state and ten other negative parity states populated via $L=4$ transfer in the ${}^{51}\mathrm{V}(d,p){}^{52}\mathrm{V}$ reaction. This is the first measurement of spectroscopic strength for $L=4$ states in ${}^{52}\mathrm{V}$ via ($d,p$). In total, the $L=4$ strength observed here sums to only $28.9\left(11\right)\%$ of the sum rule for $g_{9/2}$ neutron strength, a result that is consistent with the summed strengths observed in recent ($d,p$) measurements of the even-Z $N=29$ isotones ${}^{51}\mathrm{Ti}, {}^{53}\mathrm{Cr}$, and ${}^{55}\mathrm{Fe}$. The $\left(\alpha {,}^3\mathrm{He}\right)$ reaction and the use of particle-$\gamma$ coincidences would provide more sensitivity to search for the missing $g_{9/2}$ strength.

• Received 26 September 2023
• Accepted 5 January 2024

DOI:https://doi.org/10.1103/PhysRevC.109.024302