Microscopic structure of low-lying $0^{+}$ states in the deformed ${}^{158}\mathrm{Gd}$

We study in the quasiparticle-phonon model the shell structure and the phonon content of the low-lying excited $0^{+}$ states in ${}^{158}\mathrm{Gd}$. We show that the model accounts for the large abundance of $0^{+}$ states observed in recent experiments and provides a detailed and exhaustive information about the properties of all these states, especially the extent and nature of their collectivity. This is achieved through an explicit investigation of the structure of the model wave functions and, more objectively, the calculation and comparative analysis of $E2$ and $E0$ transition probabilities, and, especially, two-nucleon transfer spectroscopic factors.

Figure 1

(Color online) Energies of $0^{+}$ states calculated in QPM for two different deformations compared to the experimental data and the levels calculated in PSM and IBM.

Figure 2

(Color online) $E0$ and $E2$ strength distributions in ${}^{158}\mathrm{Gd}$.

Figure 3

(Color online) $(p,t)$ spectroscopic factors computed in QPM for two different deformation parameters in ${}^{158}\mathrm{Gd}$.

Figure 4

Running sum of the two-quasiparticle amplitudes contributing to the RPA $(p,t)$ spectroscopic factors in ${}^{158}\mathrm{Gd}$. The dashed line accounts for the contributions $\mid {\Gamma }_q\mid >0.08$ only.

Figure 5

The contribution to the running sum of the $(p,t)$ transfer amplitudes coming from the forward (dashed line) and backward (dot-dashed line) RPA amplitudes for the $0_1^{+}$ (top panel) and $0_2^{+}$ (bottom panel) states.