Investigation of 0 + states in mercury isotopes after two-neutron transfer

Using the high-resolution Q3D magnetic spectrograph at the Maier-Leibnitz Laboratory (MLL) Tandem accelerator in Munich, we studied 0 excitations in the mercury isotopes 198Hg, 200Hg, and 202Hg after two-neutron transfer. We only observed 4-6 excited 0 states per nucleus up to about 3-MeV excitation energy, far fewer than in other experiments of this (p, t) campaign. The results reveal a sharp drop in the number of low-lying 0 states towards the 208Pb shell closure. We discuss the low-energy 0 state density as a function of the valence nucleon number Nval. The 0 excitation energies and the measured (p, t) transfer cross sections indicate a structural change throughout the Hg isotopes, with the most notable result being the peaking in the cross section of the low-lying excited 0+2 state in 200Hg.


Introduction
Because of its capability to measure the characteristic forward-peaking of L = 0 transfers, the Q3D magnetic spectrograph [1] at the Maier-Leibnitz Laboratory (MLL) Tandem accelerator in Munich -in combination with the focal plane detector [2]-has turned out to be a very successful instrument for the identification of 0 + excitations.This feature has been extensively used to identify 0 + states throughout the rare-earth region from gadolinium up to platinum [3][4][5][6][7].For some nuclei, the number of identified 0 + states increased sharply with the analysis of the Q3D measurement.The large number of low-lying 0 + states in 154 Gd [8] was interpreted as a new signature for the shape-phase transition from spherical to deformed nuclei [9].The unexpected high number of observed 0 + excitations triggered various calculations reproducing the density and distribution of 0 + states [10][11][12][13].Now, with the experiments on the even mercury isotopes 198−202 Hg [14,15], we move further to the 208 Pb shell closure.This allows us to investigate 0 + states in the vicinity of the prolate-oblate shape-phase transition in the a e-mail: christian.bernards@yale.edub Present address: Physik Department, Technische Universität München, D-85748 Garching, Germany Hf-Hg region [16] and to test if the prolate-oblate shape-phase transition affects the low-energy 0 + state density of these nuclei.

Experiment & Analysis
To identify L = 0 transfers from the Hg 0 + ground state (GS) in the target material to an excited 0 + state of the Hg isotope of interest, e.g., a transfer from the 200 Hg GS to an excited 0 + state in 198 Hg, we measured spectra at 5 • , 17.5 • , and 30 • laboratory angle relative to the incoming proton beam.A more detailed description of the experimental setup at the Q3D, the specifications of the enriched Hg targets, and the analysis is given in Refs.[14,15].The characteristic forward-peaking of L = 0 transfers was determined by evaluating the ratio R(5/17.5)≡ σ(5 • )/σ(17.5 • ) for each observed transfer.As a safe lower limit to prevent incorrect 0 + assignments, we used R(5/17.5)> 3.

Results
The resulting 0 + assignments for 198 Hg, 200 Hg, and 202 Hg -based on the R(5/17.5)ratio of our dataare listed in Table 1.In total, we assigned four new 0 + states up to ∼ 3-MeV excitation energy in these three Hg isotopes investigated.Tentative assignments are mostly due to a poor population of these particular states.Absolute cross sections for each state are given in Refs.[14,15].Some 0 + assignments in the data sheets [17][18][19] were not confirmed.Whenever possible, we tested assignments from the (p, t) data for consistency with γγ coincidence data of a fusion-evaporation experiment [20] and data of a neutron-capture experiment at ILL Grenoble [21,22].

Discussion
Figure 1 shows the complete data set of 0 + excitations assigned in this (p, t) campaign at the Q3D spectrograph, ranging from Gd to Hg isotopes.One notes a significantly higher 0 + state density in 154 Gd, which was interpreted as a new signature for the shape-phase transition from spherical to deformed nuclei [8].The prolate-oblate shape-phase transition observed in Ref. [16] does not show an effect on the low-energy 0 + density.The number of low-lying 0 + states rather declines with larger nucleon mass, down to only four low-energy 0 + assignments in 198 Hg and 202 Hg.  [3-7, 14, 15].The labeled nuclei on the right-hand side show the decline of 0 + state density throughout the prolate-oblate shape-phase transitional region, with 194 Pt concluded to be the closest to the critical point [16].Figure based on Ref. [14].
The effect of a decline in the number of low-energy 0 + states towards the 208 Pb shell closure is reproduced by Interacting Boson Model (IBM) [23] calculations and illustrated in Fig. 2. Please see Ref. [14] for more details on the calculations.Figure 2 shows that the number of observed 0 + states strongly increases with N val as the valence space expands, but saturates near midshell starting at about N val = 22 valence nucleons.Figure 2 shows a small peak at N val = 8, corresponding to 200 Hg.By directly comparing further properties of the investigated Hg isotopes one notes more differences shown in Fig. 3: the sequence and level energies of the low-lying states change rapidly at 200 Hg and the 0 + 2 state in 200 Hg is strongly populated with about 12% of the ground-state cross section.Historically, 0 + state two-nucleon transfer cross sections approaching or exceeding 15% have signaled structural effects such as phase transitional regions or shape coexistence [9].In Ref. [24], the enhanced 0 + 2 cross section in 200 Hg has been associated with an oblate single particle energy gap, but other explanations like mixing or coexistence cannot be ruled out.Another indicator for structural changes, the two-neutron separation energy S 2n (or the differential δS 2n ), shows at most a weak anomaly [25,26].

Conclusion
The experiments on the Hg isotopes complete a high-resolution (p, t) campaign using the Q3D spectrograph.We observe fewer low-energy 0 + states in 198, 200, 202 Hg than in other nuclei investigated in this (p, t) campaign.Plotted as a function of valence nucleon number N val , we note a sharp drop in the number of 0 + states in the near-magic region compared to the transitional and deformed regions, but a saturation towards midshell.The low-energy 0 + density seems not to be affected by the prolate-oblate shape phase transition [16] in the Hf-Hg region.
The 0 + 2 state in 200 Hg has a large two-nucleon transfer cross section, which might be an indicator for a structural change throughout the Hg isotopes at N = 120.To understand this effect, it would be very helpful to learn more about the E0 ground-state transition of the 0 + 2 state.

Figure 2 .
Figure 2. Number of 0 + states up to 3 MeV assigned in this (p, t) campaign as a function of valence nucleon number N val .The error bars include tentative assignments.The red line corresponds to the maximum number of sd IBM 0 + states, where as the green crosses indicate the calculated number of 0 + states using realistic parameters, if available.Based on Ref.[15].

6 Figure 3 .
Figure3.Low-energy states (left) and relative observed cross sections of 0 + excitations (right) for198, 200, 202 Hg as a function of valence nucleon number N val .The significant changes in excitation energies for the low-lying states and the unusual strong population of the 0 + 2 state at N val = 8, corresponding to200 Hg, are often interpreted as an indicator for a structural change.Based on Ref.[15].

Table 1 .
Assigned 0 + states in198, 200, 202Hg and their relative R(5/17.5)ratio.Newly assigned 0 + states are marked with an asterisks, tentative (0 + ) assignments are denoted in italic.Each Hg isotope is labeled with its corresponding valence neutron number N val .