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

Spectroscopy of $^{54}$Ti and the systematic behavior of low energy octupole states in Ca and Ti isotopes