$E2$ decay characteristics of the $M1$ scissors mode of ${}^{152}\mathrm{Sm}$

The $E2/M1$ multipole mixing ratio of the $1_{\text{sc}}^{+}\to 2_1^{+}\gamma$-ray transition and therefore the $F$-vector $E2$ decay of the scissors mode of the shape-phase transitional nucleus ${}^{152}\mathrm{Sm}$ have been measured with the nuclear resonance fluorescence method at the High-Intensity $\gamma$-ray Source ($\mathrm{HI}\gamma \mathrm{S}$). Furthermore, parity quantum numbers of several dipole-excited states have been remeasured, making use of the polarized $\gamma$-ray beam at $\mathrm{HI}\gamma \mathrm{S}$, and partially reassigned. The new data enable an unambiguous determination of the proton and neutron effective boson quadrupole charges within the proton-neutron interacting boson model. With the well-constrained parameter set, a new mixed-symmetry state is predicted.

Figure 1

Schematic detector setup along with the angular distributions of $E1$ (blue) and $M1$ (red) decay transitions of a photoexcited $J=1$ state to the $0^{+}$ ground state are depicted in a plane perpendicular to the beam axis. The polarization of the impinging $\gamma$-ray beam is indicated by black arrows. The detector positions are optimized for the discrimination of both electromagnetic characters. The colors of the rectangles correspond to the sensitivity of the detectors to the angular distributions for positive (red) and negative (blue) parity of dipole-excited states.

Figure 2

Photon-scattering spectra of ${}^{152}\mathrm{Sm}$ taken at the $\mathrm{HI}\gamma \mathrm{S}$ facility [15]. The colors of the spectra correspond to Fig. 1. The energy profile of the beam is indicated by the dashed Gaussian curve (orange). Gray brackets below the spectra connect transitions from the same initial state.

Figure 3

Asymmetries of the observed transitions with their uncertainties (black, orange). The reassigned values of Ref. [19] are highlighted in orange. The ideal values 1 and $-1$ are indicated for the asymmetries of a $0^{+}\to 1^{+}\to 0^{+}$ cascade and $0^{+}\to 1^{-}\to 0^{+}$ cascade (black solid line), respectively. The expected values for the asymmetries taking into account the geometry of the setup are also shown. They amount to 0.88 for the $0^{+}\to 1^{+}\to 0^{+}$ cascade (red solid line), $-0.91$ for the $0^{+}\to 1^{-}\to 0^{+}$ cascade (blue solid line), 0.06 for the $0^{+}\to 1^{+}\to 2^{+}$ cascade with ${\delta }_{1\to 2}=0$ (red dashed line) and −0.08 for the $0^{+}\to 1^{-}\to 2^{+}$ cascade (blue dashed line).

Figure 4

Summed $M1$ transition strength of stable samarium isotopes from Ziegler et al. [19] (orange squares). The orange dotted line is included to guide the eye over the QPT. Results from this work combined with values of Ziegler et al. for energy regions that were not studied here are represented by the black diamond. Remeasured values of ${}^{150}\mathrm{Sm}$ from Ref. [29] together with values of Ref. [19] are depicted by a blue triangle and which is slightly displaced with respect to the data point for the same isotope for better visibility.

Figure 5

Determination of the multipole mixing ratio ${\delta }_{1\to 2}$ for the branching transition of the $J^{\pi }=1^{+}$ state at $2991\mathrm{keV}$ into the $2_1^{+}$ state at 121.8 keV. The asymmetry values obtained from the Geant4 simulation are shown as black circles interpolated by a red line. The experimental asymmetry and its uncertainty is depicted by the horizontal orange band. The multipole mixing ratio is given by the projection of the intersection point to the abscissa (blue).

Figure 6

Effective $F$-scalar and $F$-vector boson quadrupole charges as a function of the $P$-factor for the values obtained from transitions observed within this work (black) and rescaled to the total scissors $M1$ strength (see text, orange) for ${}^{152}\mathrm{Sm}$ and the values from Beck $etal.$ for ${}^{156}\mathrm{Gd}$ (blue). Predictions are from Ref. [9] (gray lines).

Figure 7

$\frac{B(M1;1_{\text{sc}}^{+}\to 2_1^{+})}{B(M1:1_{\text{sc}}^{+}\to 0_1^{+})}$ ratio as a function of $\zeta$ for different values of $\chi$ is depicted logarithmically. The experimental value and its uncertainty is indicated by the horizontal line. For a U(5) spherical configuration ($\zeta =0$) the $M1$ branching ratio is undefined since both transitions are forbidden. Notably, the ratio never goes below the experimental value and equals the Alaga value of 0.5 modified by the effects of the finite boson number in the SU(3)-limit ($\zeta =1$).