$E2$ decay strength of the $M1$ scissors mode of ${}^{156}\mathrm{Gd}$ and its first excited rotational state

The $E2/M1$ multipole mixing ratio ${\delta }_{1\to 2}$ of the $1_{\mathrm{sc}}^{+}\to 2_1^{+}$ $\gamma$-ray decay in ${}^{156}\mathrm{Gd}$ and hence the isovector $E2$ transition rate of the scissors mode of a well-deformed rotational nucleus has been measured for the first time. It has been obtained from the angular distribution of an artificial quasimonochromatic linearly polarized $\gamma$-ray beam of energy 3.07(6) MeV scattered inelastically off an isotopically highly enriched ${}^{156}\mathrm{Gd}$ target. The data yield first direct support for the deformation dependence of effective proton and neutron quadrupole boson charges in the framework of algebraic nuclear models. First evidence for a low-lying $J^{\pi }=2^{+}$ member of the rotational band of states on top of the $1^{+}$ band head is obtained, too, indicating a significant signature splitting in the $K=1$ scissors mode rotational band.

Figure 1

Gamma-ray spectra from the ${}^{156}\mathrm{Gd}(\overrightarrow{\gamma },{\gamma }^{\prime })$ reaction taken at the $\mathrm{HI}\gamma \mathrm{S}$ facility [23]. Detectors were placed at a polar angle of $\vartheta =135°$ and azimuthally in the horizontal polarization plane (a) of the incident $\gamma$-ray beam and perpendicular to it (b). The $1_{\mathrm{sc}}^{+}\to 0_1^{+}$ $M1$ transition with 3.070 MeV transition energy and the mixed $E2/M1$ transition to the $2_1^{+}$ state at 2.981 MeV dominate the spectra. Other fragments of the SM are indicated by arrows in (a). The energy profile of the $\overrightarrow{\gamma }$-ray beam is indicated by the dashed Gaussian curve in (b). The data points were obtained from the relative luminosity determined from the known cross sections [28] for the corresponding $0_1^{+}\to 1^{+}\to 0_1^{+}$ photon scattering cascades.

Figure 2

The intensity ratio $N_{\parallel }/N_{\perp }$ measured for the $0_1^{+}\stackrel{\overrightarrow{\gamma }}{\to }{1}_{\mathrm{sc},1}^{+}\to 2_1^{+}$ sequence at a polar angle of $\vartheta =135°$ is compared to the ratio of angular distributions $W(135°,0°;{\delta }_{1\to 2})/W(135°,90°;{\delta }_{1\to 2})$ [cf. Eq. (1)], indicated by the blue line. The two possible solutions for the multipole mixing ratio [cf. Eq. (2)] are marked in red, while the result ${\delta }_{1\to 2}=-0.07(1{)}_{\mathrm{stat}}(2{)}_{\mathrm{syst}}$ is shown enlarged in the inlay. Only this solution is consistent with the Alaga rule for the decay branching ratio indicating a small $E2$ contribution to the $1_{\mathrm{sc}}^{+}\to 2_1^{+}$ transition.

Figure 3

Candidate for the $2_{\mathrm{sc}}^{+}\to 2_1^{+}$ transition at 3.000(1) MeV observed in all four HPGe detectors. The peak contains about 640(90) counts. Its intensity and azimuthal asymmetry suggest its interpretation as the decay transition to the $2_1^{+}$ state of the $2_{\mathrm{sc},1}^{+}$ state at an excitation energy of 3.089 MeV.