PRL 102, 212501 (2009)
PHYSICAL REVIEW LETTERS
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-Ray Spectroscopy at the Limits: First Observation of Rotational Bands in 255 Lr S. Ketelhut,1,* P. T. Greenlees,1 D. Ackermann,2 S. Antalic,3 E. Cle´ment,4 I. G. Darby,5,† O. Dorvaux,6 A. Drouart,4 S. Eeckhaudt,1 B. J. P. Gall,6 A. Go¨rgen,4 T. Grahn,1,‡ C. Gray-Jones,5 K. Hauschild,7 R.-D. Herzberg,5 F. P. Heßberger,2 U. Jakobsson,1 G. D. Jones,5 P. Jones,1 R. Julin,1 S. Juutinen,1 T.-L. Khoo,8 W. Korten,4 M. Leino,1 A.-P. Leppa¨nen,1,x J. Ljungvall,4 S. Moon,5 M. Nyman,1 A. Obertelli,4 J. Pakarinen,1,‡ E. Parr,5 P. Papadakis,5 P. Peura,1 J. Piot,6 A. Pritchard,5 P. Rahkila,1 D. Rostron,5 P. Ruotsalainen,1 M. Sandzelius,9 J. Sare´n,1 C. Scholey,1 J. Sorri,1 A. Steer,10 B. Sulignano,4 Ch. Theisen,4 J. Uusitalo,1 M. Venhart,3,† M. Zielinska,11 M. Bender,12,13 and P.-H. Heenen14 1
Department of Physics, University of Jyva¨skyla¨, FIN-40014 Jyva¨skyla¨, Finland 2 Gesellschaft fu¨r Schwerionenforschung (GSI), D-64291 Darmstadt, Germany 3 Department of Nuclear Physics and Biophysics, Comenius University, 84248 Bratislava, Slovakia 4 CEA, Centre de Saclay, IRFU/Service de Physique Nucle´aire, F-91191 Gif-sur-Yvette, France 5 Department of Physics, University of Liverpool, Oxford Street, Liverpool, L69 7ZE, United Kingdom 6 Institut Pluridisciplinaire Hubert Curien, F-67037 Strasbourg, France 7 CSNSM, IN2P3-CNRS, F-91405 Orsay Campus, France 8 Argonne National Laboratory, Argonne, Illinois 60439, USA 9 Department of Physics, Royal Institute of Technology, Stockholm, SE-10691, Sweden 10 Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom 11 Heavy Ion Laboratory, Warsaw University, ul. Pasteura 5A, 02-093 Warsaw, Poland 12 Universite´ Bordeaux, Centre d’Etudes Nucle´aires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan, France 13 CNRS/IN2P3, Centre d’Etudes Nucle´aires de Bordeaux Gradignan, UMR5797, F-33175 Gradignan, France 14 Service de Physique Nucle´aire The´orique, Universite´ Libre de Bruxelles, B-1050 Bruxelles, Belgium (Received 14 November 2008; published 29 May 2009) The rotational band structure of 255 Lr has been investigated using advanced in-beam -ray spectroscopic techniques. To date, 255 Lr is the heaviest nucleus to be studied in this manner. One rotational band has been unambiguously observed and strong evidence for a second rotational structure was found. The structures are tentatively assigned to be based on the 1=2 ½521 and 7=2 ½514 Nilsson states, consistent with assignments from recently obtained decay data. The experimental rotational band dynamic moment of inertia is used to test self-consistent mean-field calculations using the Skyrme SLy4 interaction and a density-dependent pairing force. DOI: 10.1103/PhysRevLett.102.212501
PACS numbers: 21.10.Re, 23.20.Lv, 27.90.+b
Because of the strongly repulsive Coulomb force, superheavy nuclei would fission instantaneously without nuclear shell effects, which for nuclei up to 208 Pb are especially large at the position of the magic numbers. In superheavy nuclei, the situation is more complicated, as a large shell correction can occur without a significant gap in the level spacing. This is due to the predominance of high-j spherical shells close to the Fermi energy, which have a very high degeneracy. A large shell correction can be generated by the occurrence of a low-j orbital amongst the high-j levels, giving a reduced level density [1]. Predictions of the next shell closures beyond 208 Pb remain uncertain, which is partly due to this effect. Theoretical calculations give values for the proton magic number ranging from 114 for most macroscopic-microscopic models [2] to 120 and 126 for relativistic and nonrelativistic nuclear mean-field calculations [3,4]. The neutron magic number is predicted by most calculations to be 184, with some parameterizations favoring 172 instead. Calculations of the positions of individual states are especially sensitive to changes in the parameterizations, which are themselves based on experimental data far away from the region of the heaviest 0031-9007=09=102(21)=212501(4)
elements. Though experiments have recently reached nuclei up to 297 118 [5], these investigations give very little spectroscopic information due to the small cross sections of around 1 pb. In contrast to the heaviest elements currently known, nuclei in the region of 254 No can be produced with cross sections of the order of hundreds of nanobarns. For these nuclides, the rapid rearrangement of single-particle levels with deformation greatly reduces the level density around the Fermi energy for certain prolate shapes, which leads to large additional binding and gives rise to collective rotational bands. The relatively large cross section enables in-beam experimental investigation of single-particle and collective excitations, thus providing spectroscopic data which can be used to constrain nuclear structure models for the heaviest elements. Rotational band properties can be used to test various aspects of modern self-consistent mean-field calculations. For example, the variation of the moment of inertia with spin can provide information concerning the strength and evolution of the pairing interaction, while odd-mass nuclei provide a test of the single-particle spectra predicted by the effective interaction [6]. The first in-beam studies in this region led to the
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Ó 2009 The American Physical Society
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PHYSICAL REVIEW LETTERS
used analogue shaping amplifiers and total data readout TDR time-stamping ADC cards. With digital electronics the
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individual germanium detectors could count at approximately 20 kHz with no adverse affect on spectrum quality. This increased count rate capability meant more in-beam data could be processed, such that the 255 Lr yield could be doubled. All data were read out synchronously with the TDR data acquisition system [27] and analyzed with the software GRAIN [28]. Figure 1(a) shows a spectrum of prompt ray singles which occur in a time window of 0:2 s, approximately 1 s before the fusion-evaporation recoil event is detected at the focal plane. The spectrum is dominated by peaks at the energies of the Lr K and K x rays between 125 and 145 keV (scaled by a factor of 5 for clarity). Though the statistics in this spectrum are limited, a sequence of six peaks with rotational-like spacing is visible with energies of 196.6(5), 247.2(5), 296.2(5), 342.9(5), 387(1) and 430(1) keV (marked with dotted lines). Support for the assignment of this sequence of rays to a rotational band is given by the investigation of recoilgated - coincidences, presented in Fig. 1(b). The figure depicts a sum of spectra projected from a recoil-gated - coincidence matrix, in coincidence with the transitions marked by dotted lines. The spectrum is almost background free in the region of the transitions from 0 to 450 keV, such that almost all of the counts can be found at the position of either the peaks or the x rays. The band shows a striking similarity to the rotational structure found by Chatillon et al. in 251 Md [13], which was assigned to be based on the 1=2 ½521 state. Inspection of Fig. 1(b) shows no evidence for a second, signature-partner rotational band which would be expected if the structure was based on a high-K orbital such as 7=2.
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discovery of rotational bands in the even-even nuclei 252;254 No and 250 Fm [7–10]. Odd-mass nuclei are more difficult to study, as the decay intensity is usually fragmented over several bands. Rotational bands have been reported only for 253 No [11,12] and 251 Md [13]. Recent experimental work carried out in this region is reviewed in Ref. [12]. This Letter reports on the results of two experiments carried out to study the rotational properties of the Z ¼ 103 nucleus, 255 Lr. These studies are at the extreme limit possible with modern techniques, and state-of-the-art digital electronics have been employed in order to obtain data of highest quality. Though 255 Lr was first observed in 1969 [14,15], experimental information concerning the level structure is still limited. Chatillon et al. determined the ground and first excited state to have the configuration 1=2 ½521 and 7=2 ½514, respectively [16]. Both of these states decay by -particle emission, the 7=2 ½514 state being at an excitation energy of just 37 keV. An isomeric state has been found by measuring delayed electrons from converted electromagnetic transitions decaying to the ground state [17,18], using the same technique as in recent studies of 252;254 No and 250 Fm [10,19–22]. A number of rays were observed in the decay of the isomer, with energies 244, 301, 387, 492, and 588 keV, though no clear decay scheme was constructed. The isomer is speculated to be a three quasiparticle state built by coupling the odd proton to a two-neutron quasiparticle configuration. Two experiments have been performed at the Accelerator Laboratory of the University of Jyva¨skyla¨ 255 Lr (JYFL) to study via the reaction 209 Bið48 Ca; 2nÞ255 Lr. The 48 Ca beam delivered by the K130 cyclotron irradiated 209 Bi targets with thicknesses of 420 g=cm2 and 460 g=cm2 in the first and second experiment, respectively. The targets were mounted on a carbon backing of 40 g=cm2 . The beam energy was chosen to be 221 MeV at the beginning of the first experiment. An improvement of the yield was achieved when changing to 219 MeV for the last quarter of the beam time. The recoils were separated from projectiles and transfer products by the gas-filled separator RITU [23], and implanted into the double-sided silicon strip detector (DSSD) of the focal-plane detector setup GREAT [24]. With an average beam intensity of 12 pnA, a total of 1140 particles from 255 Lr were detected in approximately 200 hours of irradiation. The beam energy was chosen to be 219 MeV in the second experiment, producing 520 particles after approximately 50 hours of irradiation with an average beam intensity of 24 pnA. Prompt rays were detected with JUROGAM, an array of 43 Compton-suppressed germanium detectors with a total photopeak efficiency of 4.2% at 1332 keV [25]. In the second experiment the preamplifier signals from JUROGAM were digitized immediately using TNT2 100 MHz flash ADC cards [26], rather than the normally
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FIG. 1. (a) Spectrum of ray singles in delayed coincidence with fusion-evaporation residues. The energies shown have an error of 1 keV unless marked otherwise. (b) Sum of -ray spectra projected from the recoil-gated - coincidence matrix in coincidence with transitions marked by dotted lines. (c) As in (b), but for the transitions marked with dashed lines.
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As stated earlier, the ground state of 255 Lr has been determined through decay properties to be 1=2 ½521. The properties of this orbital and its important influence on the stability of superheavy elements were discussed by Ahmad et al. [29], showing that the decoupling parameter, a, is close to 1. Such a decoupling parameter results in the band with signature ¼ 1=2 being pushed up in energy with respect to the ¼ þ1=2 band, such that the decay proceeds mainly through E2 transitions in the ¼ þ1=2 band. Calculated decay patterns for the three orbitals expected close to the Fermi surface in 251 Md and 255 Lr can be found in the work of Chatillon et al. [13]. The decay patterns in 255 Lr are expected to be very similar. In view of the fact that no signature-partner band is observed, the similarity to the band observed in 251 Md, and the observed - coincidences, the sequence of rays is assigned to be a rotational band based on the 1=2 ½521 state. The -tagged -ray spectra in Fig. 2 support this assignment. The figure shows prompt rays detected in delayed coincidence with fusion-evaporation events, which are subsequently followed by detection of decay events in the same pixel of the DSSD within a maximum time interval of 90 seconds. For clarity, the spectrum of the recoil-gated ray singles of Fig. 1 is shown again in Fig. 2(a). The fact that both the 1=2 ½521 ground state and 7=2 ½514 isomeric state decay by emission allows the rays feeding these states to be independently selected. Figure 2(b) shows rays which are followed by decay from the 1=2 ½521 state, while Fig. 2(c) shows those followed by decay from the 7=2 ½514 state. Figure 2(b) clearly shows peaks at 247, 296, and 343 keV, which are assigned to the 1=2 ½521 rotational band. In contrast, there is no evidence of this band in Fig. 2(c), which is consistent with the interpretation based on the ray data alone. Figures 1 and 2 show evidence for a second set of evenly spaced
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FIG. 2. (a) As in Fig. 1(a). (b),(c) Alpha-tagged -ray spectra with correlations to particles emitted from the (b) 1=2 ½521, and (c) 7=2 ½514 states, respectively. Transitions of the proposed rotational band on top of the 1=2 ½521 state are marked by dotted lines in (b) and of the 7=2 ½514 state by dashed lines in (c). The maximum correlation time was 90 seconds.
week ending 29 MAY 2009
peaks—marked by dashed lines in Figs. 1 and 2(c). As shown in Fig. 1(c), the sum of projections from the recoilgated - coincidence matrix shows that six of the nine marked transitions are in coincidence with at least one of the other transitions. The energy spacing between the peaks is 23–25 keV, which is approximately half of that between the transitions assigned to the 1=2 ½521 band. It is therefore reasonable to assume that these transitions represent the two signatures of a strongly-coupled rotational structure. As shown in the work of Chatillon et al. [13], of the two high-K orbitals expected at low excitation energy in 255 Lr (7=2 ½514 and 7=2þ ½633), only rotational bands based on the 7=2 ½514 configuration are expected to decay mainly by E2 transitions. The magnetic properties of the 7=2þ ½633 configuration are such that the decay of this band should be dominated by highlyconverted M1 transitions which are likely to be unobserved in a -ray spectroscopic measurement. The sequence of transitions with energies 189(1), 239(1), 288.4(5), 338(1), 384(1) and 215(1), 264.6(5), 314.0(5), 360(1) keV are therefore tentatively assigned to be E2 transitions in both signatures of a strongly-coupled rotational band based on the 7=2 ½514 configuration. The observations made here based on -ray spectroscopy and the earlier deductions made on the basis of the -decay chain of 255 Lr form a rather consistent picture, lending weight to the earlier assignments of the ground and isomeric state configurations. The decay work showed that an internal transition between the 7=2 ½514 and 1=2 ½521 states competes with the decay of the 7=2 ½514 state in 255 Lr. Thus -ray spectra correlated with the decay of the 1=2 ½521 ground state may be expected to show rays from both bands, while -ray spectra correlated with the decay of the 7=2 ½514 should only show rays from that band. This expectation is borne out in Figs. 2(b) and 2(c), as the 1=2 ½521 rotational band is not observed in Fig. 2(c). It is interesting to note that the strongest rays observed in the decay of the assumed three-quasiparticle isomer (244, 301, 387, 492, and 588 keV [17,18]) do not correspond to those of the rotational bands observed here. This may indicate that the decay of the isomeric state does not proceed via transitions to the higher spin members of these bands. In order to test the rotational properties predicted by modern self-consistent theoretical models, the dynamical moments of inertia for the K ¼ 1=2 bands in 251 Md and 255 Lr have been calculated using the cranked HartreeFock-Bogolyubov method and the Skyrme SLy4 interaction. A density-dependent pairing interaction with zero range and a strength of V ¼ 1250 MeV fm3 is used. The formalism is identical to that described in Refs. [6,30]. The calculated dynamical moment of inertia is plotted as a function of rotational frequency in Fig. 3, and compared to that deduced from the experimentally observed transition energies. The moment of inertia deduced from the data is larger for 251 Md than for 255 Lr. It is
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E. C Marie Curie Fellowship, the UK EPSRC, and the U. S. Department of Energy (Contract No. DE-AC0206CH11357). M. V and S. A were supported by the Slovak Research and Development Agency (Contract No. APVV-20-006205) and VEGA (Contract No. 1/4018/ 07). We thank the UK/France (EPSRC/IN2P3) Loan Pool and the GAMMAPOOL European Spectroscopy Resource for the loan of detectors for JUROGAM. This work has benefited from the use of TNT2-D cards, developed and financed by CNRS/IN2P3 for the GABRIELA project.
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FIG. 3 (color online). Dynamical moment of inertia versus rotational frequency of the K ¼ 1=2 rotational bands in 251 Md (red triangles, dashed line) and 255 Lr (blue circles, solid line). The points with error bars represent the experimental data, the lines theoretical calculations using cranked HFB with the SLy4 interaction. See text for details.
interesting to note that a similar difference is observed for the neighboring even-even nuclei 250 Fm and 254 No (see Ref. [13]). The theoretical moment of inertia underestimates the data by 7–10@2 =MeV, but the behavior as a function of rotational frequency is very well reproduced, as is the larger moment of inertia for 251 Md. Overall, the reproduction of the experimental data is encouraging, though it is interesting to question why the theory underestimates the experimental value. It is difficult to single out a particular aspect which may be responsible for this difference—the underlying single-particle spectra are known to be at odds with experimental data, the moment of inertia is sensitive to the pairing parameterization (see, e.g., Duguet et al. [30]) and the approximate particle number projection techniques used may also have an effect. Further investigation would be necessary to address these points and come to a definite conclusion. Improved agreement between theory and experiment in this region is essential to subsequently give confidence that the predictions of theory for the superheavy elements are reliable. In summary, rotational bands based on the 1=2 ½521 ground and 7=2 ½514 states have been identified in 255 Lr, the heaviest nucleus to be so far studied in-beam. The rotational properties of the K ¼ 1=2 bands in 251 Md and 255 Lr have been calculated using modern self-consistent mean-field methods and tested against the experimental data. The agreement between theory and experiment is rather good, though the absolute magnitude of the calculated moment of inertia is slightly underestimated. Further theoretical investigation would be required to address this discrepancy. This work has been supported by the EU-FP6-I3 project EURONS No. 506065, the Academy of Finland [CoE Nuclear and Accelerator Based Physics Programme at JYFL, grants to P. T. G (111965) and C. S (209430)], the
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[email protected] † Present address: Instituut voor Kern- en Stralingsfysica, KU Leuven, B-3001 Leuven, Belgium. ‡ Present address: Department of Physics, University of Liverpool, Oxford Street, Liverpool, L69 7ZE, U.K. x Present address: Radiation and Nuclear Safety Authority, STUK, Regional Laboratory in Northern Finland, Rovaniemi, Finland. [1] M. Bender, W. Nazarewicz, and P.-G. Reinhard, Phys. Lett. B 515, 42 (2001). [2] S. C´wiok et al., Nucl. Phys. A 611, 211 (1996). [3] K. Rutz et al., Phys. Rev. C 56, 238 (1997). [4] M. Bender et al., Phys. Rev. C 60, 034304 (1999). [5] Y. Oganessian et al., Phys. Rev. C 74, 044602 (2006). [6] M. Bender, P. Bonche, T. Duguet, and P.-H. Heenen, Nucl. Phys. A 723, 354 (2003). [7] P. Reiter et al., Phys. Rev. Lett. 82, 509 (1999). [8] R.-D. Herzberg et al., Phys. Rev. C 65, 014303 (2001). [9] J. Bastin et al., Phys. Rev. C 73, 024308 (2006). [10] P. T. Greenlees et al., Phys. Rev. C 78, 021303(R) (2008). [11] P. Reiter et al., Phys. Rev. Lett. 95, 032501 (2005). [12] R.-D. Herzberg and P. T. Greenlees, Prog. Part. Nucl. Phys. 61, 674 (2008). [13] A. Chatillon et al., Phys. Rev. Lett. 98, 132503 (2007). [14] V. Druin et al., Sov. J. Nucl. Phys. 12, 146 (1971). [15] K. Eskola et al., Phys. Rev. C 4, 632 (1971). [16] A. Chatillon et al., Eur. Phys. J. A 30, 397 (2006). [17] K. Hauschild et al., Phys. Rev. C 78, 021302(R) (2008). [18] S. Antalic et al., Eur. Phys. J. A 38, 219 (2008). [19] B. Sulignano et al., Eur. Phys. J. A 33, 327 (2007). [20] S. K. Tandel et al., Phys. Rev. Lett. 97, 082502 (2006). [21] R.-D. Herzberg et al., Nature (London) 442, 896 (2006). [22] A. P. Robinson et al., Phys. Rev. C 78, 034308 (2008). [23] M. Leino et al., Nucl. Instrum. Methods Phys. Res., Sect. B 99, 653 (1995). [24] R. Page et al., Nucl. Instrum. Methods Phys. Res., Sect. B 204, 634 (2003). [25] C. Beausang et al., Nucl. Instrum. Methods Phys. Res., Sect. A 313, 37 (1992). [26] L. Arnold et al., IEEE Trans. Nucl. Sci. 53, 723 (2006). [27] I. Lazarus et al., IEEE Trans. Nucl. Sci. 48, 567 (2001). [28] P. Rahkila, Nucl. Instrum. Methods Phys. Res., Sect. A 595, 637 (2008). [29] I. Ahmad et al., Phys. Rev. Lett. 39, 12 (1977). [30] T. Duguet, P. Bonche, and P.-H. Heenen, Nucl. Phys. A 679, 427 (2001).
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