Reduction of collectivity at very high spins in ${}^{134}\mathrm{Nd}$: Expanding the projected-shell-model basis up to 10-quasiparticle states

Background: The recently started physics campaign with the new generation of $\gamma$-ray spectrometers, “GRETINA” and “AGATA,” will possibly produce many high-quality $\gamma$ rays from very fast-rotating nuclei. Microscopic models are needed to understand these states.

Purpose: It is a theoretical challenge to describe high-spin states in a shell-model framework by the concept of configuration mixing. To meet the current needs, one should overcome the present limitations and vigorously extend the quasiparticle (qp) basis of the projected shell model (PSM).

Method: With the help of the recently proposed Pfaffian formulas, we apply the new algorithm and develop a new PSM code that extends the configuration space to include up to 10-qp states. The much-enlarged multi-qp space enables us to investigate the evolutional properties at very high spins in fast-rotating nuclei.

Results: We take ${}^{134}\mathrm{Nd}$ as an example to demonstrate that the known experimental yrast and the several negative-parity side bands in this nucleus could be well described by the calculation. The variations in moment of inertia with spin are reproduced and explained in terms of successive band crossings among the 2-qp, 4-qp, 6-qp, 8-qp, and 10-qp states. Moreover, the electric quadrupole transitions in these bands are studied.

Conclusions: A pronounced decrease in the high-spin $B\left(E2\right)$ of ${}^{134}\mathrm{Nd}$ is predicted, which suggests reduction of collectivity at very high spins because of increased level density and complex band mixing. The possibility for a potential application of the present development in the study of highly excited states in warm nuclei is mentioned.

Figure 1

Calculated energy levels for ${}^{134}\mathrm{Nd}$ and compared with experimental data [45, 46]. Following Ref. [46], we use notations (H) and (I) for the $4^{-}$ bands.

Figure 2

Calculated moment of inertia of the yrast band for ${}^{134}\mathrm{Nd}$, and compared with experimental data [45, 46]. The theoretical result labeled as “Theo 1” refers to the full calculation with the configuration space of (1) while “Theo 2” the one without 8- and 10-qp states.

Figure 3

Calculated band diagram (bands before configuration mixing) for the positive-parity bands near the yrast line of ${}^{134}\mathrm{Nd}$. See the text for details.

Figure 4

Calculated $B\left(E2\right)$ values for the yrast and the negative-parity $5^{-}$ bands of ${}^{134}\mathrm{Nd}$, as compared with available experimental data [46, 47].