Effects of proton angular momentum alignment on the two-shears-like mechanism in ${}^{101}\mathrm{Pd}$

The recently observed possible antimagnetic rotation band in ${}^{101}\mathrm{Pd}$ is investigated by the cranked shell model with pairing correlations treated by a particle-number-conserving method, in which the blocking effects are taken into account exactly. The experimental moments of inertia and reduced $B\left(E2\right)$ transition probabilities and their variations with the rotational frequency $\omega$ are well reproduced. By analyzing the $\omega$ dependence of the occupation probability of each cranked Nilsson orbital near the Fermi surface and the contributions of valence orbitals in each major shell to the total angular momentum alignment, the upbending mechanism of $\nu h_{11/2}$ in ${}^{101}\mathrm{Pd}$ is understood clearly. The proton angular momentum alignment and its influence on the two-shears-like mechanism are also discussed.

Figure 1

The cranked Nilsson levels near the Fermi surface of ${}^{101}\mathrm{Pd}$ for (a) protons and (b) neutrons. The positive-parity (negative-parity) levels are denoted by blue (red) lines. The signature $\alpha =+1/2\left(\alpha =-1/2\right)$ levels are denoted by solid (dotted) lines. The Nilsson parameters ($\kappa$ and $\mu$) are taken from the traditional values [54]. The deformation parameters ${\varepsilon }_2=0.125$ and ${\varepsilon }_4=-0.02$ are taken from Ref. [55].

Figure 2

The experimental (solid circles) and calculated kinematic MOI's $J^{\left(1\right)}$ with (black solid line) and without (red dashed line) pairing correlations for $\nu 1/2^{-}\left[550\right]$ in ${}^{101}\mathrm{Pd}$. The data are taken from Ref. [34].

Figure 3

The experimental (solid circles) and calculated $B\left(E2\right)$ values with (black solid line) and without (red dashed line) pairing correlations for $\nu 1/2^{-}\left[550\right]$ in ${}^{101}\mathrm{Pd}$. The inset shows the experimental $J^{\left(2\right)}/B\left(E2\right)$ values. The data are taken from Ref. [34].

Figure 4

Occupation probability $n_{\mu }$ of each orbital $\mu$ (including both $\alpha =\pm 1/2$) near the Fermi surface of $\nu 1/2^{-}\left[550\right]$ in ${}^{101}\mathrm{Pd}$. The top and bottom rows are for protons and neutrons, respectively. The positive-parity (negative-parity) levels are denoted by blue solid (red dotted) lines. The Nilsson levels far above the Fermi surface ($n_{\mu }\sim 0$) and far below ($n_{\mu }\sim 2$) are not shown.

Figure 5

The experimental (solid circles) and calculated (black solid line) angular momentum alignment $\langle J_x\rangle$ for $\nu 1/2^{-}\left[550\right]$ in ${}^{101}\mathrm{Pd}$. The contributions of neutrons and protons to $\langle J_x\rangle$ calculated from PNC-CSM are denoted by blue dashed line and red dot-dashed line, respectively.

Figure 6

Contributions of (a) proton and (b) neutron $N=4$ and 5 major shells to the angular momentum alignment $\langle J_x\rangle$ for $\nu 1/2^{-}\left[550\right]$ in ${}^{101}\mathrm{Pd}$. The contributions of diagonal ${\sum }_{\mu }{j}_x\left(\mu \right)$ and off-diagonal ${\sum }_{\mu <\nu }{j}_x\left(\mu \nu \right)$ parts in Eq. (6) from the proton and neutron $N=4$ shell are also shown as dashed lines.

Figure 7

Contributions of each (a) proton and (b) neutron orbital from $N=4$ major shell to the angular momentum alignments $\langle J_x\rangle$ for $\nu 1/2^{-}\left[550\right]$ in ${}^{101}\mathrm{Pd}$. The diagonal (off-diagonal) part $j_x\left(\mu \right)\left[j_x\left(\mu \nu \right)\right]$ in Eq. (6) is denoted by black solid (red dotted) lines.

Figure 8

Angular momentum vectors of neutrons $J_{\nu }$ and the four $\pi g_{9/2}$ proton holes $j_{\pi }$, at rotational frequencies from 0.3 to 0.6 MeV for $\nu 1/2^{-}\left[550\right]$ in ${}^{101}\mathrm{Pd}$. Each proton angular momentum vector contains the contribution of two $g_{9/2}$ proton holes.