Shell-model-like approach based on cranking covariant density functional theory to the antimagnetic rotation band in ${}^{101}\mathrm{Pd}$

The antimagnetic rotation band $\nu h_{11/2}$ in ${}^{101}\mathrm{Pd}$ is investigated using cranking covariant density functional theory with a shell-model-like approach to treating the pairing correlations, in which the particle number is conserved strictly and the blocking effects are taken into account exactly. Four sets of pairing strength are adopted in the present calculations. The tendencies of the experimental moments of inertia, $B\left(E2\right)$ values, and spins are well reproduced with suitable pairing strengths. The up-bending mechanism of the antimagnetic rotation (AMR) band $\nu h_{11/2}$ in ${}^{101}\mathrm{Pd}$ is studied in terms of the component of the total angular momentum alignment and the occupation numbers around the Fermi surface. It can be found that the up-bending is mainly triggered by the proton $1g_{9/2}$ orbital. Moreover, the proton angular momentum alignment, which mainly comes from the rearrangement of proton occupations in $1g_{9/2}$ orbitals and the increasing components of $1g_{9/2}$, plays an important role in the two-shears-like mechanism.

Figure 1

The experimental (full circle) and calculated kinematic MOIs ${\Im }^{\left(1\right)}$ as a function of rotational frequency $\hslash \omega$ with different pairing strengths: (a) $G_n=G_p=0\mathrm{MeV}$ (blue dashed line), (b) $G_n=0.70\mathrm{MeV}$, $G_p=0.65\mathrm{MeV}$ (red dash-dot-dot line), (c) $G_n=1.05\mathrm{MeV}$, $G_p=0.98\mathrm{MeV}$ (green solid line), and (d) $G_n=1.40\mathrm{MeV}$, $G_p=1.30\mathrm{MeV}$ (purple dash-dot line) for ${}^{101}\mathrm{Pd}$. The experimental data are taken from Ref. [60].

Figure 2

The experimental (full circles) and calculated $B\left(E2\right)$ values as a function of the rotational frequency with different pairing strengths: (a) $G_n=G_p=0\mathrm{MeV}$ (blue dashed line), (b) $G_n=0.70\mathrm{MeV}$, $G_p=0.65\mathrm{MeV}$ (red dash-dot-dot line), (c) $G_n=1.05\mathrm{MeV}$, $G_p=0.98\mathrm{MeV}$ (green solid line), and (d) $G_n=1.40\mathrm{MeV}$, $G_p=1.30\mathrm{MeV}$ (purple dash-dot line) for ${}^{101}\mathrm{Pd}$. The inset shows the $B\left(E2\right)$ values as a function of total angular momentum quantum number $I$. The data are taken from Ref. [60].

Figure 3

The experimental (full circles) and calculated total angular momentum quantum number as a function of the rotational frequency with different pairing strengths: (a) $G_n=G_p=0\mathrm{MeV}$ (blue dashed line), (b) $G_n=0.70\mathrm{MeV}$, $G_p=0.65\mathrm{MeV}$ (red dash-dot-dot line), (c) $G_n=1.05\mathrm{MeV}$, $G_p=0.98\mathrm{MeV}$ (green solid line), and (d) $G_n=1.40\mathrm{MeV}$, $G_p=1.30\mathrm{MeV}$ (purple dash-dot line) for ${}^{101}\mathrm{Pd}$. The data are taken from Ref. [60]

Figure 4

The experimental (full circles) and calculated expectation values of angular momentum along the $x$ axis, $J_x$, as functions of $\hslash \omega$ with different pairing strengths: (a) $G_n=G_p=0\mathrm{MeV}$, (b) $G_n=0.70\mathrm{MeV}$, $G_p=0.65\mathrm{MeV}$, (c) $G_n=1.05\mathrm{MeV}$, $G_p=0.98\mathrm{MeV}$, and (d) $G_n=1.40\mathrm{MeV}$, $G_p=1.30\mathrm{MeV}$ for neutrons (blue dash-dot lines), protons (red dashed lines), and total contribution (green solid lines) for ${}^{101}\mathrm{Pd}$. The data are taken from Ref. [60].

Figure 5

Angular momentum alignment $j_x$ of neutrons (left column) and protons (right column) for ${}^{101}\mathrm{Pd}$ as functions of rotational frequency $\hslash \omega$ with different pairing strengths: (a) $G_n=G_p=0\mathrm{MeV}$, (b) $G_n=0.70\mathrm{MeV}$, $G_p=0.65\mathrm{MeV}$, (c) $G_n=1.05\mathrm{MeV}$, $G_p=0.98\mathrm{MeV}$, and (d) $G_n=1.40\mathrm{MeV}$, $G_p=1.30\mathrm{MeV}$. The angular momentum alignment composition of $1h_{11/2}$, $1g_{7/2}$, $N=50$ core ($\hslash \omega =0\mathrm{MeV}$), and other orbits of neutrons is illustrated by different colors, as is the composition of $1g_{9/2}$ and other orbits of protons.

Figure 6

Occupation numbers of single-particle orbits (a) $\nu 1h_{11/2}$, (b) $\nu 1g_{7/2}$ for neutrons, and (c) $\pi 1g_{9/2}$ for protons of ${}^{101}\mathrm{Pd}$ as functions of rotational frequency $\hslash \omega$ with different pairing strengths: (a) $G_n=G_p=0\mathrm{MeV}$ (blue dashed lines), (b) $G_n=0.70\mathrm{MeV}$, $G_p=0.65\mathrm{MeV}$ (red dash-dot-dot lines), (c) $G_n=1.05\mathrm{MeV}$, $G_p=0.98\mathrm{MeV}$ (green solid lines), and (d) $G_n=1.40\mathrm{MeV}$, $G_p=1.30\mathrm{MeV}$ (purple dash-dot lines).