Detailed experimental study of excited states in $^{50}$Ti via the $(d,p)$ and $(d,pγ)$ reactions

Abstract: Excited states of semi-magic $<sup>{50}$Ti were studied up to the neutron-separation energy via the $(d,p)$ and $(d,pγ)$ reactions. In total, 82 excited states were identified based on the measurement of angular distributions with the Super-Enge Split-Pole Spectrograph (SE-SPS) at Florida State University. From the experimental data, sum rules related to vacancies were calculated for the $2p_{3/2}$, $2p_{1/2}$, $1f_{5/2}$, $1g_{9/2}$, and $2d_{5/2}$ neutron single-particle orbitals and compared to predictions obtained with the time-dependent continuum shell model (TDCSM), the quasiparticle-phonon model (QPM), and the relativistic equation of motion theory (REOM$<sup>3$). A comparison for the $(d,p)$ data obtained for $<sup>{51}$Ti and $<sup>{50}$Ti is also presented, focusing on differences of the single-particle strength fragmentation in even-$A$ and odd-$A$ nuclei.