Quantum fluctuations in the collective $0^{+}$ states of deformed nuclei

The occurrence of low-energy collective motion is a widespread phenomenon in quantum systems. To describe fluctuations about the equilibrium deformation and to understand the nature of excited $0^{+}$ states in deformed nuclei, we improve the many-body wave functions by superimposing angular-momentum-projected states constructed with different quadrupole deformations. We take deformed rare-earth nuclei as examples, compare quantitatively the calculated low-lying $0^{+}$ bands and the associated electric monopole transition matrix elements with experimental data. The analysis of the resulting wave functions for the excited $0^{+}$ states indicates clear features of quantum oscillations, with large fluctuations in deformation for soft nuclei and strong anharmonicities in the oscillations for rigidly deformed nuclei.

Figure 1

Comparison of calculated $0_2^{+}$ state with experimental data for Gd, Dy, and Er isotopes. The energy levels $2_1^{+}$, $4_1^{+}$, and $6_1^{+}$ of ground-state rotational band are also shown. Calculated results (open circles) are compared with data (filled squares).

Figure 2

Calculated energy levels for low-lying states of the ground-state band and second $0^{+}$ band are compared with data.

Figure 3

Calculated distribution function of deformation for the first three $0^{+}$ states in ${}^{154}$Gd and ${}^{160}$Gd.

Figure 4

Calculated probability function of deformation for the ground state $0_1^{+}$ and the excited $0_2^{+}$ state in ${}^{154}$Gd and ${}^{160}$Gd. Symbols correspond to the discrete deformations used for the integration in Eq. (4).