Collectivity of neutron-rich Ti isotopes

The structure of the neutron-rich nucleus ${}^{58}$Ti was investigated via proton inelastic scattering in inverse kinematics at a mean energy of 42.0 MeV/nucleon. By measuring the deexcitation $\gamma$ rays, three transitions with the energies of 1046(11) keV, 1376(18) keV, and 1835(27) keV were identified. The angle-integrated cross section for the 1046-keV excitation, which corresponds to the decay from the first 2${}^{+}$ state, was determined to be 13(7) mb. The deformation length ${\delta }_{p,p^{\prime }}$ was extracted from the cross section to be ${0.83}_{-0.30}^{+0.22}$ fm. The energy of the first 2${}^{+}$ state and the ${\delta }_{p,p^{\prime }}$ value are comparable to the ones of ${}^{56}$Ti, which indicates that the collectivity of the Ti isotopes does not increase significantly with neutron number until $N=36$. This fact indicates that ${}^{58}$Ti is outside of the region of the deformation known in the neutron-rich nuclei around $N=40$.

Figure 1

(a) Doppler-shift corrected $\gamma$-ray energy spectrum for the proton inelastic scattering on ${}^{58}$Ti. (b) The histogram is of the $M=1$ events. (c) $\gamma$-ray spectrum gated on the 1046-keV $\gamma$ line.

Figure 2

Level scheme of ${}^{58}$Ti proposed in this work.

Figure 3

(a) Plot of the excitation energies of the first 2${}^{+}$ states as a function of the neutron number for the Ti (circles), Cr (triangles), and Fe (squares) isotopes. The filled circle is the result from the present work. Solid, dashed, and dotted lines are the results of the shell model calculation within the $pf$ shell using the GXPF1A interaction for Ti, Cr, and Fe isotopes, respectively [30, 31, 32]. (b) Plot of ${\delta }_{p,p^{\prime }}$ for the Ti isotopes as a function of the neutron number. The filled circle is the result from the present work; open circles are those of the stable Ti isotopes taken from Ref. [29]. Triangles show ${\delta }_C$ estimated from the $B\left(E2\right)$ values.