Evidence for oblate structure inPb186

RAPID COMMUNICATIONS PHYSICAL REVIEW C 72, 011304(R) (2005) Evidence for oblate structure in 186 Pb J. Pakarinen,1,∗ I. G. Darby,2 S. Eeckhaudt,1 T. Enqvist,1 T. Grahn,1 P. T. Greenlees,1 V. Hellemans,3 K. Heyde,3 F. Johnston-Theasby,4 P. Jones,1 R. Julin,1 S. Juutinen,1 H. Kettunen,1 M. Leino,1 A.-P. Leppänen,1 P. Nieminen,5 M. Nyman,1 R. D. Page,2 P. M. Raddon,4 P. Rahkila,1 C. Scholey,1 J. Uusitalo,1 and R. Wadsworth4 2 1 Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014, Jyväskylä, Finland Department of Physics, Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom 3 Department of Subatomic and Radiation Physics, Proeftuinstraat, 86 B-9000 Gent, Belgium 4 Department of Physics, University of York, Heslington, York Y01 5DD, United Kingdom 5 Department of Nuclear Physics, The Australian National University, Canberra, ACT 0200, Australia (Received 14 April 2005; published 29 July 2005) In-beam γ γ coincidence data have been collected for 186 Pb by combining the JUROGAM Ge-detector array and the GREAT spectrometer with the RITU gas-filled recoil separator for recoil-decay tagging measurements. In addition to the known prolate yrast band in 186 Pb, these data have enabled a new low-lying side band to be identified. Based on the analysis of its decay pattern and comparison with Interacting Boson Model (IBM) calculations, the new band is associated with an oblate shape. DOI: 10.1103/PhysRevC.72.011304 PACS number(s): 27.70.+q, 21.10.Re, 23.20.Lv, 25.70.Gh In Pb isotopes close to the neutron midshell at N = 104, experimental evidence for shape coexisting configurations and associated collective bands has been observed. These structures intrude down to energies close to the spherical ground state and can be associated with intruder 2p–2h and 4p–4h proton shell-model excitations across the Z = 82 energy gap [1–5]. Calculations using the deformed mean-field approach, essentially equivalent to the shell-model method, reveal three different shapes (spherical, oblate, and prolate configurations). It remains a challenge for both theoretical and experimental studies to obtain a consistent and detailed description of all the observed phenomena. In α-decay studies, the first two excited states of the midshell nucleus 186 Pb were observed to be 0+ states [6]. On the basis of α-decay hindrance factors, the 532(21) keV 0+ 2 state was associated with a mainly π (2p–2h) configuration, whereas the 650(23) keV 0+ 3 state was associated with a π (4p–4h) configuration. Consequently, together with the spherical ground state, the three 0+ states with largely different structures establish a unique shape-triplet in 186 Pb. The 650 keV 0+ 3 state was assumed to be the band head of a collective yrast band that, because of similarities with yrast bands in Hg and Pt isotones, has been assigned to a prolate shape [7–9]. As pointed out in Ref. [6], in order to verify the conclusions drawn from the α-decay studies, it is very important to observe a second, nonyrast collective band of oblate character also. The observation of such a band should shed light on shape mixing and the evolution of shape at higher spin. To date, collective yrast bands have been identified in the four even–even isotopes 182−188 Pb [7,8,10,11]. In these nuclei, the 0+ band head is bypassed owing to the competing highenergy E2 transition from the first excited 2+ state to the ∗ Corresponding author: [email protected] 0556-2813/2005/72(1)/011304(5)/$23.00 spherical ground state. Similar yrast bands have been observed in even–even Hg and Pt isotopes with 100
N
108 [1,5] and recently in 190 Po [12]. All these bands can be associated with prolate intrinsic structure by using a deformed mean-field approach, at least for the higher-spin members. 186 In addition to the lowest 532 keV 0+ Pb, a 2 state in systematic lowering of the first excited 0+ state in the even– even 188−202 Pb isotopes [13] has been observed. Evidence for the microscopic nature of these states comes, for example, from a low-spin sequence of nonyrast states in 196 Pb that can be described as a π (2p–2h) shell-model intruder excitation [14]. However, so far 188 Pb is the only Pb isotope for which a well-developed nonyrast collective band has been observed that may well be indicative of the oblate minimum [15]. Yrast bands associated with oblate intruder structures have also been observed in 192 Po, 194 Po, and 198 Rn nuclei [5]. The level spacing in all the observed oblate bands is larger than that of the prolate bands. Therefore, in spite of the low energy of the oblate 0+ state in 186 Pb, the oblate band is expected to lie well above the yrast line and therefore to be weakly populated in fusion-evaporation reactions. The production cross section of 186 Pb in available fusion-evaporation reactions is only of the order of 100 µb, and thus tagging techniques are needed to select γ rays emitted by 186 Pb. Owing to the relatively long half-life of 4.8 s for the 186 Pb α decay, it has so far been difficult to employ the recoil-decay tagging (RDT) [16,17] method for this nucleus. Moreover, a high-efficiency Ge-detector array must be available to obtain γ γ coincidence information, which is needed for the identification of the nonyrast states. All these factors mean that previous attempts to identify the low-lying oblate intruder band in 186 Pb have failed. New spectrometer systems combined with the upgraded RITU gas-filled recoil separator [18] at the Accelerator Laboratory of the University of Jyväskylä (JYFL) have made it possible to perform a successful RDT γ γ coincidence experiment for 186 Pb. A beam of 83 Kr ions was accelerated to an energy of 355 MeV by the K130 cyclotron and used to populate excited 011304-1 ©2005 The American Physical Society RAPID COMMUNICATIONS 187 178 183 Pb Pt Au 5300 5500 5700 6100 5900 6300 6500 Energy [keV] FIG. 1. Energy spectrum of α particles from the 83 Kr+106 Pd reaction measured in the DSSSDs of the GREAT spectrometer. 186 106 83 186 states of Pb via the Pd( Kr,3n) Pb reaction. The 106 Pd target was a metallic foil of thickness 1 mg/cm2 and 98.5% isotopic enrichment. Prompt γ rays were detected at the target position of RITU by the JUROGAM Ge-detector array consisting of 33 EUROGAM Phase 1 [19] and 9 GASP-type [20] Compton suppressed Ge detectors. The beam intensity was limited to 6 pnA by the Ge detector counting rates. The detectors were distributed over six angular positions with respect to the beam direction with five of them at 158◦ , ten at 134◦ , ten at 108◦ , five at 94◦ , five at 86◦ and seven at 72◦ . The total photo peak efficiency of the JUROGAM array for 1332 keV γ rays was 4.1%. Fusion-evaporation residues were separated from primary and scattered beams and other reaction products by use of the gas-filled recoil separator RITU. The transmission of RITU for the Pb residues in the present experiment was estimated to be 30%. The GREAT spectrometer [21] was employed at the focal plane of RITU. In the GREAT spectrometer fusion-evaporation residues and their α decay were detected by two double-sided silicon strip detectors (DSSSDs) mounted side by side. The strip pitch of each DSSSD was 1 mm in both directions, giving a total of 4800 pixels. A transmission multiwire proportional counter upstream of the DSSSDs was used to obtain energy loss and time-of-flight information for the recoils. A box of 28 PIN diodes was used to detect α particles that escaped from the DSSSDs. Data were collected by using the new total data readout system [22]. It operates without a hardware trigger and is designed to minimize dead time in the acquisition process. All detector electronics channels run independently and are associated in software, the data words all being time-stamped from a global 100 MHz clock. The resulting α-particle energy spectrum is shown in Fig. 1. During 151 h of effective beam time, a total of ∼106 186 Pb α decays were recorded in the 6.38 MeV peak, giving an estimated cross section of 185 µb for the 106 Pd(83 Kr,3n)186 Pb reaction. The temporal and spatial correlation for RDT were performed with the GRAIN software package [23]. Prompt γ rays observed in coincidence with a recoil followed by a 945 662 606 550 486 415 0 60 (b) 40 α-tagged γ γ coincidences gate on 550 keV 20 652 Hg 187 Tl Hg 5 0 40 30 20 10 0 40 30 20 10 0 200 (c) α-tagged γ γ coincidences gate on 945 keV (d) α-tagged γ γ coincidences gate on 479 keV 508 184 10 0 182 Counts / keV Hg Tl Counts / keV 185 186 5 3 Hg 15 10 463 183 (a) α-tagged singles γ rays 401 424 20 15 337 Pb 392 186 Counts / keV 4 10 Counts / 10 keV 25 261 PHYSICAL REVIEW C 72, 011304(R) (2005) 10 Counts / keV J. PAKARINEN et al. 300 400 700 500 600 Energy [keV] 800 900 FIG. 2. (a) Singles γ -ray energy spectrum gated with fusionevaporation residues and tagged with 186 Pb α decays. (b), (c), and (d) Recoil-gated, α-tagged γ γ coincidence spectra with a gate on the 550, 945, and 479 keV transitions, respectively. subsequent 186 Pb α decay in the same pixel in the GREAT strip detectors within 15 s (approximately three half-lives of 186 Pb) were selected in the data analysis. Even with such a long correlation time the high granularity of the GREAT DSSSDs allowed the recoils corresponding to 186 Pb to be extracted. The analysis of the data was completed with the RADWARE software package [24]. The spectrum of recoil-gated prompt γ rays is dominated by γ rays originating from 187 Tl and 186 Hg produced via pn and 2pn channels, respectively. From recoil-gated data, crosssection estimates of 250 µb and 270 µb were deduced for these reactions, respectively. Figure 2(a) shows the spectrum of singles γ rays gated by recoils and tagged with 186 Pb α decays. This spectrum is dominated by transitions of the known + 186 prolate yrast band and the 2+ Pb, but it 1 → 01 transition in also reveals other peaks of lower intensity. The high efficiency of the JUROGAM array allowed the collection of sufficient RDT γ γ coincidence events to place a large number of nonyrast transitions into a level scheme. Sample coincidence spectra are shown in Figs. 2(b)–(d). Based on the analysis of coincidence relations, the partial level scheme shown in Fig. 3 was constructed. Because of deorientation of recoiling ions [25] and overlapping transition energies, information for spin assignments from γ -ray angular distributions was difficult to obtain, especially at low spin. Experimental information concerning the observed γ -ray transitions is summarized in Table I. R is the ratio of α-tagged singles γ -ray intensities between detectors at 158◦ (ring 1) and 94◦ +86◦ (rings 4+5). For a known stretched, pure E2 011304-2 RAPID COMMUNICATIONS EVIDENCE FOR OBLATE STRUCTURE IN 186 Pb PHYSICAL REVIEW C 72, 011304(R) (2005) TABLE I. Measured γ -ray transitions; γ -ray energy, relative intensity, (tentatively) assigned spins, and multipolarity information are listed. (16 ) Eγ (keV) Irel Ii → If R (14 ) 662.2(1) 260.6(1) 337.1(1) 414.8(1) 485.8(5) 549.6(6) 605.6(8) 652.2(2) 100(6) 79(8) 74(7) 56(5) 28(3) 13.4(9) 7.1(5) 2.2(2) + 2+ 1 → 01 + + 41 → 21 + 6+ 1 → 41 + + 81 → 61 + 10+ 1 → 81 + 121 → 10+ 1 + (14+ 1 ) → 121 + (161 ) → (14+ 1) 1.0(2) 0.9(2) 1.1(2) — 1.4(4) 1.3(4) — — 945.2(3) 391.5(2) 401.3(2) 424.1(2) 462.7(2) 507.6(3) 551.3(9) 5.1(6) 4.0(7) 5.5(7) 4.2(5) 3.9(5) 1.8(3) 0.5(3) 674.5(6) 414.5(5) 478.8(2) 487.4(4) 1.4(5) 2.1(7) 3.8(5) 2.3(6) + (2+ 2 ) → 01 + (42 ) → (2+ 2) + (6+ ) → (4 2 2) + + (82 ) → (62 ) + (10+ 2 ) → (82 ) + (122 ) → (10+ 2) + (14+ ) → (12 2 2) + (4+ 2 ) → 21 + (42 ) → 4+ 1 + (6+ ) → 6 1 2 + + (82 ) → 81 3967.7 3684.0 (14 ) 652.2 551.3 3315.5 3132.8 (12 ) 605.6 507.6 2710.0 12 549.6 462.7 478.8 414.8 1.0(4) 0.9(4) 1.1(3) 1.5(1.0) — — — 4 1259.9 0 0 650 532 2 337.1 260.6 922.8 1738.4 (6 ) 1674.7 6 424.1 487.4 485.8 8 2162.4 (8 ) 2160.5 10 2625.2 (10 ) 414.5 674.5 401.3 1337.0 (4 ) 391.5 (2 ) 945.2 662.2 945.2 662.2 0 0.0 FIG. 3. Level scheme of 186 Pb deduced from the present data, including the two excited 0+ states taken from Ref. [6]. The widths of the arrows are proportional to the measured intensities. — — 0.6(3) — transition in 187 Tl a ratio of 1.2(2) was deduced, while for a dipole transition the corresponding value was 0.6(2). The yrast E2 cascade in 186 Pb has recently been observed up to I π = 14+ , where the I π = 12+ and I π = 14+ states are tentatively assigned [9]. In the present work, this cascade up to I π = 10+ is confirmed, and the 2710 keV level is assigned + to I π = 12+ , as the 12+ 1 → 101 transition has the angular distribution ratio of a stretched E2. Moreover, the coincidence data reveal candidates for the 14+ → 12+ and 16+ → 14+ transitions [Fig. 2(b)], the former having 4 keV higher energy than that reported in Ref. [8] and 10 keV higher than that reported in Ref. [9]. The 945 keV state, which de-excites to the ground state, is analogous to the 953 keV state in 188 Pb [15] and can be tentatively assigned as the 2+ 2 state. The 1337 keV level is tentatively assigned to I π = 4+ as it de-excites to the + + 2+ 1 , 41 and 22 states. An I = 3 assignment is unlikely, as that would make the level highly nonyrast. For similar reasons the 1738 and 2162 keV levels are tentatively assigned + to I π = 6+ 2 and 82 , respectively. The former assignment is in accord with the angular distribution information for the interband 479 keV transition, indicating its nonstretched E2 character. Based on the coincidence relationships and intensity balance, the 463, 508, and 551 keV transitions are assumed to form an E2 cascade feeding the 8+ 2 state and thus, together with the 392, 401, and 424 keV transitions, a K = 0 band of E2 transitions. The 424 and 463 keV transitions could possibly correspond to the 425 and 464 keV transitions observed in Ref. [9]. It is intriguing to consider whether the newly observed band has characteristics that may be associated with oblate deformation. First, a similar K = 0 side band built on top of a 2+ 2 state was observed in 188 Pb and associated with an oblate shape [15]. Unfortunately, owing to the dominant high-energy E2(2+ 2 → 0+ ) ground-state transition and other overlapping transitions, 1 + the E2(2+ 2 → 02 ) transition to the band head as well as the + possible branch to the 0+ 3 state from the 22 state remain + 188 186 unobserved in Pb and in Pb. In addition, the 2+ 2 → 21 186 transition was not observed in Pb. The intensity limits still allow these transitions in 186 Pb to have B(E2) values of 5, 25 + and 30 times higher, respectively, than that for the 2+ 2 → 01 transition. A remarkable feature of the side band in 186 Pb is the strong I → I and weak I → I − 2 interband transitions to the prolate yrast band. The observed 674 keV branch from the + 4+ 2 to the 21 state represents only about 3% of the B(E2) value + of the 392 keV intraband transition, whereas for the 4+ 2 → 41 414.5 keV transition the corresponding value is 34%. The nonobservation of the other I → I − 2 interband transitions allows intensity limits to be set. The upper limit for their B(E2) values is determined to be 3% of that of the competing intraband transition. If the new side band was a beta-vibrational band based on the prolate minimum, the competing I → I − 2 and I → I E2 branches from the side band to the yrast band should, according to the Alaga rules [26], have similar B(E2) values. Therefore, the I → I − 2 transitions having the highest energy should be the dominant ones. This is clearly not what was 011304-3 RAPID COMMUNICATIONS J. PAKARINEN et al. PHYSICAL REVIEW C 72, 011304(R) (2005) observed. Similar arguments make a gamma band an unlikely explanation for the observed band. However, such a γ band would presumably lie higher in energy and mix with the oblate band to some extent. This possibility has been discussed by Dracoulis et al. in 188 Pb, where a candidate for the odd-spin sequence of the γ band was observed [27]. The observed intensities for the I → I interband transitions + + from the 4+ 2 , 62 and 82 states represent B(E2) values, which are 20%–60% of those for the competing intraband transitions (M1-transitions of I = 0 between K = 0 bands are forbidden). The deduced intensity limits for the similar I → I transitions from the higher-lying states of the observed side band do not rule out the existence of E2 transitions of a similar strength. As pointed out in Ref. [15], the strong I → I interband transitions may be due to mixing of two different shapes. The mixing of different shapes in heavy nuclei may result in considerable E0 components in I → I transitions. Based on the missing γ -ray intensities in coincidence gates, dominant E0 components were deduced in several interband I → I transitions in 188 Pb [15]. The present coincidence data for 186 Pb do not indicate any strong E0 components in the corresponding interband transitions within the statistical error bars. However, it should be noted that, because of the high energies of these transitions in 186 Pb compared with 188 Pb, possible E0 components of monopole strengths similar to those in 188 Pb may well be obscured by the much faster E2 components in 186 Pb. Further support for association of the new side band with the 2p–2h structure can be found in mixing calculations. In a recent study that concentrated on describing intruder bands and configuration mixing, the nucleus 188 Pb was studied by using the algebraic formulation of the Interacting Boson Model (IBM). This approach allows the appearance of intruder states to be approximated by incorporating 2p–2h and 4p–4h excitations across the proton closed shell at Z = 82, next to the regular states of the 0p–0h configuration corresponding to the closed proton shell at Z = 82. For details on the choice of the parameters used within this approach, see Refs. [28] and [29]. Applying this description to the case of 186 Pb, two collective band structures result that can be associated mainly with 4p–4h and 2p–2h excitations. A detailed account of both the calculated energies of these bands and their electromagnetic properties will be presented in a forthcoming paper. Within the context of the present paper, the B(E2) values for both intraband and interband transitions are shown, starting with the mainly 2p–2h band in Table II. The effective charges in the E2 transition operator were fitted to the two known B(E2) values in 188 Pb [30]. The sequence of calculated E2 decays, starting from the higher spin states, allowed the construction of two collective bands. The excitation energies of the bands are in rather good agreement with the experimental values. + The mixing amplitudes of the 0+ 2 and the 03 states are very similar to the results derived by Page et al. [31], although the mixing is somewhat more pronounced. It is clear from Table II that the calculated I → I − 2 interband transitions are considerably weaker than the strong I → I interband transitions. These results are consistent with the observed TABLE II. Calculated B(E2) values for transitions starting from the mainly 2p–2h band. Primes indicate an interband transition to the mainly 4p–4h band. The absence of primes denotes an intraband transition. If B(E2) (W.u.) If′ B(E2) (W.u.) 14+ 12+ 190 12+ 10+ 194 10+ 8+ 194 8+ 6+ 187 6+ 4+ 172 4+ 2+ 121 2+ 0+ 75 14′+ 12′+ 12′+ 10′+ 10′+ 8′+ 8′+ 6′+ 6′+ 4′+ 4′+ 2′+ 2′+ 57 6 41 3 35 1 34 <1 37 !1 50 !1 83 Ii experimental E2 branching, giving support to the idea that the side band is related more strongly to a microscopic 2p–2h structure. The two constructed bands can now be linked with a collective interpretation by using a method to connect the IBM algebraic approach with a geometric collective rotational model analysis. The calculated IBM quadrupole moments were equated with the corresponding quadrupole moments of K = 0 bands. This allows an intrinsic quadrupole moment to be extracted within the collective rotational model for the two bands calculated within the IBM. For the band of the mainly 4p–4h configuration, corresponding to the experimental yrast band, this results in a positive sign, indicating prolate deformation. For the side band originating mainly from the 2p–2h configuration, a negative sign was obtained, indicating oblate deformation and supporting the present experimental results. The kinematic moments of inertia (J (1) ) for the observed candidate oblate band and the prolate yrast band in 186 Pb are plotted in Fig. 4. For comparison, values of J (1) for the prolate bands in 182,184,188 Pb and oblate bands in 188,196 Pb are shown. Also included are the oblate bands based on a mainly proton 4p–2h shell-model configuration in 192 Po and 194 Po. The J (1) curves for the prolate bands in the even–even isotopes 182−188 Pb are very similar (especially at high spin). The J (1) values for the oblate bands are lower than those for the prolate bands, which is at least partially due to their small deformation. The curve for the candidate oblate band in 186 Pb differs from the others. It extends from small J (1) values at low spin to values that are higher than those for the prolate bands. As shown in Fig. 4, similar behavior is also observed for the oblate band in 188 Pb, but starting at higher spin. It is difficult to associate this up-bend in 186 Pb with any alignment of valence nucleons, as it occurs at such low spin. Therefore it may be due to a shape change toward a more deformed oblate structure. Such structures are predicted to occur at relatively 011304-4 RAPID COMMUNICATIONS EVIDENCE FOR OBLATE STRUCTURE IN 186 Pb PHYSICAL REVIEW C 72, 011304(R) (2005) In summary, by employing an upgraded spectrometer system in a RDT measurement, high-quality in-beam γ γ coincidence data for 186 Pb have been collected. A new low-lying side band has been identified. On the basis of observed strong I → I and weak I → I − 2 interband transitions to the prolate yrast band, this band is associated with an oblate shape. This interpretation is further supported by configuration mixing calculations within the interacting Boson model. The moment of inertia behavior of the new band may indicate a shape change toward a more deformed oblate shape. 45 40 182 (1) _ 2 ℑ [h /MeV] 35 184 30 186 25 188 20 192 194 15 186 10 188 5 196 Pb (prolate) Pb (prolate) Pb (prolate) Pb (prolate) Po (oblate) Po (oblate) Pb (oblate) Pb (oblate) low excitation energy in the even–even Pb isotopes close to the neutron midshell [33,34]. This work has been supported by the EU-FP5-IHP-Accessto-JYFL Project (contract HPRI-CT-1999-00044), the EUFP5-IHP-RTD-EXOTAG Project (contract HPRI-CT-199950017), by the Academy of Finland under the Finnish Centre of Excellence Programme 2000-2005 (project 44875) and by the EPSRC (UK). Financial support from the “FWO-Vlaanderen,” the University of Ghent, as well as from the OSTC (Grant IUAP P5/07) is acknowledged (by V. Hellemans and K. Heyde). The UK/France (EPSRC/IN2P3) Loan Pool and EUROBALL Owners Committee is also acknowledged for the EUROGAM detectors of JUROGAM. 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