Probing the E 2 properties of the scissors mode with real photons

The E2/M1 multipole mixing ratio δ1→2 of the 1+sc → 2+1 γ-ray transition of 156Gd and 164Dy has been measured using the linearly polarized photon beams of the HIγS facility. The employed method of photonscattering experiments in combination with polarized, quasi-monochromatic beams and a dedicated detector setup is highly sensitive to the electric quadrupole-decay properties of the scissors mode.


Introduction
The study of the properties of the nuclear scissors mode [1][2][3] provides an essential insight into the nature of the restoring forces between the proton and neutron subsystems.Hence, the isovector low-lying J π K = 1 + 1 scissors mode of deformed nuclei has been studied extensively in the past with main focus on strong M1 transitions to the ground-state band [4,5,and Refs. therein].Despite the quadrupole-collective origin of the nuclear scissors mode, the E2 properties of the scissors mode were unknown until recently [6].Likewise, information on the predicted existence of the scissors mode's rotational band with the J = 1 state as band head is limited [7,8].First information on the E2 decay transition strength of the scissors mode was extracted [6] from a highstatistics photon-scattering experiment on 156 Gd using quasi-monochromatic photon beams provided by the High Intensity γ-ray Source (HIγS) [9] at Duke University, Durham, NC, USA.The data allowed for measuring a finite value of the E2/M1 multipole mixing ratio and, thus, first measurement of an E2 transition between mixedsymmetric and a fully-symmetric states in axially deformed nuclei.The obtained results indicate that highestprecision photon-scattering experiments [4,10] with linearly polarized photons [11] are highly sensitive to the electric quadrupole-decay properties of the scissors mode.It is the purpose of this manuscript to present first results obtained from a subsequent experiment on the welldeformed nucleus 164 Dy at HIγS.

Experimental details and results
The investigation of the E2 properties of the scissors mode is based on the well-known properties of the electromagnetic decay of the 1 + sc scissors mode state to the 2 + 1 state.* e-mail: tbeck@ikp.tu-darmstadt.de The linear polarization of the impinging photon beam causes an anisotropic azimuthal distribution of the scattered photons which is detected using the γ 3 setup [12].It includes four high-purity Germanium (HPGe) detectors forming a setup which is especially sensitive to the E2/M1 mixing ratio of the 1 + sc → 2 + 1 transition [13,14].Here, the multipole mixing ratio is given in the phase convention of Krane et al. [15].The quantities T (E2) and T (M1) denote the electric quadrupole and magnetic dipole transition operators, respectively.The ratio N i /N j of γ-ray intensities observed in detectors i and j is sensitive to the multipole mixing ratio δ 1→2 of the 1 + sc → 2 + 1 transition.Subsequently, the multipole mixing ratio is obtained by comparison of the observed ratio to the respective ratio of angular distributions 1 sequence.This method produces two equitable solutions; one close to zero, the other corresponding to dominant E2 character.Hence, further constraints based on the comparison of experimental decay intensity ratios to expectations from the Alaga rule [16] are needed to identify [6] the consistent solution for the multipole mixing ratio.

156 Gd
The results of the pioneering experiment on 156 Gd are presented in detail elsewhere [6].In the following, the robustness of the method towards systematic uncertainties shall be addressed.Due to the compact geometry of the detector setup the angular distribution functions have to be integrated over the solid angles of the individual detectors considering the mean free path of 3 MeV photons in the detector material.The exact positioning of the target sample relative to the impinging γ-ray beam and the detector setup was achieved using a cross-line laser system.Nevertheless, an uncertainty contribution associated with a displacement of the target parallel to the beam axis remains and is estimated to be smaller than ±5 mm.Naturally, this results in altered solid angles of the respective detectors.However, for small values of the multipole mixing ratio δ 1→2 the resulting systematic uncertainty is of comparable size to the statistical uncertainty.Figure 1 shows the result for the multipole mixing ratio of the decay of the strongest fragment of the scissors mode of 156 Gd indicating the robustness of the method towards a displacement of the target sample along the beam axis.Comparison of the measured intensity ratio to the ratio of integrated angular distributions W(135 sequence indicated by the blue line.The two possible solutions for the multipole mixing ratio are marked in red.The brown and green lines mark the ratio of angular distributions integrated over the altered detector solid angles caused by a displacement of the target sample by ±5 mm in the direction of the γ-ray beam.

164 Dy
Following the first successful application of the presented method, its advancement to cases with different detector setups and lower statistics is currently pursued.While the experiment on 156 Gd featured a polarimeter-like setup of four HPGe detectors at backward angles, an advanced geometry had been implemented for the measurement of the E2 decay of the scissors mode of 162,164 Dy.Two detectors were mounted at a polar angle of ϑ = 90 • with respect to the incoming beam and at azimuthal angles ϕ of 0 • and 90 • with respect to the horizontal polarization plane.In addition, two HPGe detectors were placed at (ϑ, ϕ) = (135 • , 225 • ) and (135 • , 315 • ), resulting in three unique detector combinations defined by the symmetry properties of the angular distribution functions.
Figure 2 shows the resulting ratios of integrated angular distributions W(ϑ i , ϕ i , δ 1→2 )/W(ϑ j , ϕ j , δ 1→2 ) for two detectors i and j as a function of the E2/M1 multipole mixing ratio.In the following, first results of the two detectors in polarimeter geometry, i.e. at a polar angle of ϑ = 90 • and azimuthal angles ϕ of 0 • and 90 • corresponding to the 164 Dy( γ , γ ) Figure 3. Gamma-ray spectra of the 164 Dy( γ, γ ) reaction.Detectors were placed at a polar angle of ϑ = 90 • and in the horizontal polarization plane (red) of the incident γ-ray beam and perpendicular to it (blue).The spectra are dominated by the decays of three scissors mode states to the ground state and to the 2 + 1 state.The energy profile of the γ-ray beam is indicated by the dashed Gaussian curve.
For the 1 + sc state located at 3.173 MeV a finite value of the multipole mixing ratio δ 1→2 , which significantly differs from zero, is obtained from the 1 + sc → 2 + 1 decay transition at 3.100 MeV.From the squared multipole mixing ratio 1 ,M1 and the partial decay width [17] a preliminary transition strength B(E2; 1 + sc → 2 + 1 ) well below 1 W.u. is determined.Naturally, the integration of the results of the re-EPJ Web of Conferences 178, 02022 (2018) https://doi.org/10.1051/epjconf/201817802022CGS16 maining detector combinations (cf. Figure 2) will slightly alter this result.

Summary and Outlook
The results of 156 Gd and 164 Dy indicate that properties of the scissors mode's electric quadrupole decay can be obtained from highest-precision photon-scattering experiments with linearly polarized photons.However, further experiments are essential to shed light on the distribution of E2 strength compared to M1 strength in a single nucleus as well as its evolution with the number of valence neutrons.

Figure 2 .
Figure 2. Evolution of the ratio of integrated angular distributions W(ϑ i , ϕ i , δ 1→2 )/W(ϑ j , ϕ j , δ 1→2 ) with the multipole mixing ratio of the 1 + sc → 2 + 1 transition for different detector combinations color coded in the schematic setup (upper left corner).Due to the symmetry properties of the angular distribution functions three different detector combinations have to be considered.