Yrast band of ${}^{109}\mathrm{Ag}$ described by tilted axis cranking covariant density functional theory with a separable pairing force

A separable form of the Gogny pairing force is implemented in tilted axis cranking covariant density functional theory for the description of rotational bands in open shell nuclei. The developed method is used to investigate the yrast sequence of ${}^{109}\mathrm{Ag}$ for an example. The experimental energy spectrum, angular momenta, and electromagnetic transition probabilities are well reproduced by taking into account pairing correlations with the separable pairing force. An abrupt transition of the rotational axis from the long-intermediate plane to the long-short one is obtained and discussed in detail.

Figure 1

Rotational excitation energy as a function of the angular momentum in comparison with the data [36] (solid dots). The solid and dashed lines represent the results calculated by TAC-CDFT with and without pairing correlations, respectively. Here, the excitation energies are the energy differences with respect to the ground state.

Figure 2

(a) The neutron pairing energy as well as (b) the pairing gap as a function of rotational frequency. The solid and dashed lines represent the cases of 1-qp and 3-qp configurations, respectively.

Figure 3

Angular momenta as a function of rotational frequency in comparison with the data [36] (solid dots). The solid and dashed lines represent the results calculated by TAC-CDFT with and without pairing correlations, respectively.

Figure 4

Tilt angles for the 1-qp and 3-qp configurations as a function of the rotational frequency. The solid and open circles represent the results calculated by TAC-CDFT with and without pairing correlations, respectively.

Figure 5

Neutron ${\mathit{J}}_{\nu }$ and proton ${\mathit{J}}_{\pi }$ angular momentum vectors for the 1-qp and 3-qp bands with and without pairing correlations. The solid and dashed lines represent the results with different values of rotational frequency. Note that ${\mathit{J}}_{\nu }$ for the 1-qp band is negligible at $\hslash \omega =0.15$ MeV.

Figure 6

The angle $\varphi$ between the proton and neutron angular momenta as a function of the total angular momentum for 1-qp and 3-qp configurations calculated by TAC-CDFT with and without pairing correlations.

Figure 7

Alignments of the neutron angular momenta on the $x$ axis for both the 1-qp and 3-qp configurations, calculated by TAC-CDFT with and without pairing, respectively. The numbers below the abscissa denote the rotational frequency at which the plotted alignments have been obtained.

Figure 8

The calculated $B\left(E2\right)$ and $B\left(M1\right)$ values as a function of the angular momentum in comparison with the data [36] (solid dots). The solid and dashed lines represent the results calculated by TAC-CDFT with and without pairing correlations, respectively. The $B\left(M1\right)$ values are also calculated with scaled Dirac effective mass and denoted by the dash-dotted (with pairing) and dotted lines (without pairing).