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

Excited states of the $N=32$ nucleus ${}^{54}\mathrm{Ti}$ have been studied, via both inverse-kinematics proton scattering and one-neutron knockout from ${}^{55}\mathrm{Ti}$ 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 ${}^{54}\mathrm{Ti}$ for the first time. A comparison of $(p,p^{\prime })$ 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.

Figure 1

Energy loss in a Si PIN diode vs time of flight from the A1900 extended focal plane to the S800 object scintillator of the incoming beam used for particle identification.

Figure 2

Projectile-frame $\gamma$-ray spectra of ${}^{54}\mathrm{Ti}$ measured via (a) inverse-kinematics proton scattering and (b) one-neutron knockout from ${}^{55}\mathrm{Ti}$. The solid curve is the fit of geant4 simulations to the spectrum obtained from $(p,p^{\prime })$. (c) Spectrum of $\gamma$ rays obtained from $(p,p^{\prime })$ gated on the 1264-keV $\gamma$ ray.

Figure 3

Partial level scheme of ${}^{54}\mathrm{Ti}$ showing levels populated in the present work. Arrow widths are proportional to the $\gamma$-ray intensities measured in the $(p,p^{\prime })$ reaction.

Figure 4

$E3$ strength distributions for ${}^{40,42,44,46,48}\mathrm{Ca}$ calculated with the RPA.

Figure 5

Comparison of the systematic behavior of RPA calculations of LEOS energy and $E3$ strength for ${}^{40,42,44,46,48}\mathrm{Ca}$ with data. The black squares show the energies of the $3_1^{-}$ states and the $B(E3;\uparrow )$ values for the $3_1^{-}$ states from electron scattering. The green diamonds show the total $E3$ strength for all $3^{-}$ states observed in electron scattering below 6 MeV, and the centroids of this $E3$ strength.

Figure 6

$E3$ strength distributions for ${}^{40,48,50,52}\mathrm{Ca}$ calculated with the RPA.

Figure 7

Comparison of the systematic behavior of RPA calculations of LEOS energy and $E3$ strength for ${}^{48,50,52}\mathrm{Ca}$ and ${}^{54}\mathrm{Ti}$ with data. The black squares show the energies of the $3_1^{-}$ states and the $B(E3;\uparrow )$ values for the $3_1^{-}$ states from proton scattering in inverse kinematics (Ref. [1] and the present work).

Figure 8

$E3$ strength distributions for ${}^{48}\mathrm{Ca}$ and ${}^{50,52,54}\mathrm{Ti}$ calculated with the RPA.