Spectroscopy of ⁵⁴Ti and the systematic behavior of low energy octupole states in Ca and Ti isotopes

Excited states of the $N=32$ nucleus $^{54}$Ti have been studied, via both inverse-kinematics proton scattering and one-neutron knockout from $^{55}$Ti by a liquid hydrogen target, using the GRETINA $\gamma$-ray tracking array. Inelastic proton-scattering cross sections and deformation lengths have been determined. A low-lying octupole state has been tentatively identified in $^{54}$Ti for the first time. A comparison of $(p,p')$ results on low-energy octupole states in the neutron-rich Ca and Ti isotopes with the results of Random Phase Approximation calculations demonstrates that the observed systematic behavior of these states is unexpected.