Clément, E

Görgen, A

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EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCHProposal to the ISOLDE-Neutron-Time-of-Flight CommitteeShape coexistence in neutron-rich Sr isotopes:Coulomb excitation of 96SrE. Cle´ment1,2∗, A. Go¨rgen2∗, J. Cederka¨ll1, P. Delahaye1, L. Fraile1,F. Wenander1, D. Voulot 1, C. Dossat2, W. Korten2, J. Ljungvall2, A. Obertelli2,Ch. Theisen2, M. Zielin´ska2, T. Czosnyka3, J. Iwanicki3, J. Kownacki3, P. Napiorkowski3,K. Wrzosek3, P. Van Duppen4, T. Cocolios4, M. Huyse4, O. Ivanov4, M. Sawicka4,I. Stefanescu4, J. Van de Walle4, S. Franchoo5, F. Dayras6, G. Georgiev6,A. Ekstro¨m7, M. Guttormsen8, A.C. Larsen8, S. Siem8, N.U.H. Syed8, P.A. Butler9,A. Petts9, D.G. Jenkins10, V. Bildstein11, R. Gernha¨user11, T. Kro¨ll11, R. Kru¨cken111 PH Department, CERN, Geneva, Switzerland2DAPNIA/SPhN, CEA Saclay, France3Heavy Ion Laboratory, Warsaw, Poland4IKS Leuven, Belgium5IPN Orsay, France6CSNSM Orsay, France7Department of Physics, Lund University, Sweden8 Department of Physics, University of Oslo, Norway9 Oliver Lodge Laboratory, University of Liverpool, UK,10Department of Physics, University of York, UK,11TU Mu¨nchen, GermanySpokespersons: E. Cle´ment and A. Go¨rgenContactperson: E. Cle´mentSeptember 29, 2006AbstractThe nuclei in the mass region A ' 100 around Sr and Zr show a dramatic change of the nuclear ground-state shape from near spherical for N ≤ 58 to strongly deformed for N ≥ 60. Theoretical calculationspredict the coexistence of slightly oblate and strongly prolate deformed configurations in the transitionalregion. However, excited rotational structures based on the highly deformed configuration, which becomesthe ground state at N = 60, are not firmly established in the lighter isotopes, and the earlier interpretation ofa very abrupt change of shape has been challenged by recent experimental results in favor of a rather gradualchange. We propose to study the electromagnetic properties of the neutron-rich nucleus 9638Sr58 by low-energyCoulomb excitation using the REX-ISOLDE facility and the MINIBALL detector array. Both transitionaland diagonal matrix elements will be extracted, resulting in a complete description of the transition strengthsand quadrupole moments of the low-lying states. These results will provide important benchmarks for theunderstanding of the shape evolution in this mass region.∗co-spokesperson1CERN-INTC-2006-033+INTC-P-21629 September 2006MotivationThe neutron rich Sr and Zr isotopes are characterized by a sudden onset of quadrupole deformation at neutronnumber N = 60. This becomes evident already from the excitation energies of the first 2+ states. Fig. 1 showsthe dramatic drop in the excitation energy of the 2+ states at N = 60 for both the Sr and Zr isotopes. Whiletheoretical calculations, for example using the Nilsson-Strutinsky method with Woods-Saxon potential [1],the relativistic mean field theory [2], or the Hartree-Fock-Bogoliubov approach with Gogny interaction [3]reproduce this onset of deformation qualitatively, they differ in the details of the deformation parametersand excitation energies. Most calculations predict slightly oblate ground-state deformations for the lighterisotopes and strongly deformed prolate shapes for the heavier ones. In the transitional region around N = 60the different shapes are expected to coexist in a narrow energy range. Potential energy curves for 96Sr and98Sr are presented in Fig. 1. The absolute minimum in 96Sr is found to be oblate, while the strongly deformedprolate minimum is found about 1 MeV above. Oblate and prolate minima are almost degenerate in 98Sr.This scenario is supported by the observation of excited 0+ states at 1229 and 1465 keV in 96Sr and at only215 keV in 98Sr. However, oblate shapes are difficult to prove experimentally, and so far there is no clearexperimental evidence for oblate shapes in the neutron-rich Sr or Zr isotopes.50 52 54 56 58 60 62 64Neutron Number1001000E exc(2+)   [keV]SrZr-0.4 -0.2 0 0.2 0.4 0.6β201234E   [MeV]96Sr98SrFigure 1: Left: Excitation energies of the 2+1 states for the chains of Sr and Zr isotopes. Right: Potentialenergy as a function of quadrupole deformation for 96Sr and 98Sr [3].The nuclear structure of neutron rich Sr and Zr isotopes has been studied extensively in the pastboth in prompt and decay spectroscopy using the ISOL technique, spontaneous fission sources, or fusion-fission reactions [4–7]. Level schemes of 96Sr and 98Sr are shown in Fig. 2. The highly collective rotationalground-state band of 98Sr points to a large ground-state deformation, and the 0+2 state at 215 keV, whichdecays to the ground state via an enhanced E0 transition of ρ2(E0) = 0.053 [8], supports the scenario ofshape coexistence. The situation is less clear in 96Sr. The ground-state band has a vibrational-like character,and the small B(E2; 2+1 → 0+1 ) value extracted from the lifetime of 7(4) ps [4] is consistent with a near-spherical ground state. Two low-lying 0+ states were established by Jung et al. [9] at 1229 and 1465 keV andwere interpreted as candidates for a deformed band head. An extremely strong electric monopole transitionof ρ2(E0) = 0.18 was observed between the 0+3 and 0+2 states [5, 10], indicating the presence of a sizeabledeformation and strong mixing of the configurations. Electric monopole transitions from the excited 0+states to the ground state were not observed. The sequence of the 0+3 (1465 keV), 2+3 (1629 keV), and 4+2(1975 keV) states was interpreted as the well-deformed rotational band equivalent to the ground-state bandin 98Sr, even though the 2+3 → 0+3 transition remained unobserved.Recently prompt spectroscopy experiments yielded a rather regular rotational structure above the4+2 state extending up to spin 18+ [6, 7]. Lifetimes could be established for the 10+ and 12+ states in thisband [6], from which a relatively small deformation of only β2 = 0.25 was derived, much smaller than theground-state deformation of 98Sr, which is assumed to be β2 ≈ 0.4. It was argued that the 0+2 (1229 keV) and2+2 (1506 keV) states form the low-spin members of this moderately deformed band, and it was concludedthat the onset of deformation around N = 58 is not as abrupt as previously thought, but rather gradual [6].The 0+3 and 2+3 states could still be interpreted as being based on a very deformed configuration, especiallyin the light of the strong E0 transition. However, the higher-spin members of such a structure, which are notobserved, should then rapidly become yrast. The extremely strong E0 transition can only occur if the 0+2and 0+3 states are strongly mixed, and the branching ratio of the transitions from the 4+2 state indicates alsoa strong mixing of the 2+2 and 2+3 states [7], so that the low-spin levels are displaced in energy and cannot2Figure 2: Partial level schemes of 96Sr [6, 7] and 98Sr [8].easily be grouped into rotational bands. The measurement of transition strengths and intrinsic quadrupolemoments is therefore essential to understand the complex shape coexistence and the onset of deformation inthis region. Only the quadrupole moments can give direct evidence for the predicted oblate shapes.We propose to study 96Sr by projectile Coulomb excitation at low energy well below the Coulombbarrier. This well-established technique can provide a complete set of both transitional and diagonal matrixelements. The B(E2, 0+1 →2+1 ) value that is only poorly known from a lifetime measurement (7± 4 ps) willbe established with high precision. The B(E2) values related to the 0+2,3 and 2+2,3 states will give importantinsight into the structure of these states and their collectivity and mixing. The measurement will be sensitiveto the spectroscopic quadrupole moment of at least the 2+1 and possibly the excited 2+ states, giving directinformation about the shapes involved, in particular about a possible oblate deformation of the ground-stateband. Modern theoretical approaches like configuration-mixing calculations using the generator coordinatemethod (e.g. [11]) are capable of calculating static and transitional matrix elements of shape-coexistingstates, and the proposed measurement would represent an important test of such models.Experimental detailsSr ions have not yet been accelerated at REX-ISOLDE. The production yield for 96Sr (T1/2 = 1.07 s) hasbeen measured to be 5.7 · 106 per µC of protons using the SC driver and a UCx target. In order to obtaina beam of 96Sr free from isobaric contaminants such as 96Rb, we propose to extract 96Sr19F molecules fromthe production target. The mass separator will be tuned to the mass 115 of the molecule. Even thoughtcontaminants like 115In will get into the EBIS, a rather pure beam of 96Sr can be extracted after the break-upof the molecule. Using a neutron converter before the primary target will help to minimize the In produc-tion. This extraction scheme and the resulting production yield should be tested and optimized before theexperiment. This beam development has strong synergies with the development of Ba beams, which havesimilar chemical properties, for the ISOLDE experiment IS411. The 96Sr ions will be accelerated to themaximum energy of about 2.9 · A MeV by the REX accelerator.We propose to use a secondary 120Sn target for the Coulomb excitation of the projectiles. Thischoice is a compromise between the Coulomb excitation cross section and the mass asymmetry for a betterdistinction in energy between scattered projectiles and target recoils. The prompt γ rays emitted afterCoulomb excitation will be detected in the MINIBALL spectrometer of germanium detectors in coincidencewith the scattered particles detected in an annular segmented silicon-strip detector. The silicon detector(CD) covers scattering angles between 16.3◦ and 53.3◦ in the laboratory frame. The detection of scatteredprojectiles corresponds to a range of scattering angles between 29.5◦ and 93◦ in the center-of-mass frame,whereas the detection of the recoiling target covers the range 73.5◦ ≤ θcm ≤ 147.5◦. Both projectile andtarget will be detected in the overlapping range. The particle energies are shown as a function of scattering3angle in Fig. 3. The distinction between 96Sr and 120Sn is problematic only for the innermost rings of thesilicon detector which contribute only little to the total excitation cross section. In order to minimize thedead time in the CD detector, a slow extraction of the 96Sr ions from the EBIS should be attempted.scattering angle in lab (deg.)10 20 30 40 50 60Energy MeV6080100120140160180200220240 = [16.3-53.3]CDlab θE = 7 MeV∆Scattering angle in CM (degrees)20 40 60 80 100 120 140Coulex cross section [mbarn]012345 oblate2+2 spherical2+2 prolate2+2Projectile detectedTarget detectedFigure 3: Left: Kinetic energy of the projectiles and target recoils as a function of the laboratory scatteringangle. The energy loss in the target has been taken into account. Right: Differential Coulomb excitationcross section for the 2+2 state for different signs of the quadrupole moment. The vertical lines indicate therange of scattering angles covered by the silicon detector for detection of either the projectile or the targetrecoil.To minimize systematic errors, the γ-ray yields measured for the 96Sr projectiles will be normalizedto the γ rays following the Coulomb excitation of the 120Sn target (E(2+)=1171 keV), for which the matrixelements are well known. The excitation probability of higher-lying states can be normalized to that ofthe 2+1 state. In this case the absolute number of incident96Sr ions is not needed and systematic errorsfrom beam contaminants can be excluded. The analysis will be performed using the code GOSIA [12,13] todetermine the set of transitional and diagonal matrix elements that best describes the observed γ-ray yieldsin a χ2 minimization.Coulomb excitation calculations and rate estimatesIn order to evaluate the feasibility of the experiment we have performed Coulomb excitation calculationsbased on the known spectroscopic information and different hypotheses for the collectivity of the states.The known spectroscopic parameters for the low-lying states in 96Sr are listed in table 1. Even though thelifetime of the 2+1 state has a very large uncertainty, this value can be used to estimate the population ofthe state. Depending on the properties of the higher-lying states and the static quadrupole moments, thecross section to populate the 2+1 state integrated over the range of scattering angles covered by the silicondetector is of the order of 1 to 1.5 barn.Urban et al. [6] deduced a transitional quadrupole moment of Qt0 = 2.20(15) eb from lifetimesmeasured for the 12+ and 10+ states, from which they derived a quadrupole deformation of β2=0.25 for therotational cascade above the 4+2 state. If we assume that the 0+2 and 2+2 states belong to this rotationalband, we can use the rotor model to extrapolate the transitional matrix elements between these states,and together with the branching ratios this allows estimating the Coulomb excitation cross sections. Thesign of the deformation enters the calculations via the reorientation effect. Table 2 shows the cross sectionscalculated for various states and for different signs of the quadrupole moments of the 2+1 and 2+2 states.Rigid rotor values were assumed for the diagonal matrix elements. The cross sections are integrated overthe range of scattering angles covered by the silicon detector. The differential cross section for the 2+2 stateis shown in Fig. 3 for different signs of the deformation. Even though the absolute cross section for the 2+2state is about two orders of magnitude smaller than for the 2+1 state, there is a very strong dependence onthe sign of the quadrupole moment.In order to determine the beam time required to perform the proposed measurement, we use themeasured production yield for 96Sr of 5.7 · 106 per µC of protons from the SC driver as a conservativeestimate. Higher yields are expected using the PS Booster. Assuming a proton intensity of 2 µC/s and atransmission of 1% for the REX accelerator, we expect 105 pps on the MINIBALL target. With a total4Table 1: Experimentally known lifetimes [4] and branching ratios [7].Ii τ If Eγ [keV] rel. Iγ2+1 7 (4) ps 0+1 815 1000+2 167 (17) ps 2+1 414 1000+3 9.7 (1.4) ns 0+2 235 E02+1 650 1002+2 < 9 ps 0+1 1506 56(15)2+1 691 1002+3 0+1 1629 12.2(11)2+1 813 1000+2 398 5.3(4)4+1 2+1 978 1004+2 2+1 1160 50(3)2+2 469 1002+3 348 22(4)Table 2: Estimate of the Coulomb excitation cross sections in mb assuming different combinations of signsfor the quadrupole moments of the 2+1 and 2+2 states. A negative sign corresponds to an oblate and positiveto a prolate shape. See text for further details.Ipi 2+1 (−) 2+2 (−) 2+1 (+) 2+2 (−) 2+1 (−) 2+2 (+) 2+1 (+) 2+2 (+)2+1 1460 1130 1470 11404+1 40 37 40 370+2 25 23 24 232+2 21 22 11 114+2 2.2 2.6 0.8 0.9absorption efficiency of 7% at 1.3 MeV for MINIBALL comprising eight triple clusters and a target thicknessof 2 mg/cm2, we find the γ-ray yields given in table 3.Our recent Coulomb excitation experiments with radioactive 74Kr and 76Kr beams from SPIRAL,which successfully achieved similar goals, can be used to estimate the required beam time. The total levelof statistics for the 2+1 → 0+1 , 0+2 → 2+1 , and 2+2 → 2+1 transitions in76Kr was 40000, 2000, and 1000,respectively, which was sufficient to determine the static quadrupole moments for both the 2+1 and 2+2 states.To reach a similar level of statistics, we require 7 days of radioactive 96Sr beam, excluding time for set-up andtest measurements to optimize the extraction scheme. The production yield fo 98Sr should also be measuredduring such beam tests in order to evaluate the feasibility of a possible follow-up experiment on 98Sr.Table 3: Estimated γ intensities using the assumptions described in the text.Ii If Eγ [keV] counts/day2+1 0+1 815 114404+1 2+1 978 2740+2 2+1 414 2482+2 2+1 691 602+2 0+1 1506 204+2 2+2 469 62+3 2+1 814 30SummaryWe propose to study the shape evolution and shape coexistence in the neutron-rich Sr isotopes throughCoulomb excitation of 96Sr. Both transitional and diagonal matrix elements will be determined in a dif-ferential Coulomb excitation measurement utilizing the reorientation effect. The set of transitional matrixelements linking the low-lying states will give insight into the collectivity of the different rotational structuresand their mixing. The static quadrupole moments of the 2+1 and 2+2 states will shed light on possible oblate5shapes which are predicted theoretically. The experimental determination of the matrix elements for theshape coexisting states will give important constraints for modern nuclear structure theories describing suchphenomena. We ask for seven days of 96Sr beam to perform the proposed experiment.Beam requirementsBeam Min. intensity Target material Ion Source Shifts96Sr 105 pps UCx Positive surface 21 (data taking)+3 (set-up)References[1] J. Skalski, S. Mizutori, W. Nazarewicz; Nucl. Phys. A 617, 282 (1997)[2] G.A. Lalazissis, M.M. Sharma; Nucl. Phys. A 586, 201 (1995)[3] S. Hilaire, M. Girod;http://www-phynu.cea.fr/science-en-ligne/carte potentiels microscopiques/carte potentiel nucleaire.htm[4] H. Mach et al., Nucl. Phys. A 523,197 (1991)[5] G. Lhersonneau et al., Phys. Rev. C 49, 1379 (1994)[6] W. Urban et al., Nucl. Phys. A 689 (2001)[7] C.Y. Wu et al., Phys. Rev. C 70, 064312 (2004)[8] Nucl. Data. Sheets 98, 335 (2003)[9] G. Jung et al., Phys. Rev. C 22, 252 (1980)[10] K. Kawade et al., Z. Phys. A 304, 293 (1982)[11] M. Bender, P. Bonche, P.H. Heenen, Phys. Rev. C 74, 024312 (2006)[12] D. Cline, Ann. Rev. Nucl. Part. Sci. 36, 683 (1986)[13] T. Czosnyka, GOSIA2, 2005, MINIBALL User’s Workshop 2005[14] A. Go¨rgen et al., Acta. Phys. Pol. B36, 1281 (2005)[15] E. Cle´ment et al., in preparation6

Shape coexistence in neutron-rich Sr isotopes: Coulomb excitation of $^{96}$ Sr

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Shape coexistence in neutron-rich Sr isotopes: Coulomb excitation of 96^{96}96Sr

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Shape coexistence in neutron-rich Sr isotopes: Coulomb excitation of $^{96}$ Sr