Magnetic rotations in ${}^{198}\mathrm{Pb}$ and ${}^{199}\mathrm{Pb}$ within covariant density functional theory with pairing correlations

The observed shears bands in ${}^{198}\mathrm{Pb}$ and ${}^{199}\mathrm{Pb}$ are investigated within the framework of tilted axis cranking covariant density functional theory, and the separable pairing force is adopted to consider the pairing correlations. The energy spectra, total angular momenta, and transition probabilities agree well with the experimental data. The bandhead energy differences are reproduced satisfactorily without any ad hoc renormalizations when the pairing correlations are taken into account. The angular momentum vectors are discussed in detail to analyze the pairing effects on magnetic rotations.

Figure 1

Rotational excitation energies calculated by TAC-CDFT for the bands 1 and 3 in ${}^{198}\mathrm{Pb}$ (upper panels) and bands 1 and 2 in ${}^{199}\mathrm{Pb}$ (lower panels) as a function of total angular momentum, in comparison with the data [36, 37] (solid dots). The solid and dashed lines represent the calculated results with and without pairing correlations, respectively.

Figure 2

Total angular momenta calculated by TAC-CDFT for bands 1 and 3 in ${}^{198}\mathrm{Pb}$ (upper panels) and bands 1 and 2 in ${}^{199}\mathrm{Pb}$ (lower panels) as a function of rotational frequency, in comparison with the data [36, 37] (solid dots). The solid and dashed lines denote the calculated results with and without pairing correlations, respectively.

Figure 3

Neutron ${\mathit{J}}_{\nu }$ and proton ${\mathit{J}}_{\pi }$ angular momentum vectors for bands 1 and 3 in ${}^{198}\mathrm{Pb}$ (upper panels) and bands 1 and 2 in ${}^{199}\mathrm{Pb}$ (lower panels). Results with and without pairing correlations are distinguished by different types of arrows.

Figure 4

The calculated $B\left(M1\right)$ values for bands 1 and 3 in ${}^{198}\mathrm{Pb}$ (upper panels) and bands 1 and 2 in ${}^{199}\mathrm{Pb}$ (lower panels) as a function of the total angular momentum, in comparison with the data. The red dotted and blue dash-dotted lines represent the calculated $B\left(M1\right)$ values with and without pairing correlations, respectively. The results with pairing correlations and a scaled Dirac effective mass are denoted by red solid lines. The $B\left(M1\right)$ values in Ref. [28] where an overall factor 0.3 is introduced are also shown and denoted by blue dashed lines. Solid dots and squares denote experimental data from DSAM [39] and FDM [40], respectively.

Figure 5

The calculated $B\left(E2\right)$ values for bands 1 and 3 in ${}^{198}\mathrm{Pb}$ (upper panels) and bands 1 and 2 in ${}^{199}\mathrm{Pb}$ (lower panels) as a function of the total angular momentum, in comparison with the data [39]. The solid and dashed lines denote the calculated results with and without pairing correlations, respectively.