97/37 Rb 60 : The Cornerstone of the Region of Deformation around A∼100

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. 97/37 Rb 60 : The Cornerstone of the Region of Deformation around A100 Sotty, C.; Zielińska, M.; Georgiev, G.; Balabanski, D. L.; Stuchbery, A. E.; Blazhev, A.; Bree, N.; Chevrier, R.; Gupta, S. Das; Daugas, J. M.; Davinson, T.; De Witte, H.; Diriken, J.; Gaffney, L. P.; Geibel, K.; Hadyńska-Klȩk, K.; Kondev, F. G.; Konki, Joonas; Kröll, T.; Morel, P.; Napiorkowski, P.; Pakarinen, Janne; Reiter, P.; Scheck, M.; Seidlitz, M.; Siebeck, B.; Simpson, G.; Törnqvist, H.; Warr, N.; Wenander, F. Sotty, C., Zielińska, M., Georgiev, G., Balabanski, D. L., Stuchbery, A. E., Blazhev, A., Bree, N., Chevrier, R., Gupta, S. D., Daugas, J. M., Davinson, T., De Witte, H., Diriken, J., Gaffney, L. P., Geibel, K., Hadyńska-Klȩk, K., Kondev, F. G., Konki, J., Kröll, T., . . . Wenander, F. (2015). 97/37 Rb 60 : The Cornerstone of the Region of Deformation around A100. Physical Review Letters, 115(17), Article 172501. https://doi.org/10.1103/PhysRevLett.115.172501 2015 97 37Rb60: The Cornerstone of the Region of Deformation around A∼100 C. Sotty,1,2 M. Zielińska,3,4 G. Georgiev,1,* D. L. Balabanski,5A. E. Stuchbery,6A. Blazhev,7N. Bree,2R. Chevrier,8 S. Das Gupta,9,†J. M. Daugas,8T. Davinson,10 H. De Witte,2J. Diriken,2,11 L. P. Gaffney,12,2,‡K. Geibel,7 K. Hadyńska-Kl¸ek,3F. G. Kondev,13 J. Konki,14,15,16 T. Kröll,17 P. Morel,8P. Napiorkowski,3J. Pakarinen,14,15,16 P. Reiter,7 M. Scheck,17,‡M. Seidlitz,7B. Siebeck,7G. Simpson,18 H. Törnqvist,14 N. Warr,7and F. Wenander14 1CSNSM, CNRS/IN2P3, Université Paris-Sud, UMR8609, F-91405 ORSAY-Campus, France 2KU Leuven, Instituut voor Kernen Stralingsfysica, 3001 Leuven, Belgium 3Heavy Ion Laboratory, University of Warsaw, 02-093 Warsaw, Poland 4IRFU/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette, France 5ELI-NP, IFIN-HH, 30 Reactorului Street, 077125 Bucharest, Mˇagurele, Romania 6Department of Nuclear Physics, RSPE, Australian National University, Canberra, Australian Capital Territory 2601, Australia 7Institute for Nuclear Physics, University of Cologne, Zülpicher Straße 77, D-50937 Cologne, Germany 8CEA, DAM, DIF, F-91297 Arpajon cedex, France 9Dipartimento di Fisica, Universitá di Camerino, I-62032 Camerino, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Perugia, I-06123 Perugia, Italy 10Department of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom 11Belgian Nuclear Research Centre SCK·CEN, Boeretang 200, B-2400 Mol, Belgium 12Oliver Lodge Laboratory, University of Liverpool, Liverpool L69 7ZE, United Kingdom 13Nuclear Engineering Division, Argonne National Laboratory, Argonne, Illinois 60439, USA 14ISOLDE, CERN, CH-1211 Geneva 23, Switzerland 15Department of Physics, University of Jyväskylä, P.O. Box 35, FI-40014 University of Jyväskylä, Finland 16Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FI-00014 Helsinki, Finland 17Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany 18LPSC, CNRS/IN2P3, Université Joseph Fourier Grenoble 1, CNRS/IN2P3, INPG, F-38026 Grenoble Cedex, France (Received 3 August 2015; published 20 October 2015; publisher error corrected 5 November 2015) Excited states of the neutron-rich nuclei 97;99Rb were populated for the first time using the multistep Coulomb excitation of radioactive beams. Comparisons of the results with particle-rotor model calculations provide clear identification for the ground-state rotational band of 97Rb as being built on the πg9=2 ½4313=2þNilsson-model configuration. The ground-state excitation spectra of the Rb isotopes show a marked distinction between single-particle-like structures below N¼60 and rotational bands above. The present study defines the limits of the deformed region around A∼100 and indicates that the deformation of 97Rb is essentially the same as that observed well inside the deformed region. It further highlights the power of the Coulomb-excitation technique for obtaining spectroscopic information far from stability. The 99Rb case demonstrates the challenges of studies with very short-lived postaccelerated radioactive beams. DOI: 10.1103/PhysRevLett.115.172501 PACS numbers: 27.60.+j, 23.20.Lv, 25.70.De, 29.38.-c The spherical symmetry of atomic nuclei is well established for the cases where both the proton (Z) and neutron (N) numbers are near magic numbers. Most atomic nuclei, however, have nonspherical shapes. The best-known and well-studied region of prolate-deformed nuclei is the “rare-earth region,”centered between 50 <Z<82 and 82 <N<126. A less known region of deformed nuclei, which is predicted to show even larger deformations [1], is centered around mass 100 (A∼100) between the 28 <Z<50 and 50 <N<82 major shells. These nuclei are neutron rich, and well away from the valley of stability, so they are challenging to study experimentally. The A∼100 prolate-deformed Sr-Zr region (Z¼38;40) has attracted considerable attention since its prediction [2] and experimental observation [3]. Spectroscopic studies of these neutron-rich nuclei were undertaken at on-line mass separators and by γ-ray spectroscopy in spontaneous fission [4–6]. A key feature is the sudden onset of deformation when progressing from neutron number N¼58 to N¼60. However, the abrupt change of the deformation quickly washes out when moving away from Z¼38 [4]. Nuclei at the border of this deformed region, in which the addition or the removal of a single nucleon results in a large shape change, hold the key to its understanding. Tracking Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. PRL 115, 172501 (2015) PHYSICAL REVIEW LETTERS week ending 23 OCTOBER 2015 0031-9007=15=115(17)=172501(6) 172501-1 Published by the American Physical Society the shape changes in the odd-neutron nuclei has shown that the νg7=2orbit plays a crucial role. A number of rotational bands, based on Nilsson orbits with νg7=2parentage, have been observed in the odd-ASr and Zr nuclei (see Ref. [6] and references therein). The evolution of the deformation as a function of the proton number is not so well studied. Ground-state rotational bands in the odd-A39Y nuclei are suggested to be built on the πg9=2½4225=2þNilsson state [7]. However, the onset of deformation in the 37Rb isotopes is less understood. Ground-state spin and moment studies of the Rb isotopes [8] revealed a sudden onset of deformation in 97Rb60 but failed to clearly identify whether it is associated with the πg9=2½4313=2þor the πp3=2½3013=2− Nilsson orbital. Mean-square-charge radii [9] and twoneutron separation energies [10] confirmed the sudden structural change at N¼60 in the Rb nuclei. In contrast, mean-square-charge radii [9], mass measurements [11], and Coulomb-excitation [12] studies demonstrated that deformation in the Kr (Z¼36) isotopes develops smoothly across N¼60. In this Letter we report Coulomb-excitation measurements on the neutron-rich isotopes 97Rb60 and 99Rb62 produced as radioactive beams. The excited states in these odd-Anuclei at the border of the A∼100 deformed region were observed for the first time, finding that they form rotational bands built on the ground state. The results provide clear-cut evidence for enhanced quadrupole collectivity of the 97;99Rb nuclei and firmly identify the deformation-driving configuration of the odd proton. They also establish the limits both in Nand Z(cornerstone) of the region of deformed nuclei around A∼100. Prior to the present experiment, the experimental information on Rb isotopes at and beyond N¼60 was limited to ground-state properties and no excited states were known. An excited rotational band was observed in 96Rb59 [13] providing evidence for shape coexistence in that nucleus. During the data analysis of the present work an isomeric E1transition in 97Rb was reported [14,15]. The experiment was performed at the REX-ISOLDE facility [16] at CERN. The species of interest were produced by a 1.4 GeV proton beam on a UCxtarget. They were surface ionized and mass separated through the High Resolution Separator (HRS) before being sent to the REX-TRAP [17] for bunching and charge breeding in REX-EBIS [18]. The short half-lives of 97Rb [T1=2¼ 169.1ð6Þms] and 99Rb [T1=2¼54ð4Þms] required short trapping and breeding times [82 (70) and 69 ms (69 ms), respectively, for 97Rb (99Rb)] in order to minimize in-flight decay. The beam was postaccelerated to 2.85ð3ÞMeV=uby the REX-LINAC [19], delivering average beam intensities for 97Rb and 99Rb of 5×105pps and a few times 103pps, respectively. A 2.1mg=cm260 Ni target was used to Coulomb excite the nuclei of interest. The experimental setup consisted of the Miniball γ-ray spectrometer [20] coupled to a double-sided silicon strip detector [21]. The γ rays depopulating the excited states were measured in coincidence with target nuclei scattered into the doublesided silicon strip detector. To avoid unsafe Coulomb excitation [22], the particle detection was limited to the center-of-mass angular range of 74°–113°. Examples of the γ-ray spectra are presented in Fig. 1. γ-γcoincidence matrices were constructed to establish the level schemes of 97Rb and 99Rb shown in Fig. 2. The γ-ray intensities (see Tables Iand II and Fig. 1) were obtained using singles spectra except for the 355.5-keV transition in 97Rb and the two 222-keV transitions in 99Rb. The 355.5-keV transition was contaminated by the 355.3keV transition in 97Sr, also populated in Coulomb excitation. Because of the low statistics, the two 222-keV transitions in 99Rb could not be separated and the total intensity is given in Table II. 100 200 300 400 500 600 E [keV] γ Counts/0.5 keV 20 40 60 68.1 65 136.5 123.7 103.1 104 118 191.8 183 222 326 226.8 242.7 355.5 345.8 379.2 492.0 80 100 120 140 x 8 0 1000 2000 3000 4000 5000 x15 Rb 99 Rb 97 222 FIG. 1 (color online). Doppler corrected γ-ray energy spectra for 97Rb (upper panel) and 99Rb (lower panel). Transitions, identified as belonging to Rb isotopes, are marked with their energies. Contaminating transitions, from the Coulomb excitation of Sr isotopes, are marked with circles. 123.7 103.1 242.7 136.5 355.5 226.8 345.8 492.0 379.2 3/2 0.0 5/2 68.1 7/2 191.8 9/2 294.9 11/2 15/2 537.6 1029.6 13/2 674.1 68.1 191.8 97Rb 65 118 104 222 326 183 222 (3/2 ) 0 (5/2 ) 65 (7/2 ) 183 (9/2 ) 287 (11/2 ) 509 99Rb FIG. 2 (color online). Level schemes for 97Rb and 99Rb as obtained in the present experiment. Pure E2transition are marked in red while mixed (M1=E2) are in blue. PRL 115, 172501 (2015) PHYSICAL REVIEW LETTERS week ending 23 OCTOBER 2015 172501-2 The beam composition was evaluated by the ΔE-E technique using an ionization chamber (ΔE) and a Si (E) detector. The beam composition for the mass 97 beam was 74(6)% 97Rb, 19(6)% 97Sr, and 7(1)% 97Y. The entire Y contribution and the predominant part of the Sr contribution were due to the in-flight decay of 97Rb during the ∼150 ms trapping and breeding of the ions. The beam composition for the mass 99 case [85(3)% 86Kr, 6(2)% 99Rb, 7(2)% 99Sr, and 2(1)% 99Y] showed considerable 86Kr contamination from EBIS residual gas due to a very similar mass-over-charge ratio to the 99Rb beam. The much worse 99Rb-to-99Sr ratio was a result of the relatively long trapping and breeding times (∼140 ms) compared to the half-life of 99Rb. This shows that lifetimes of the order of 50 ms are about the limit of applicability for postaccelerated Isotope Separator OnLine (ISOL) beam techniques. Matrix elements were extracted from the measured transition intensities using the code GOSIA [23]. For the six strongest transitions the data were divided into three subsets corresponding to three different ranges of centerof-mass scattering angles (74°–83°, 83°–99°, 99°–113°) in order to exploit the angular dependence of the excitation probability. Sixteen E2and six M1matrix elements, coupling the seven observed states, were fitted to the 23 measured γ-ray intensities. The Coulomb excitation of a specific state is governed mostly by E2matrix elements. However, the decay intensities, which are the actual experimental observables, may be strongly influenced by the M1matrix elements. The E2excitation probabilities cannot be unambiguously determined without additional constraints on M1matrix elements. As neither lifetimes nor mixing ratios are available, a model-dependent approach was used. In the 97Rb case it was assumed that E2transitions deexciting each state follow the Alaga rules [24] and therefore the ratio of their matrix elements (hJ∥E2∥J−1i=hJ∥E2∥J−2i) depends only on a geometrical factor (Clebsch-Gordan coefficients). This assumption can be justified first by noting that all observed states form a rotational band, and second, that all observations are consistent with particle-rotor model calculations, as discussed below. In the first stage of the analysis the h7=2þ∥E2∥3=2þi matrix element in 97Rb was determined relative to the observed excitation of the target nucleus 60Ni. This procedure used the observed γ-ray intensities in 97Rb and 60Ni, as well as known spectroscopic data for the latter [BðE2Þand the quadrupole moment [25] ]. In the fit, all matrix elements in 97Rb were allowed to vary with only the constraints from the Alaga rules. Corrections for the beam composition were taken into account. In the second step of the analysis the remaining matrix elements were obtained relative to h7=2þ∥E2∥3=2þi. A similar analysis of the 99Rb data was not possible due to the much lower statistics, nonobservation of target excitation, and the presence of an unresolved doublet at 222 keV. A more model-dependent approach was adopted, with all E2matrix elements in 99Rb coupled assuming the rotational model, i.e., hIf∥E2∥Iii¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi 2Iiþ1 pðIi;K;2;0jIf;KÞffiffiffiffi 5 16 qeQ0, where ðIi;K;2;0jIf;KÞ is a Clebsch-Gordan coefficient, and Q0is the transitional quadrupole moment, directly related to the nuclear deformation. Only a single Q0and four M1matrix elements were fitted to the entire band. The value Q0¼2.8þ0.4 −0.6eb was obtained. This approach has been validated using the 97Rb data, which yielded a Q0ð97RbÞvalue (see Fig. 3) consistent with the weighted mean value from the individual Q0ðJÞ. Figure 3compares the transitional quadrupole moments Q0for individual levels in 97Rb to experimental values for Zr, Sr, and Kr isotones at N¼58–62. The deformation of the ground-state band in 97Rb obtained from the present experiment is in agreement with the result of the earlier laser-spectroscopy measurement of the ground-state spectroscopic quadrupole moment [8]. The Q0values obtained for 97Rb remain remarkably constant within the TABLE I. Intensities for γ-ray transitions observed in 97Rb and corresponding BðE2Þand BðM1Þtransition probabilities. No transition probabilities could be determined for the 68-keV transition because of the unknown E2=M1mixing ratio. Ex Iπ iIπ f Eγ Iγ×103 BðE2ÞBðM1Þ (keV) (keV) [e2b2][μ2 N] 68.1 5=2þ3=2þ68.1 114(34) 191.8 7=2þ3=2þ191.8 4.96(19) 0.22þ8 −10 191.8 7=2þ5=2þ123.7 67(2) 0.33þ11 −14 0.28þ11 −12 294.9 9=2þ5=2þ226.8 4.47(19) 0.18þ4 −2 294.9 9=2þ7=2þ103.1 18.68(36) 0.12þ2 −10.29þ6 −4 537.6 11=2þ7=2þ345.8 2.99(16) 0.24þ4 −5 537.6 11=2þ9=2þ242.7 7.48(23) 0.093þ14 −20 0.15þ3 −3 674.1 13=2þ9=2þ379.2 1.61(14) 0.22þ3 −2 674.1 13=2þ11=2þ136.5 0.98(17) 0.056þ6 −50.28þ6 −5 1029.6 15=2þ11=2þ492.0 0.39(7) 0.28þ4 −4 1029.6 15=2þ13=2þ355.5 0.64(11) 0.052þ7 −80.20þ7 −5 TABLE II. Intensities for γ-ray transitions observed in 99Rb. Ex Iπ iIπ f Eγ Iγ a (keV) (keV) 65 ð5=2þÞð3=2þÞ65 1640(100) 183 ð7=2þÞð3=2þÞ183 90(20) 183 ð7=2þÞð5=2þÞ118 970(60) 287 ð9=2þÞð5=2þÞ222 170ð80Þ 287 ð9=2þÞð7=2þÞ104 230(110) 509 ð11=2þÞð7=2þÞ326 50(17) 509 ð11=2þÞð9=2þÞ222 170ð80Þ aTotal intensity given for the unresolved 222 keV doublet. PRL 115, 172501 (2015) PHYSICAL REVIEW LETTERS week ending 23 OCTOBER 2015 172501-3 band and similar in magnitude to those observed for N¼ 60;62 Zr and Sr isotopes. Within experimental uncertainties there is no change in the deformation between 97Rb and 99Rb, similar to what is observed in the Sr and Zr isotopes. The sudden onset of ground-state deformation at N¼60, as a function of the proton number, starts only from the Rb isotopes. Thus, (i) 97Rb is the southwest border of the welldeformed A∼100 region, and (ii) although right at the border, the deformation of 97Rb is essentially the same as that observed inside the deformed region. Particle-rotor model calculations based on a standard Woods-Saxon potential [30] were performed to shed light on the structure of the ground-state band of 97Rb. A Nilsson diagram is shown in Fig. 4. Particular attention was given to the BðM1Þ=BðE2Þratios shown in the upper panel of Fig. 5, which were determined solely from γ-ray energies and branching ratios (see, e.g., [32]). Calculations were performed for both positive and negative parity states because the measured magnetic moment of the ground state suggests, but does not distinguish between, the Nilsson orbits ½4313=2þand ½3013=2−.The quadrupole deformation parameter was set to β2¼0.31, consistent with the average of the measured Q0values. The hexadecapole deformation was varied between β4¼0and β4¼0.06, the latter value being that predicted by Möller et al. [33]. The level energies, ground-state moments, and E2transition strengths were described equally well for either a ½4313=2þor a ½3013=2−band. The lower panel of Fig. 5compares BðE2Þcalculations for the ½4313=2þband with experimental values obtained from the GOSIA analysis. These comparisons justify the use of the Alaga rules to constrain the fit during the data analysis. The M1transition strengths for ½4313=2þand ½3013=2−bands are also quite similar in magnitude because the two bands have similar intrinsic gfactors (gKvalues). Nevertheless, the BðM1Þ=BðE2Þratios in the upper panel of Fig. 5rule out the ½3013=2−candidate. Coriolis mixing between the K¼3=2ground-state band and adjacent K¼1=2bands causes the M1transitions to show a sawtoothlike signature dependence. The Coriolismixed wave functions show that mixing between the ½4313=2þand ½4401=2þbands is responsible for the J 246810 N=58 N=60 N=62 Zr 100 Zr 102 Sr 96 Sr 98 Sr 100 Rb 97 Rb 99 s Rb, Q 95 s Rb, Q 97 Kr 94 Kr 96 [eb] 0 Q 0 1 2 3 4 g.s. FIG. 3 (color online). Transitional quadrupole moments, Q0, for the even-even Kr, Sr, Zr [12,25–29] and the odd-mass Rb isotopes (present measurement) as a function of spin. The values for the ground states of 95;97;99Rb (left side) were obtained either from the analysis of the present data (squares), under the assumption of the rotational model, or from spectroscopic quadrupole moments (triangles) [8]. The values for the excited states were calculated from measured transition probabilities. Some of the values for the even-even cases are slightly displaced on the xaxis for clarity. β 2 0.0 0.1 0.2 0.3 0.4 –18 –15 –12 50 38 9/2[404] 7/2[413] 5/2[422] 1/2[440] g9/2 p3/2 f5/2 p1/2 5/2[303] 3/2[301] 1/2[301] 1/2[321] 7/2[303] 3/2[312] 1/2[310] 3/2[431] 1/2[431] E [MeV] s.p. 28 38 FIG. 4 (color online). Nilsson diagram for protons in the A∼ 100 region. The single-particle energies are calculated using the Woods-Saxon model with the “universal parametrization”and β4¼β2 2=6and β6¼0, where β2,β4, and β6are deformation parameters [31]. 3/23/2+ B(M1)/B(E2) [ µN/e2b2] 0 1 2 3 J J - 2 B(E2) [e2b2] J 7/2 9/2 11/2 13/2 15/2 0 0.1 0.2 0.3 0.4 J J - 1 FIG. 5 (color online). Particle-rotor model calculations for 97Rb compared with experiment. Upper panel: BðM1Þ=ðE2Þratios. Lower panel: BðE2Þvalues. See text for more details. PRL 115, 172501 (2015) PHYSICAL REVIEW LETTERS week ending 23 OCTOBER 2015 172501-4 observed dip in the M1strength of the 11=2þ→9=2þ transition, seen in the upper panel of Fig. 5. There are two properties of the ½4401=2þband that lead to the observed pattern. The first is that the magnetic decoupling parameter is negative, b0≃−3, which produces a sawtooth pattern in phase with the data. The second is that the energy decoupling parameter a≃4.5is large, thus, pushing down the K¼1=2states with spin Jπ¼ 1=2þ;5=2þ;9=2þ;…, to mix strongly with the K¼3=2 ground-state band, while the K¼1=2states with spin Jπ¼3=2þ;7=2þ;11=2þ;…, are pushed up in energy and hardly mix with the ground-band levels. Coriolis mixing of the 9=2þstates causes the reduced BðM1; 11=2þ→ 9=2þÞtransition rate. The negative parity alternative, mixing of the ½3101=2− band with the ½3013=2−band, cannot explain the data. It predicts the wrong signature dependence of the M1 transitions because b0≃þ1. Thus, the observed trends in the M1transition rates and BðM1Þ=BðE2Þratios confirm the πg9=2½4313=2þ Nilsson configuration for the ground-state band of 97Rb. This assignment is in agreement with the conclusions of a recent theoretical study of odd-ARb isotopes [34]. The isomeric E1transition that has since been identified in 97Rb probably originates from a negative parity Nilsson configuration [14,15]. The sudden onset of deformation at N¼60 in the Rb isotopes suggests a tip of the balance from the spherical shell gap at Z¼38 for N≤58 to the deformed shell gap at Z¼38 for N¼60;62. The spherical and deformed shell gaps at Z¼38 are indicated in Fig. 4. Deformed shell gaps near β2¼0.3also occur for neutrons at N¼60 and N¼62. Thus, the deformed shell gaps for both protons and neutrons evidentally play an important role in the sudden onset of deformation and its near constant value once established [6]. In summary, the first identification of excited states in the neutron-rich nuclei 97;99Rb was achieved by multistep Coulomb excitation of these odd-mass radioactive beams. The level schemes and transition probabilities were determined in the ground-state rotational bands. Detailed information on the M1transition strengths in 97Rb provided clear-cut experimental evidence for the πg9=2 ½4313=2þNilsson-configuration assignment. 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