A study on the transition between seniority-type and collective excitations in 204Po and 206Po

Low-lying yrast states in 204Po and 206Po have been investigated by the γ-γ fast timing technique with LaBr3(Ce) detectors. Excited states of these nuclei were populated in the 197Au(11B,4n) and the 198Pt(12C,4n) fusion-evaporation reactions, respectively, at the FN-Tandem Facility at the University of Cologne. The lifetimes of the 4+1 states in both nuclei were measured, along with an upper limit for the 2 + 1 state in 204Po. The preliminary results are discussed in the scope of the systematic behavior of the transition strengths between yrast states in polonium isotopes.


Introduction
The evolution from seniority-type to collective structure is a process which provides a stringent test for the contemporary nuclear structure models. The yrast structures of polonium isotopes below the N = 126 shell closure are suitable for studying this evolution. In a recent study [1], an increased strength for the seniority-changing 2 + 1 → 0 + 1 transition in 206 Po has been reported, leading to the conclusion that the 2 + 1 state of 206 Po has a predominantly collective character. It has to be noted however, that the energy level pattern of the yrast states of 206 Po and the hindered transition probability of the 8 + 1 → 6 + 1 transition indicate that seniority-type structure is preserved to a certain extent. This fact either implies a spin dependence in the evolution from seniority-type regime to collectivity or questions the conclusions in Ref. [1]. The later stems from the fact that in the seniority regime, the E2 transition strength of seniority changing transitions, such as the 2 + 1 → 0 + 1 transition, increases in a parabolic way with increasing the number of valence particles and reaches a maximum at the middle of the j-shell [2]. This behavior is identical to the one in the collective regime and therefore the evolution of the E2 transition strength for the 2 + 1 → 0 + 1 transitions cannot be used as a decisive fingerprint for locating the transition from single-particle (seniority-type) to collective mode. For the latter purpose, more unambiguous information can be obtained from the evolution of the E2 strengths of seniority-preserving transitions, such as the 4 + 1 → 2 + 1 transition, because it has two distinctive * e-mail: milenas@phys.uni-sofia.bg behaviors in each regime. In seniority regime it follows a parabola with a minimum at the middle of the j-shell, while in the collective regime the parabola follows the evolution of the B(E2; 2 + 1 → 0 + 1 ) strengths, i.e. it has a maximum at the middle of the j-shell [2].
Our study is focused on the Po isotopes in the vicinity of 208 Pb. The main goal is to derive the absolute E2 strengths for the 4 + 1 → 2 + 1 transitions. This can reveal where and how the transition from seniority type to collective mode occurs. Such study requires the lifetimes of the 4 + 1 states of 206 Po and 204 Po to be measured. Until now, such information is missing due to experimental difficulties that stem from the fact that 4 + 1 states in both isotopes are positioned between the long-lived 8 + 1 states and the short-lived 2 + 1 states. In this work we report preliminary results on the B(E2) transition strengths of the seniorityconserving 4 + 1 → 2 + 1 transitions in 204 Po and 206 Po.

Experiment
The experiment was performed at the FN Tandem facility at the University of Cologne. Excited states of 204 Po were populated in the 197 Au( 11 B,4n) fusion-evaporation reaction at a beam energy of 55 MeV. A thick (110 mg/cm 2 ) self supporting 197 Au foil was used as a target. The excited states of 206 Po were populated in the 198 Pt( 12 C,4n) reaction at a beam energy of 65 MeV. The used target was 10 mg/cm 2 198 Pt foil. The fast-timing array consisted of eight HPGe detectors and nine ø1.5 x 1.5 LaBr 3 (Ce) scintillators (referred later in the text as LaBr). To suppress the Compton background, six of the LaBr detec-tors were placed inside bismuth-germanate (BGO) Compton suppressors. The other three had lead shields to suppress background events associated with scattered γ-rays. Time-to-Amplitude Converters (TACs) recorded the time differences between the timing signals for every unique detector-detector combination [3]. To process and collect the energy signals from the detectors and the amplitudes of the TAC signals, 80 MHz synchronized digitizers were used. The data were analyzed using the "soco.v2" software developed at the Institute of Nuclear Physics in Cologne [4]. For the lifetime determination the Generalized Centroid Difference method (GCDM) was used, discussed in detail in [5]. In this method, two independent time spectra are obtained, constructed as the time difference between two signals generated by two γ-rays that connects an excited state. If the transition which feeds the state provides the start signal to the TAC and the decay transition from this state -the stop signal, the Delayed (D) time distribution is obtained. In the reverse case, Anti-delayed (AD) time distribution is obtained. Assuming no background contributions, the difference between the centroids (first moment of the time distribution) of the delayed and antidelayed time spectra is expressed as : where τ is the mean lifetime of the given state and E f and E d are the energies of the feeding and the decaying transition respectively. In this formula, PRD is the prompt response difference, defined as the linearly combined zerotime response of the whole fast-timing array [6]. The PRD is used as a single correction for the lifetime determination, according to Eq. (1), and one of the main tasks is to determine its energy dependence. For calibration of the PRD, 152 Eu source has been used. It produces coincident γ-rays in the 40-1408 keV energy region, which corresponds to the energy region of interest. The lifetimes of the relevant excited states in the daughters 152 Gd and 152 Sm are known precisely and nearly no background contribution is present in the coincidence spectrum. In Figure 1, LaBr spectrum is obtained in coincidence with the decay transition from 2 + 1 to g.s. in 152 Gd. Time-difference spectra of the 779-344 keV cascade are shown along with the corresponding centroid difference, PRD, peak-to-background (p/b) ratio and lifetime value. Using Eq. (1) the PRD was obtained. Repeating the same procedure for the rest of the feeding transitions of 344 keV state, data points for PRD were obtained. For precise calibration over larger energy region, multiple γ f eeder -γ decay combinations were used.
The final PRD data points are fitted using the function [6] PRD(E γ ) = a The final result of the PRD-curve is presented in Figure 2. The precision is defined as two times the standard rootmean-squared deviation (2σ) of the PRD fit corresponding to 8 ps. Full projections of the symmetric γ-γ matrices obtained with the HpGe detectors (red spectrum) and the     LaBr detectors (blue spectrum) are shown in Figure 3. Partial level scheme of 206 Po, relevant for the analysis, is also shown on the picture. To extract the lifetime, triple HpGe-LaBr-LaBr coincidences were used. The doubly gated HpGe and LaBr spectra, relevant for the analysis of the 4 + 1 state in 206 Po are shown in Figure 4. The doubly gated HpGe spectrum is generated from HpGe-LaBr-HpGe triple coincidences. The good energy resolution of the HpGe detectors allows a precise coincidence cascade selection. By placing the first LaBr gate on the 477 keV decay transition, the de- where ∆C FEP corresponds to the centroid difference related to FEP events only. ∆C BG is the time response of the background and p/b is the peak-to-background ratio of the considered γ-ray. As ∆C BG cannot be measured directly, it has to be interpolated from measuring background time spectra, generated at different energies above and below the FEP. The analysis to derive the correction for background contributions is performed for each FEP separately. These corrections are presented on the lower two panels of Figure 4. The result for the lifetime of the 4 + 1 state is given in Table 1.
The same analysis was carried out for the second nucleus 204 Po. Full projections of the corresponding γ-γ matrices obtained with HpGe detectors and LaBr detectors are illustrated in Figure 5, along with corresponding level scheme.
Along with the value for the lifetime of 4 + 1 state in 204 Po, given in Table 1, an upper limit for the lifetime of the 2 + 1 state was measured. The HpGe gate has been placed on the 516 keV transition, while LaBr gates were placed on the 426 keV and 684 keV transitions respectively. Thus, a summed lifetime for the 4 + 1 and 2 + 1 states together was obtained and evaluated to 31.4(64) ps. Subtracting from this value the previously measured value for the lifetime of 4 + 1 state, an upper limit of 17 ps is deduced. Using the measured lifetimes, the reduced transition probabilities B(E2) for corresponding transitions in both nuclei are derived. The results from the analysis are summarized in Table 1. Figure 6 shows the graphical representation of the B(E2) values for the case of N = 122 isotones. It can be seen that the evolution of the E2 strengths for the 4 + 1 → 2 + 1 transition follows the one for the 2 + 1 → 0 + 1 which rises up towards mid-shell. This indicates that the 4 + 1 state of 206 Po has a collective character. The same situation is observed for 204 Po (not shown). These conclusions are in agreement with the conclusion from Ref. [1] that the transition to collectivity occurs before 204 Po. At the same time, the behavior of the B(E2; 8 + 1 → 6 + 1 ) in N = 122 isotonic chain  The obtained time-difference spectra are also shown, with the corresponding value for the centroid difference. Middle and bottom panels show the Compton background correction procedure. Here, the PRD curve is shifted in parallel in order to cross the energy axis at the energy of the decay transition (middle panel) and feeding transition (bottom panel) respectively. has a seniority character. All together, this strongly suggests that the transition from seniority regime to collective mode has a spin dependence. However, theoretical calculations are needed to validate this observation.

Conclusion
We have measured the lifetimes of low-lying yrast states in 204 Po and 206 Po using a HpGe-gated picosecond-sensitive fast-timing technique. The lifetimes of the 4 + 1 states in both nuclei were determined, along with a deduced upper limit for the 2 + 1 state in 204 Po using GCDM. The evolution of the B(E2) strengths for the 2 + 1 → 0 + 1 and the 4 + 1 → 2 + 1 transitions of 206 Po and 204 Po indicates that these states are of collective nature.