Configuration-constrained total Routhian surfaces with particle-number-conserving pairing

The total-Routhian-surface (TRS) calculation provides a powerful theoretical tool to describe the collective rotations of nuclei. It gives a straightforward way to determine nuclear deformation which can change with increasing rotational frequency. In most cases, however, TRS calculations with a conventional pairing approach (e.g., Bardeen-Cooper-Schrieffer pairing) encounter a nonconvergence problem when applied to sidebands which are built on broken-pair excited intrinsic configurations. To overcome this problem, we have developed the TRS calculations with a particle-number-conserving pairing method in which the pairing correlation is treated with the merit of the shell model. In this paper, we present the first results of the calculations, focusing on the sidebands of the ${}^{178}$W nucleus, investigating deformation changes and incurred effects on the rotational behaviors of sidebands.

Figure 1

Configuration-constrained TRS's for the $K^{\pi }={15}^{+}$ band of ${}^{178}$W at different rotational frequencies labeled in each panel. The black dot indicates the minimum which defines the deformation of the multi-qp rotational state. The energy difference between neighboring contours is 100 keV.

Figure 2

Calculated and experimental MoI's [(a), (d)], the corresponding ${\beta }_2,\gamma$ deformations obtained from TRS calculations [(b), (e)], and calculated pairing energies [(c), (f)] for $K^{\pi }={15}^{+}$ and $7^{-}$ bands in ${}^{178}$W. The experimental MoI's are obtained with the data from Refs. [21, 22]. “Fixing deformation” means that the calculation is done with a deformation fixed at that of the bandhead state. The pairing strengths for proton and neutron are $G_p=0.46$ MeV and $G_n=0.32$ MeV, respectively. “CSM” is for the usual cranking Woods-Saxon calculation with the LN pairing.

Figure 3

Calculated occupation probability $n_{\mu }$ of each pair of the cranked neutron orbitals $\mu$ (signature partners $\alpha =\pm 1/2$) near the Fermi surface (left), and the contributions to the total angular momentum (right) in the $K^{\pi }={15}^{+}$ band of ${}^{178}$W. Note that the dashed lines in (d) indicate the results from the fixing-deformation calculation.

Figure 4

Similar to Fig. 3, but for protons.

Figure 5

Calculated and experimental MoI's for the $K^{\pi }={25}^{+}$ (a), ${28}^{-}$ (b), ${29}^{+}$ (c), and ${30}^{+}$ (d) bands in ${}^{178}$W. Experimental data are taken from Refs. [21, 22]. See Table for their configurations. The pairing strengths for proton and neutron are $G_p=0.46$ MeV and $G_n=0.32$ MeV, respectively.

Figure 6

Similar to Fig. 2, but for the $K^{\pi }={15}^{+}$ band in ${}^{176}$Hf. The experimental MoI is obtained from Ref. [31]. The pairing strengths for proton and neutron are $G_p=0.40$ MeV and $G_n=0.28$ MeV, respectively.