Lifetime measurements of normal deformed states in ${}_{71}^{165}\mathrm{Lu}$

Picosecond lifetimes of medium spin states in ${}^{165}\mathrm{Lu}$ were measured for the first time. The reaction used to populate the nucleus of interest was ${}^{139}\mathrm{La}({}^{30}\mathrm{Si},4n){}^{165}\mathrm{Lu}$ at a beam energy of 135 MeV. The beam was provided by the XTU-tandem accelerator of Laboratori Nazionali di Legnaro, Italy. By using the differential decay curve method, lifetimes of 19 states in four different rotational bands were obtained. Therefrom the B(E2) values and the transitional quadrupole moments were deduced. The obtained $Q_t$ for the different bands are compared with total Routhian surface (TRS) calculations and particle-rotor-model calculations. The TRS calculations predict different axial symmetric shapes for the bands built on the $9/2^{-}$[514], $9/2^{+}$[404], and $1/2^{-}$[541] configurations, with a γ softness for the $9/2^{-}$[514] configuration. This band has also been studied using the particle-rotor model, the results of which, however, are consistent with a triaxial shape with a γ value of $-{15}^{\circ }$.

Figure 1

A schematic level scheme showing the meaning of direct B and indirect C feeding transitions, as well as the transition following the decay A.

Figure 2

γ-ray spectra obtained from a gate on the shifted component of the 519 keV transition (23/2${}^{-}$ → 1$9/2^{-}$ in the $9/2^{-}$[514] band). The shifted and unshifted parts of transitions in the same band are labeled. The ring-ring combination is ${34}^{\circ }-{34}^{\circ }$ and the target-stopper distances from top to bottom are 16, 40, and 180 μm.

Figure 3

Lifetime determination of the $I^{\pi }=17/2^{+}$ level of the $7/2^{+}[404]$ band (left) and the $I^{\pi }=17/2^{-}$ level of the $1/2^{-}[541]$ band (right). The γγ matrices were gated on the shifted components of the feeding transitions 538 and 433 keV, respectively. The intensities of the unshifted and shifted peaks of the decaying 475 and 335 keV transitions are shown in the middle panels. The derivative of the shifted peak is shown in the bottom panels. From this information, the lifetime was extracted and the result is shown in the upper panels. The dotted lines show the region of sensitivity where the lifetimes were determined.

Figure 4

Partial level scheme of ${}^{165}\mathrm{Lu}$, showing the five known rotational bands built on different single-particle orbitals. For a more detailed level scheme see Refs. 3, 14, 13. The states for which the lifetimes were extracted are marked with a $\star$.

Figure 5

The transition quadrupole moment plotted versus spin for the rotational bands built on the (a) $9/2^{-}$, (b) $7/2^{+}$, (c) $1/2^{-}$, and (d) $1/2^{-}$ bands respectively. The experimental $Q_t(\gamma =0^{\circ })$ and $Q_t$(γ) are marked with filled and unfilled circles. The theoretical $Q_{20}$ values from the TRS calculations are shown as solid lines. It can be seen that Q is different for different rotational bands. In the inset of (a) the experimental $Q_t$ with $Q_t$ and the theoretically obtained quadrupole moments for ${}^{161}\mathrm{Lu}$ and ${}^{163}\mathrm{Lu}$ from the particle-rotor calculations [6] are plotted against spin.

Figure 6

TRS calculations for different single-particle bands at a rotational frequency of $\hslash \omega =0.2$ MeV (corresponding to spin I ≈ 7–10 $\hslash$). The energy spacing between the contours is 200 keV. (a) The $7/2^{+}$ [404] band with the energy minimum at ${\beta }_2=0.236,{\beta }_4=0.014,\gamma =-2.1^{\circ }$, (b) the $9/2^{-}$[514] band with the energy minimum at ${\beta }_2=0.229,{\beta }_4=0.014,\gamma =-3.1^{\circ }$, and (c) the $1/2^{-}$[541] band with the energy minimum at ${\beta }_2=0.273,{\beta }_4=0.029,\gamma =-0.8^{\circ }$.