Role of neutrons in the coexistence of magnetic and antimagnetic rotation bands in ${}^{107}\mathrm{Cd}$

Negative parity high-spin states of ${}^{107}\mathrm{Cd}$ have been investigated using the reaction ${}^{94}\mathrm{Zr}({}^{18}\mathrm{O}$,5n), from the $\gamma$-ray coincidence events recorded by the Indian National Gamma Array. A magnetic dipole ($M1$) band structure was established for the first time in this nucleus decaying to the low-spin states via several paths. Lifetimes of five in-band levels in this band have been measured using the Doppler shift attenuation method. The experimentally deduced $B\left(M1\right)$ values are found to decrease with increasing spin. The experimental observations, interpreted by the tilted axis cranking calculations, suggest that the $M1$ band is developed from the shears mechanism based on the 5qp configuration $\pi \left(g_{9/2}^{-2}\right)\otimes \nu \left(h_{11/2}{g}_{7/2}^2\right)$, which is then crossed by another 5qp configuration $\pi \left(g_{9/2}^{-2}\right)\otimes \nu \left(h_{11/2}^3\right)$. The semiclassical model of the shears mechanism also reasonably reproduces the decreasing trend of the observed $B\left(M1\right)$ values as a function of spin, supporting the above interpretation. The present work highlights the unique coexistence of both magnetic and antimagnetic (observed by us earlier) rotation bands in one nucleus arising from the same proton configuration, but different neutron configurations.

Figure 1

Partial level scheme of ${}^{107}\mathrm{Cd}$.

Figure 2

Double-gated $\gamma$-ray coincidence spectrum showing the in-band transitions of the magnetic dipole band along with most of the connecting transitions (connecting the $M1$ band to the low-spin 2159- and 3115-keV states). The spectrum was created with double gate on the 286- and 798-keV transitions. The peaks marked with hash symbols denote the known transitions depopulating the low-spin states [11]. The inset (a) shows the two high energy 1272- and 1312-keV transitions. The inset (b) shows the topmost transitions of the MR band with double gate on the 702- and 724-keV in-band transitions.

Figure 3

$R_{\mathrm{DCO}}$ values for the transitions with gates on dipole and quadrupole transitions. With the gate on dipole transitions, the $R_{\mathrm{DCO}}$ values of the dipole and quadrupole transitions are shown by black circles and green squares, respectively. With the gate on quadrupole transitions, the $R_{\mathrm{DCO}}$ values of the dipole and quadrupole transitions are shown by red diamond and blue triangular shapes, respectively.

Figure 4

Experimental polarization asymmetry ${\Delta }_{\mathrm{IPDCO}}$ values for the transitions. The electric (positive ${\Delta }_{\mathrm{IPDCO}}$) and magnetic (negative ${\Delta }_{\mathrm{IPDCO}}$) transitions are shown by blue circles and green squares, respectively.

Figure 5

Representative spectra and lineshape fits for the 286-, 385-, and 491-keV transition energies in the $M1$ band of ${}^{107}\mathrm{Cd}$ for $\gamma$-ray spectra at ${140}^{\circ },{90}^{\circ }$, and ${40}^{\circ }$ with respect to the beam direction.

Figure 6

Plot of the observed excitation energy $E\left(I\right)-E\left(I_b\right)$ as a function of angular momentum $I$, and $I$ as a function of rotational frequency $\hslash \omega$ (inset), for the MR bands in ${}^{107,109}\mathrm{Cd}$. $E\left(I_b\right)$ correspond to the excitation energy of the bandhead with spin $29/2^{-}$, which is 5031 keV for the MR band in ${}^{107}\mathrm{Cd}$ and 4812 keV [27] for the MR band in ${}^{109}\mathrm{Cd}$.

Figure 7

Comparison of the calculated $E$ (MeV) vs $I$ ($\hslash$) values (a) and $I(\hslash$) vs $\hslash \omega$ (MeV) values (b) with the corresponding measured values, for the negative parity magnetic dipole band in ${}^{107}\mathrm{Cd}$. TAC(5qp-1) and TAC(5qp-2) denote the results of TAC calculations using the five-quasiparticle configurations $\pi \left(g_{9/2}^{-2}\right)\otimes \nu \left(h_{11/2}{g}_{7/2}^2\right)$ and $\pi \left(g_{9/2}^{-2}\right)\otimes \nu \left(h_{11/2}^3\right)$, respectively. $E(I{}_b$) is the excitation energy of the observed bandhead at spin $29/2^{-}$.

Figure 8

Comparison of the calculated $I(\hslash$) vs $B\left(M1\right)$ $\left[{\left({\mu }_N\right)}^2\right]$ values with the corresponding measured values for the MR bands in ${}^{107}\mathrm{Cd}$. TAC(5qp-1) and TAC(5qp-2) denote the results of TAC calculations using the five-quasiparticle configurations $\pi \left(g_{9/2}^{-2}\right)\otimes \nu \left(h_{11/2}{g}_{7/2}^2\right)$ and $\pi \left(g_{9/2}^{-2}\right)\otimes \nu \left(h_{11/2}^3\right)$, respectively. For differences in the calculated values of $B\left(M1\right)$ for 5qp-1 and 5qp-2, see text.