Collectivity in 196 , 198 Pb isotopes probed in Coulomb-excitation experiments at REX-ISOLDE

The neutron-deficient Pb isotopes have been studied in Coulombexcitation experiments employing the Miniball γ-ray spectrometer and radioactive ion beams from the REX-ISOLDE post-accelerator at CERN. The reduced transition Collectivity in Pb isotopes 2 probabilities of the first excited 2 states in Pb and Pb nuclei have been measured for the first time. Values of B(E2) = 18.2 −4.1 W.u. and B(E2) = 13.1 +4.9 −3.5 W.u., were obtained, respectively. The experiment sheds light on the development of collectivity when moving from the regime governed by the generalized seniority scheme to a region, where intruding structures, associated with different deformed shapes, start to come down in energy and approach the spherical ground state. Collectivity in Pb isotopes 3

ion beams from the REX-ISOLDE post-accelerator at CERN. The reduced transition probabilities of the first excited 2 + states in 196 Pb and 198  = -+ ( ) W.u., were obtained, respectively. The experiment sheds light on the development of collectivity when moving from the regime governed by the generalised seniority scheme to a region, where intruding structures, associated with different deformed shapes, start to come down in energy and approach the spherical ground state.
Keywords: Coulomb excitation, radioactive ion beams, gamma-ray spectroscopy, γ transitions and level energies (Some figures may appear in colour only in the online journal)

Introduction
Atomic nuclei can be considered as unique laboratories for studies of exotic phenomena. The movements of single neutrons or protons and their tendency to couple, combined with collective motions of groups of nucleons, can result in different intrinsic configurations at degenerate energies. These different configurations can present different shapes, giving rise to a phenomenon known as the shape coexistence [1]. A few prominent regions in the chart of nuclei can be found where the shape coexistence is inherent [2]. In particular, one of the most explored regions can be found around the neutron-deficient 186 Pb nucleus (see [1] and references therein). In that region, the competing deformed structures, associated with proton multiparticle-multihole excitations across the Z=82 shell closure, intrude down to the energies close to the spherical ground state [3][4][5][6][7][8][9]. The main support for this picture comes from the hindrance factors obtained in α-decay fine-structure measurements [10]. Calculations using the deformed mean-field approach, essentially equivalent to the shell-model method, associate intruder configurations with prolate and oblate shape [11][12][13][14][15]. Together with the spherical ground state, they result in a unique triplet of shape-coexisting 0 + states in 186 Pb 104 [3]. The low-lying 0 + states form the basis for the rotational bands observed in the even-mass Pb isotopes [16][17][18][19][20][21]. The level-energy systematics of Pb isotopes with A 204  is shown in figure 1.
In order to map the boundaries where the generalised seniority regime changes to the region characterised by intruding configurations it is important to measure transition probabilities between the low-lying states [22,23]. Lifetime measurements in the region of interest employing fusion-evaporation reactions are challenging due to the presence of the isomeric states preventing the prompt feeding of the low-lying states. On the other hand, these states have too short lifetimes to be measured in decay experiments. Coulomb excitation (Coulex) provides an alternative approach to direct lifetime measurements, and moreover is sensitive to quadrupole moments of excited states. However, with stable-ion beams the Coulex method can only be applied to stable or long-lived nuclei. For the Coulex of short-lived nuclei, these nuclei must be available as radioactive ion beams (RIB). Coulex of short-lived nuclei has recently been employed at the first generation RIB facilities and it is one of the most important methods for probing collectivity in exotic nuclei as the production cross sections are much higher than for example in fusion-evaporation reactions.
Today the selection of available RIBs has been successfully extended into very heavy nuclei such as Rn and Ra [24] in the leading RIB ISOL-facility REX-ISOLDE at CERN [25].  Pb and 194,196 Po nuclei [29][30][31][32][33]. The role of Coulex experiments will become increasingly important at HIE-ISOLDE and with the advent of nextgeneration RIB facilities.

Experimental technique
The experiment was performed at the REX-ISOLDE facility, CERN [25]. The nuclei of interest were produced by bombarding a high temperature UC x target with 1.4 GeV proton beam provided by PS-Booster with intensity up to 2 μA. The RIB were extracted employing the RILIS laser ion source [34]. Subsequently, they were mass selected utilising the high resolution separator before being delivered to the REXTRAP Penning trap for cooling and bunching and REXEBIS electron-beam ion source for charge breeding. Finally, the REX-ISOLDE post-accelerator was employed to deliver the RIB of 196,198 Pb at 2.82 MeV/u to the Miniball γ-ray spectrometer [35]. Miniball is an array of eight triple-cluster Ge-detectors, where each crystal is six-fold segmented. At Miniball, the RIB impinged on a 2 mg cm −2 thick 112 Cd target. The beam energy was chosen to fulfil the safe energy criterion [36], in other words to ensure that all interactions in the scattering processes were purely electromagnetic. The beam intensity on the Miniball target varied between 2.5 10 and 5.0 10 5 5´p ps. The scattered beam and target recoils were detected with the CD detector at 32.9mm downstream from the target. The CD detector consists of four individual double-sided silicon strip detector quadrants. At the front side the quadrants are divided in 16 annular strips, while the pairwise coupling of the 24 backside strips results in 12 strips in radial direction. The γ rays following the de-excitation of the Coulomb-excited states were recorded with the Miniball Ge-detector array [35]. The relatively high granularity of Miniball (144 segments) and the CD detector (768 'pixels') allowed for kinematic correction to be made.
The Ge-detectors were equipped with digital electronics employing the DGF-4C Revision D modules from XIA [37], while signals from the CD detector were passed through conventional analogue electronics consisting of RAL109 shaping/discriminator amplifiers and MADC-32 peak sensing ADCs from Mesytec [38]. The detector signals were recorded in the buffer of electronics modules during the 800 μs beam-on time window, triggered by the release of particles from the REXEBIS for post-acceleration, and during the following 800 μs beam-off time window. Outside of the beam-on time window, no beam from REX-ISOLDE was impinging on the Miniball target, thus the beam-off time window was used to assess the amount of background radiation. The buffer was subsequently read-out to disk in between the beam-on/off windows. The MARABOU data acquisition system [39], based on the multi branch system (MBS) [40] and the ROOT framework [41], was used. The MBS took care of the data read-out, event building and data transport, while ROOT provided tools for run control, histogramming, data storage and the on-and off-line analysis of the data.
For detailed analysis of the Coulex data, the understanding of the beam composition is essential. While the Pb ions were produced via laser ionisation, the neighbouring Tl nuclei were surface ionised in the target ion source. These isobaric contaminants survived all the separation and beam manipulation stages and were post-accelerated along the Pb beams of interest. In order to correct for the target excitations arising from the Tl beam impinging on the Miniball target, the beam composition was assessed carefully [42]. The beam purity of 98.7±0.5% and 98.6±0.7% was extracted for 196 Pb and 198 Pb, respectively. Apart from the Tl isobaric impurities, no other contaminants were found in the radioactive ion beam.

Analysis and results
The analysis is based on the data collected during the beam-on time window and the laserionisation ion source in operation. The laser on-off technique was employed to define the amount of target excitations originating from the beam impurities impinging on the target [42]. The experiment was performed in inverse kinematics and the scattered target recoils were always observed in coincidence with the scattered beam. This was exploited in the analysis by requesting two detected hits in the CD detector, which enabled more precise reconstruction of kinematics and therefore better Doppler correction for the energies of observed γ rays. Although the kinematic branches for the scattered beam and target recoils could not be distinguished for the two innermost strips, the statistics were sufficient to divide the CD detector in three different angular ranges in both 196 Pb and 198 Pb experiments. In figure 2, the particle energy with respect to the scattering angle is shown. The selected angular ranges for the scattered target recoils in the laboratory coordinates and the corresponding centre of mass angles for the scattered beam and target recoils are listed in table 1.
Prompt particle-γ-ray time condition (with a time gate width of 400 ns) was set to further purify the γ-ray energy spectra from the random γ rays in coincidence with the particles. An example of a particle-γ-ray time difference spectrum obtained in the 196 Pb experiment is shown in the inset of figure 2.
In figure 3, prompt particle-gated background-subtracted γ-ray energy spectra Dopplercorrected for the scattered beam and target recoils obtained in both 196 Pb and 198 Pb experiments are shown. When correcting for the scattered beam (blue curve), two prominent peaks can be found; one that can be associated with the Pb x-rays and the other with the 2 0   In the present work, the cross sections measured for 196 Pb and 198 Pb were normalised for the observed target excitation. Therefore, the least-square fit code GOSIA2, which is adapted to such cases, was used for analysis [43,44]. The power of GOSIA2 code is that it can simultaneously treat both target and beam excitations measured in a single experiment. This allows for analysis when very limited amount of experimental data is available (e.g. no existing lifetime data like in the present work) or when normalisation is not possible through Rutherford scattering yields. In the present work, the known 2 0     Pb and 198 Pb are plotted in figure 5. Full results together with spectroscopic data for 112 Cd used in the GOSIA2 analysis are given in table 2. The analysis technique is described in more details in [46].

Discussion
Very limited information on transition probabilities exists throughout the known Pb isotopic chain. The B E2; 0 2 ) values in even-mass Pb isotopes close to the doubly-magic 208 Pb have been studied in inelastic scattering experiments employing variety of beams. An αparticle scattering experiment was carried out on 208 Pb [47], while electron scattering was employed to probe the 206 Pb and 208 Pb isotopes [48]. In 1978, Joye et al measured also the quadrupole moments in the 204 Pb and 206 Pb isotopes by using beams of 4 He, 12 C and 16 O nuclei in Coulex experiments [49]. The heaviest 210 Pb isotope with known B E2; 0 2 1 1  + + ( ) value was studied in inelastic tritium and proton scattering from the radioactive 210 Pb target [50]. A couple of decades and lots of development work was required before the B E2; 0 2 ) values in other Pb isotopes could be experimentally determined. In 2006, the recoil-distance Doppler shift technique was used to measure the lifetimes of the low-lying yrast states in 186 Pb and 188 Pb [32]. In addition to measurements reported in the present work, Coulex data have been obtained for the even-mass 188 194 -Pb isotopes [42] at ISOLDE. In contrast to the lack of experimental data, several different theoretical calculations have predicted the transition probabilities of the first excited 2 + states in the Pb isotopes. The lowlying collective excitations have been studied by performing a configuration mixing of angular momentum and particle-number projected self-consistent mean-field states employing the Skyrme (Sly6) interaction [14,15,19,51]. This model qualitatively reproduced the variation of the spectra with neutron number and supported the picture of three different shapes lying close to the ground state near the N=104 midshell. The interacting boson model (IBM) approximation calculations with configuration mixing for the even-mass 188 196 -Pb isotopes have been carried out [19,52]. An iterative method based on the quasiparticle random-phase approximation (QRPA) has been developed and employed for the ( ) value matches the mean-field and QRPA predictions, but is larger than the one extracted in shell-model calculations. The measured values increase slightly when moving to the more neutron-deficient nucleus 196 Pb. The trend is similar to that of the QRPA calculations, although the measured transition probabilities are a bit smaller. According to the QRPA calculations, the 2 1 + states are associated with two-quasineutron excitations predominantly to the i 13 2 shell in 196 Pb and to the i 13 2 or f 5 2 shell in 198 Pb. This interpretation is also in-line with the IBM and mean-field calculations, which suggest that the proton multiparticle-multihole excitations (i.e. deformed structures) are highly non-yrast in 196,198 Pb [15,52]. The spectroscopic quadrupole moments Q sp extracted for the 2 1 + states are close to zero supporting the assignment of these states with the spherical shape. The overall trend of the experimental B E2; 0 2 ) values around 208 Pb and in 196,198 Pb is in line of the usual pattern, where such values maximise towards the neutron midshell. This result can be derived for example from the generalised seniority scheme or from the QRPA calculations, as in figure 6. Such pattern is observed to some extent in the Sn isotopes (Z=50) [22]. However, in the Pb isotopes this breaks down at around the midshell. The theoretical models in figure 6 that incorporate configuration mixing can reproduce the observed trend of decreasing B E2; 0 2 1 1  + + ( ) values at the neutron midshell. This, together with other complementary data, suggests that this effect is due to the shape coexistence and mixing at low spin. To verify this further, more data would be most welcome to fill in the gaps between N=106 and N=114 and to provide additional data on higher-lying excitations in the Pb nuclei.

Summary
The collectivity of the first excited 2 + states in the neutron-deficient 196 Pb and 198 Pb nuclei have been measured in Coulex experiments employing RIB in inverse kinematics. Results have been compared with the latest theoretical models and the B E2; 0 2 1 1  + + ( ) values obtained are consistent with values extracted using the QRPA in the spherical minimum and large-scale shell-model calculations in the model space including a number of neutron-hole orbitals. Accordingly, the 2 + states in the neutron-deficient 196 Pb and 198 Pb are suggested to be composed of two-quasineutron excitations to the i 13 2 or f 5 2 shells. The nuclei studied in present work lie half way in between the the closed neutron N=126 shell and the neutron midshell at N=104. Coulex in inverse kinematics is one of the very few methods to obtain information on transition probabilities in these isotopes. In order to improve the precision of the obtained experimental values, more data are needed. This could either mean simply performing a similar Coulex experiment or carrying out a complementary lifetime measurement employing a plunger device currently being developed for the RIB at Miniball [56].