Possible “umbrella”-like antimagnetic rotation mode in odd-$A {}^{101,103}\mathrm{Pd}$ and even-even ${}^{102,104}\mathrm{Pd}$

The tilted-axis cranking model based on covariant density functional theory is used to study the candidate antimagnetic rotation (AMR) bands in ${}^{101,102,103,104}\mathrm{Pd}$. The experimental energy spectra and $B\left(E2\right)$ values are reproduced well in the self-consistent and microscopic calculations. By investigating microscopically the composition and orientation of angular momentum, an “umbrella”-like antimagnetic rotation (UAMR) mode resulting from the coupling of four $g_{9/2}$ proton holes to neutron particles is clearly illustrated for the first time.

Figure 1

Excited energies $E\left(I\right)$ for the negative-parity sequences in ${}^{101,103}\mathrm{Pd}$ and positive-parity sequences in ${}^{102,104}\mathrm{Pd}$ calculated by the TAC-CDFT compared with the experimental data [7, 10, 19, 20]. The energies at $I=13.5\hslash , 18\hslash , 15.5\hslash$, and $16\hslash$ are taken as references for ${}^{101,102,103,104}\mathrm{Pd}$, respectively.

Figure 2

Calculated $B\left(E2\right)$ values and ${\Im }^{\left(2\right)}/B\left(E2\right)$ ratios for the $\pi {\left(g_{9/2}\right)}^{-4}\otimes \nu h_{11/2}{(g_{7/2},d_{5/2})}^4$ band in ${}^{101}\mathrm{Pd}$, the $\pi {\left(g_{9/2}\right)}^{-4}\otimes \nu {\left(h_{11/2}\right)}^2{(g_{7/2},d_{5/2})}^4$ band in ${}^{102}\mathrm{Pd}$, the $\pi {\left(g_{9/2}\right)}^{-4}\otimes \nu h_{11/2}{(g_{7/2},d_{5/2})}^6$ band in ${}^{103}\mathrm{Pd}$, and the $\pi {\left(g_{9/2}\right)}^{-4}\otimes \nu {\left(h_{11/2}\right)}^2{(g_{7/2},d_{5/2})}^6$ band in ${}^{104}\mathrm{Pd}$ compared with the available experimental data [7, 8, 9, 10].

Figure 3

Evolutions of deformation in the ($\beta ,\gamma$) plane with rotational frequency in the TAC-CDFT calculations. The rotational frequencies increase from 0.26 to 0.48 MeV corresponding to the $\pi {\left(g_{9/2}\right)}^{-4}\otimes \nu h_{11/2}{(g_{7/2},d_{5/2})}^4$ configuration in ${}^{101}\mathrm{Pd}$, from 0.35 to 0.62 MeV from corresponding to the $\pi {\left(g_{9/2}\right)}^{-4}\otimes \nu {\left(h_{11/2}\right)}^2{(g_{7/2},d_{5/2})}^4$ in ${}^{102}\mathrm{Pd}$, from 0.36 to 0.64 MeV corresponding to the $\pi {\left(g_{9/2}\right)}^{-4}\otimes \nu h_{11/2}{(g_{7/2},d_{5/2})}^6$ configuration in ${}^{103}\mathrm{Pd}$, and from 0.26 to 0.72 MeV corresponding to the $\pi {\left(g_{9/2}\right)}^{-4}\otimes \nu {\left(h_{11/2}\right)}^2{(g_{7/2},d_{5/2})}^6$ in ${}^{104}\mathrm{Pd}$.

Figure 4

Angular momentum vectors of the $g_{9/2}$ proton holes ($j_{\pi }$) and the $h_{11/2}$ neutrons ($j_{\nu }$) in ${}^{101,102,103,104}\mathrm{Pd}$.

Figure 5

The compositions of the proton and neutron angular momentum in ${}^{101,102,103,104}\mathrm{Pd}$.