Reduced transition probabilities to the first $2^{+}$ state in ${}^{52,54,56}\mathrm{Ti}$ and development of shell closures at $N=32,34$

The even ${}^{52-56}\mathrm{Ti}$ isotopes have been studied with intermediate-energy Coulomb excitation and absolute $B(E2;0^{+}\to 2_1^{+})$ transition rates have been obtained. These data confirm the presence of a subshell closure at neutron number $N=32$ in neutron-rich nuclei above the doubly magic nucleus ${}^{48}\mathrm{Ca}$ and provide no direct evidence for the predicted $N=34$ closure. Large-scale shell model calculations with the most recent effective interactions are unable to reproduce the magnitude of the measured strengths in the semimagic Ti nuclei and their strong variation with neutron number.

Figure 1

Representative coincidence γ-ray spectra for ${}^{76}\mathrm{Ge}$ and the even ${}^{52-56}\mathrm{Ti}$Ti isotopes Doppler reconstructed event by event in the projectile frame. The energy at mid-target for ${}^{76}\mathrm{Ge}$ was 73.5 MeV/nucleon, and the distance of closest approach was 17.6 fm as deduced from the maximum scattering angle in the center-of-mass frame of projectile and target, ${\theta }_{c.m.}<{3.1}^{°}$. For ${}^{52}\mathrm{Ti}$ the corresponding values for the $256\hspace{1em}\mathrm{mg}/{\mathrm{cm}}^2$ and $518\hspace{1em}\mathrm{mg}/{\mathrm{cm}}^2$ Au targets were 82.4 and 79.1 MeV/nucleon, respectively, with ${\theta }_{c.m.}<{3.1}^{°}$ and $<3.3{}^{°}$ and similar distances of closest approach of 13.9 fm. The spectrum measured with the thinner target is shown in the figure. For ${}^{54}\mathrm{Ti}$ and ${}^{56}\mathrm{Ti}$, the respective projectile energies were 83.3 and 78.6 MeV/nucleon, with distances of closest approach of 14.0 fm and 14.1 fm computed from ${\theta }_{c.m.}<{3.2}^{°}$ and $<{3.6}^{°}$. The arrows indicate the expected location of transitions deexciting the $2_2^{+}$ levels (see text for details).

Figure 2

Comparison of the measured $2_1^{+}$ excitation energies and absolute $B(E2;0^{+}\to 2_1^{+})$ transition strengths with the results of large-scale shell model calculations using the GXPF1 [dashed lines in panels (a) and (b)] and GXPF1A [solid lines in (a) and (b)] effective interactions. The $B(E2;0^{+}\to 2_1^{+})$ value for ${}^{52}\mathrm{Ti}$ is the weighted average of the two measurements given in Table .