Investigation of the mixed-symmetric one-quadrupole phonon 2 +1 ,ms state of the heavy nucleus 204 Hg

. Low-energy quadrupole-collective excitations of isovector character, the so-called states with proton-neutron mixed-symmetric character (MSS), have been investigated in 204 Hg which is the sole stable nucleus in the straight vicinity of 208 Pb exhibiting a 2 π − 2 ν structure. A 12 C( 204 Hg, 204 Hg ∗ ) 12 C projectile Coulomb-excitation experiment at 890 MeV was performed at Argonne National Laboratory using the ATLAS accelerator. γ -rays originating from the decay of the excited states of 204 Hg were detected using the GAMMASPHERE spectrometer. The measured Coulomb-excitation yields provide the B ( M 1) and the B ( E 2) strength distributions which unambiguously reveal the 2 +3 state at 1948 keV as the one-phonon MSS of 204 Hg.


Introduction
The appearance of collectivity from basic nuclear properties is of interest in contemporary nuclear structure research.Atomic nuclei can be considered as mesoscopic two-fluid quantum systems, which physics is determined notably by the many-body aspect, the quantum nature as well as the two-fluid character.Nuclear phenomena emerging from these properties are collectivity, shell structure and isospin.The Interacting Boson Model-2 [1,2] formalizes this picture and predicts the appearance of two fundamental one-phonon quadrupole excitations in nuclei.Both are mixtures of the underlying proton and neutron quadrupole excitations.In weakly collective nuclei the in-phase combination of proton and neutron contributions form the so-called fullysymmetric state (FSS), whereas the anti-symmetric combination is known as mixed-symmetric state (MSS) [1,3].By their origin the MSSs are sensitive to the effective pn correlations in the valence shell.MSSs are uniquely identified experimentally [4,5,6,7,8] by their strong isovector M 1 decay to the low-lying FSS.This is of importance because M 1 transitions are forbidden between FSSs and thus are a suitable observable for unambiguous identification of MSSs.The fundamental MSS in weakly collective vibrational nuclei is the one-phonon 2 + 1,ms state [3].The best examples of such MSSs in stable nuclei are found in the mass A ≈ 90 region [5,9,10].Recently a large number of quadrupole MSSs have been identified in the mass A ≈ 130 region [11,12,13,14,15,16].
Recently new experimental evidence for the formation mechanism of fully-symmetric and mixed-symmetric low-lying quadrupole-collective states was found [17].This mechanism involves coupling of the lowest 2-quasiparticle proton and neutron excitations to the Giant Quadrupole Resonance (GQR) [17].The E2 strength in the decay of FS and MS states is dominated by the GQR contributions while the M 1 properties are determined by the valence-shell configuration.Due to normalization of the wave function this concept demands that with increasing collectivity the GQR contribution also increases, resulting in a decrease of the M 1 strength.Thus the strongest M 1 transitions should occur in weakly collective vibrational nuclei, which are only two proton and two neutron holes away from doubly-magic nuclei.To improve the understanding of the formation of low-lying isovector excitations cases of MSSs in the vicinity of doubly-magic nuclei have to be identified.However, the number of such nuclei which can be studied by conventional experimental methods is low.The sole stable nucleus exhibiting two proton and two neutron holes in the region around 208 Pb is 204 Hg.Preliminary results of the search for a MSS in this nucleus are presented in this contribution.

Experiment
An experiment was performed at Argonne National Laboratory.A pulsed (12 MHz) 204 Hg beam accelerated to 890 MeV was delivered by the ATLAS accelerator facility.The beam was impinging on a 1mg/cm 2 nat C target.Deexcitation γ-rays, following the projectile Coulombexcitation reaction, were detected using the GAMMASPHERE detector array [18], consisting of 100 HPGe detectors arranged in 16 rings, at the time of the measurement.The average beam intensity was ≈ 1.3 pnA.GAMMASPHERE was used in singles mode, as no particle detector was present in the experiment.γ-ray counting rate during the experiment was ≈ 7 × 10 3 countsper-second.A total of 4.4 × 10 8 events of γ-ray fold 1 or higher have been collected during 13 h of beam time.The excited 204 Hg nuclei were recoiling with v/c ≈ 8.4% which was accounted for by Doppler correction of the obtained γ-ray spectra.The contribution of the room background

Data Analysis and Results
Events featuring a γ-ray fold ≥ 2 were used to construct a γ-γ-coincidence matrix.A showcase excerpt from this matrix for all γ-rays coincident to the 2 + 1 → 0 + 1 transition is shown in the lower panel of Fig. 1.The combined examination of the singles spectrum as well as of the coincidence matrix results in a total of 10 states decaying via emitting γ radiation observed in this experiment.Fig. 2 presents the resulting level scheme, which is in agreement with previously reported data on 204 Hg [19].
All prominent γ-ray transitions originate from decays of excited states of 204 Hg.Most of these transitions have been observed before, besides the 727-keV transition which connects the 3 − 1 and the 2 + 3 state and the transition depopulating a new state at 2871 keV.Because of the dominance of E2 excitations in low-energy Coulomb-excitation reactions we have assumed (2 + ) for the spin and the parity of this state.
Efficiency-corrected transition intensities were deduced from the singles spectrum wherever possible.The intensities of weak transitions were derived using the γ-γ-matrix.The intensities were afterwards used to determine the yield of the states excited in this experiment.Because of the quasi-4π nature of the GAMMASPHERE array these excitation yields are proportional to the Coulomb-excitation cross-section.In the analysis, excited states population yields are compared to cross-sections calculated from Coulomb-excitation theory [20].Additional information is obtained from analyzing the angular distributions of the 2 + 3 → 2 + 1 and 3 − 1 → 4 + transitions.The latter transition exhibits the expected dipole character while the other one is characterized by a superposition of dipole and quadrupole character.For the 2 + 3 → 2 + 1 transition the angular distribution in combination with the orientation tensor from Coulomb-excitation theory [20] calculated using GOSIA [21] results in a preliminary multipole mixing ratio δ = 0.40 (26) hinting at M 1 dominance.
At this stage of the analysis only a minor subset of states consisting of the 0 + 1 , 2 + 1 , 2 + 3 , and 3 − 1 states was taken into account for the Coulomb-excitation calculations.The relative yields of the 2 + 3 and 3 − 1 states have been fitted to the theory [20] using the multiple CE code CLX [22]

Figure 1 .
Figure 1.Doppler-corrected, background subtracted γ-ray spectra after projectile Coulomb excitation on a Carbon target.In the upper panel the singles spectrum is shown.In the lower panel a projection of the γ-γ-matrix, gated on the 2 + 1 → 0 + 1 transition is shown.

Figure 2 .
Figure 2. Deduced level scheme of 204 Hg.Solid lines indicate transitions observed in this experiment while dashed lines show transitions which were not observed but which intensities can be determined from beforehand known branching ratios.