Realistic description of rotational bands in rare earth nuclei by the angular-momentum-projected multicranked configuration-mixing method

Recently we proposed a reliable method to describe the rotational band in a fully microscopic manner. The method has recourse to the configuration mixing of several cranked mean-field wave functions after the angular-momentum projection. By applying the method with the Gogny D1S force as an effective interaction, we investigate the moments of inertia of the ground state rotational bands in a number of selected nuclei in the rare earth region. As another application we try to describe, for the first time, the two-neutron aligned band in ${}^{164}\mathrm{Er}$, which crosses the ground state band and becomes the yrast states at higher spins. Fairly good overall agreements with the experimental data are achieved; for nuclei, where the pairing correlations are properly described, the agreements are excellent. This confirms that the previously proposed method is really useful for the study of the nuclear rotational motion.

Figure 1

Rotational energy spectra for the g-band of the selected Gd isotopes (a)–(c), and Dy isotopes (d)–(f). The reference rotational energy, $I(I+1)/80$ MeV, is subtracted. The result of simple projection from one cranked HFB state with $\hslash {\omega }_{\mathrm{rot}}=0.01$ MeV as well as that of the projected multicranked configuration mixing (Mixed) are included in addition to the experimental data (Exp.).

Figure 2

The same as Fig. 1 but for the selected Er isotopes (a)–(c), and Yb isotopes (d)–(f).

Figure 3

Moments of inertia versus spin value for the g-band of the selected Gd isotopes (a)–(c), and Dy isotopes (d)–(f). The results of the cranked HFB (CHFB) and the configuration mixing (Mixed) are compared with the experimental data (Exp.); see the text for the precise definition of the first moment of inertia ${\mathcal{J}}^{\left(1\right)}$.

Figure 4

The same as Fig. 3 but for the selected Er isotopes (a)–(c), and Yb isotopes (d)–(f).

Figure 5

Moments of inertia calculated by the simple projections from one intrinsic HFB state with five values of the cranking frequency are compared with the result of the projected configuration-mixing employing those five HFB states for the selected Gd isotopes (a)–(c), and Dy isotopes (d)–(f).

Figure 6

The same as Fig. 5 but for the selected Er isotopes (a)–(c), and Yb isotopes (d)–(f).

Figure 7

Rotational energy spectra for the g.s. and s bands in ${}^{164}\mathrm{Er}$. The reference rotational energy, $I(I+1)/80$ MeV, is subtracted. The result of the projected multicranked configuration-mixing (Mixed) is compared with the experimental data (Exp.).

Figure 8

Energy spectra of the g.s. band in ${}^{164}\mathrm{Er}$ obtained by the simple projection from one intrinsic HFB state with five values of the cranking frequencies, $\hslash {\omega }_{\mathrm{rot}}=0.01$, 0.05, 0.10, 0.15, 0.20 MeV, compared with the result of the projected configuration mixing employing those five cranked HFB states. The energy origin is taken as the energy of the ground state of the configuration-mixing calculation.

Figure 9

Energy spectra of the s band in ${}^{164}\mathrm{Er}$ obtained by the simple projection from one intrinsic HFB state with four values of the cranking frequencies, $\hslash {\omega }_{\mathrm{rot}}=0.25$, 0.30, 0.35, 0.40 MeV, compared with the result of the projected configuration mixing employing those four cranked HFB states. The energy origin is taken as the energy of the ground state of the configuration-mixing calculation.

Figure 10

Moments of inertia versus spin value for the g.s. and s bands in ${}^{164}\mathrm{Er}$ obtained by the projected configuration-mixing calculations in comparison with the experimental data. The result of the cranked HFB (CHFB) is also included.

Figure 11

The same as Fig. 9 but the calculations with employing five values of the cranking frequencies, $\hslash {\omega }_{\mathrm{rot}}=0.250$, 0.275, 0.300, 0.325, 0.350 MeV.

Figure 12

Moments of inertia versus spin value for the s bands in ${}^{164}\mathrm{Er}$ obtained by the configuration-mixing calculations with the two different sets of rotational frequencies, $\hslash {\omega }_{\mathrm{rot}}=0.25$, 0.30, 0.35, 0.40 MeV (Mixed1), and $\hslash {\omega }_{\mathrm{rot}}=0.250$, 0.275, 0.300, 0.325, 0.350 MeV (Mixed2) in comparison with the experimental data. The scale of the ordinate is enlarged from that of Fig. 10.