application/xmlFirst lifetime measurement of [formula omitted] state in 12BeN. ImaiN. AoiH.J. OngH. SakuraiK. DemichiH. KawasakiH. BabaZs. DombrádiZ. ElekesN. FukudaZs. FülöpA. GelbergT. GomiH. HasegawaK. IshikawaM. IshiharaH. IwasakiE. KanekoS. KannoT. KishidaY. KondoT. KuboK. KuritaS. MichimasaT. MinemuraM. MiuraT. MotobayashiT. NakamuraM. NotaniT.K. OhnishiA. SaitoS. ShimouraT. SugimotoM.K. SuzukiE. TakeshitaS. TakeuchiM. TamakiH. WatanabeK. YonedaDoppler-shift attenuation methodReduced matrix elementRadioactive beam experimentPhysics Letters B 673 (2009) 179-182. doi:10.1016/j.physletb.2009.02.039journalPhysics Letters BCopyright © 2009 Elsevier B.V. All rights reserved.Elsevier B.V.0370-2693673323 March 20092009-03-23179-18217918210.1016/j.physletb.2009.02.039http://dx.doi.org/10.1016/j.physletb.2009.02.039doi:10.1016/j.physletb.2009.02.039http://vtw.elsevier.com/data/voc/oa/OpenAccessStatus#Full2014-01-01T00:14:32ZSCOAP3 - Sponsoring Consortium for Open Access Publishing in Particle Physicshttp://vtw.elsevier.com/data/voc/oa/SponsorType#FundingBodyhttp://creativecommons.org/licenses/by/3.0/JournalsS300.3PLB25645S0370-2693(09)00219-610.1016/j.physletb.2009.02.039Elsevier B.V.ExperimentsFig. 1Energy level schemes for low-lying excited states in even–even Be isotopes [14].Fig. 2Schematic view of the experimental setup. A 1-mm thick gold target was surrounded by a 5-cm thick lead shield. Two clover Ge detectors were mounted upstream of the target. An array of 32 NaI(Tl) scintillators was also placed upstream of the target.Fig. 3Energy spectrum of γ-rays measured by two clover Ge detectors. The Doppler shifted 21+→0g.s.+ and 1−→0g.s.+ transitions were observed at around 1.7 and 2.2 MeV, respectively. The solid line indicates the simulated transitions for τ2+=2.5 ps and τ1−=1.9 fs including the background and the cascade contribution from the isomeric 02+ state. The dot-dashed line indicates the estimated lineshape for the background and the cascade transition.Fig. 4(a) Reduced χ2 values as a function of τ2+. ndf stands for the number of degree of freedom. (b) Simulated lineshapes for the 21+→0g.s.+ transition of τ2+=1.1 ps (dotted line), 2.5 ps (solid line), and 3.9 ps (dashed line), superimposed on the experimental energy spectrum.Fig. 5B(E2;↓) values for even–even beryllium and carbon isotopes. Closed squares stand for the B(E2;↓) values for carbon isotopes [18,28], while open and closed circles denote to those for 10Be [29] and 12Be (present), respectively.First lifetime measurement of 21+ state in 12BeN.Imaia⁎1nobuaki.imai@kek.jpN.AoiaH.J.Ongb2H.SakuraiaK.DemichicH.KawasakicH.BabaaZs.DombrádidZ.ElekesdN.FukudaaZs.FülöpdA.GelbergeT.GomiaH.HasegawacK.IshikawafM.IshiharaaH.IwasakibE.KanekocS.KannocT.KishidaaY.KondofT.KuboaK.KuritacS.MichimasagT.MinemuraaM.MiurafT.MotobayashiaT.NakamurafM.NotanigT.K.OhnishibA.SaitocS.ShimouragT.SugimotoaM.K.SuzukibE.TakeshitacS.TakeuchiaM.TamakigH.WatanabeaK.YonedaaaRIKEN Nishina Center for Accelerator-Based Science, Hirosawa 2-1, Wako, Saitama 351-0198, JapanbDepartment of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo, Tokyo 113-0033, JapancDepartment of Physics, Rikkyo University, Nishi-Ikebukuro 3-34-1, Toshima, Tokyo 171-8501, JapandATOMKI, H-4001 Debrecen, PO Box 51, HungaryeInstitut für Kernphysik der Universität zu Köln, D-50937 Köln, GermanyfDepartment of Physics, Tokyo Institute of Technology, O-okayama 2-12-1, Meguro, Tokyo 152-8551, JapangCenter for Nuclear Study, University of Tokyo, Hirosawa 2-1, Wako, Saitama 351-0198, Japan⁎Corresponding author.1Present address: IPNS, KEK, Japan.2Present address: RCNP, Osaka University, Japan.Editor: D.F. GeesamanAbstractThe lifetime of the 21+ state at 2.1 MeV in 12Be has been measured using inelastic scattering of a 12Be beam at 43 MeV/nucleon with a gold target. Through the Doppler shift attenuation method, the mean-life of the 21+ state has been determined as 2.5±0.7 (stat) ±0.3 (syst) ps, which gives a B(E2;21+→0g.s.+) value of 4.9±1.3±0.5 in Weisskopf units. The result shows a large quadrupole strength in the ground state transition, providing further evidence on the disappearance of the N=8 magic number. The B(E2;21+→0g.s.+) value together with the deformation length measured by proton inelastic scattering yields a neutron quadrupole matrix element two times larger than those for 14C and 16O.PACS21.10.Tg23.20.g23.20.Js27.50.+nKeywordsDoppler-shift attenuation methodReduced matrix elementRadioactive beam experimentMagic numbers for the single-particle shell structure are basic ingredients for determining the low-energy nuclear properties of isotopes as they vary with atomic (Z) and neutron (N) numbers. Recent experimental studies on neutron-rich radioactive nuclei have revealed an intriguing phenomenon that the traditional magic numbers are not necessarily valid when the neutron excess becomes significantly large. Close experimental and theoretical investigations have since been carried out over a broad domain of neutron-rich nuclei for an attempt to pin down the mechanism underlying the changes of magic numbers.The neutron-rich nucleus 12Be may present a typical example of such an anomalous nucleus [1–9] where disappearance of the magic number N=8 has been suggested by a variety of observables measured in the recent experiments [5–9]. These observables all supported a common picture that the ground state wave function has a large mixture of the intruder configuration of neutron sd orbits.The breakdown of the shell gap can be attributed to the deformation of the nucleus. In the framework of the three body model where 12Be is assumed to be composed of two neutrons and the core nucleus 10Be, the deformation due to the core excitation has to be taken into account to reproduce the experimental data [10]. From the microscopic point of view, the ν(d5/2) orbit splits in a deformed potential. As a result, a part of the levels lowers, giving rise to the intruder configuration [11,12]. Such deformation may be related to the α-cluster structure which were well known for the Be isotopes [13]. It is important to note that the shell model calculation with a large model space also reproduces the large admixture in 12Be [8].The intruder configuration enhances the quadrupole collectivity of the nucleus, as evidence from the excitation energies. The excitation energies of even–even Be isotopes are presented in Fig. 1. The first 2+ states in 8,10Be are located around 3 MeV, whereas the energy for the 12Be drops to 2.1 MeV, implying the larger collectivity of 12Be. Thus it is desirable to experimentally determine the proton and neutron quadrupole strengths which would provide direct measures of the collectivity. In this regard, a useful observable is the lifetime of the first 2+ (21+) state, which is inversely proportional to the reduced E2 transition probability, B(E2;21+→0g.s.+)=B(E2;↓), between the ground state and the 21+ state. Here, the B(E2;↓) value is related to the proton matrix element for the transition through the equation, Mp=5B(E2;↓)/e2. On the other hand, the neutron matrix element Mn, which would be more affected by the intruder configurations, may be extracted by combining the values of deformation length and B(E2;↓)[15]. The pair of the proton and neutron matrix elements thus deduced would provide a stringent test for nuclear structure models to clarify the origin of the shell quenching. To date, the relevant deformation length has been determined in proton inelastic scatterings off 12Be [5].The present Letter reports on the result of the lifetime measurement, which was first performed for the 21+ state of 12Be. In this measurement, the Doppler shift attenuation method (DSAM) was applied to de-exciting γ rays from 12Be nuclei in flight, which were excited in intermediate-energy inelastic scatterings off gold target nuclei.The present experiment employed only one thick target that played two roles; to excite the intermediate-energy projectile nuclei and to slow them down. Part of the projectile nuclei are excited through nuclear reactions at any points while penetrating the target, losing their energies along the way. The excited nucleus, which continues on the path of the incident beam, eventually decays into its ground state following the lifetime. The γ rays are emitted inside or outside the target. The energies of the γ rays emitted in the target spread by the Doppler broadening due to the varying velocities. On the other hand, the γ rays emitted outside have a constant energy since the velocity of the excited nuclei no longer changes. Provided the energy spread is larger than the Doppler broadening due to the solid angle of the γ ray detector, these two components can be distinguished in the γ-ray energy spectrum. Since the yield ratio between the γ rays emitted inside and outside of the target depends on the lifetime and the beam velocity, we can determine the lifetime by analyzing the lineshape of the γ-ray energy spectrum. Namely, the present method was to be compared with the passing-through time of the excited nuclei through the target sheet unlike the procedure of the standard DSAM where the lifetime is to be compared with the stopping time of the excited nuclei in a solid material [16]. The use of a thick target facilitated measurement with radioactive nuclear beams of intensity as low as 105 particles per second.The present method is effective for measuring lifetimes of a few ps. We note that the recoil distance method has also been successfully employed to measure lifetimes of a few ps [17]. Recently we have also developed a modified recoil shadow method which is suitable for lifetime measurements of a few tens of ps [18]. These methods are particularly important for determining the B(E2;↓) value of Z<8 nuclei, where an alternative method using the intermediate-energy Coulomb excitation [19,20] may suffer from contributions of the nuclear excitations.The experiments was performed at the accelerator facility operated by the RIKEN Nishina Center and Center for Nuclear Study, University of Tokyo. A secondary 12Be beam was produced by projectile fragmentation of a 100-MeV/nucleon 18O primary beam and was separated by the fragment separator RIPS [21]. The 12Be beam then hit a 1-mm thick gold target placed at the final focal plane, where it was inelastically excited. Particle identification of the secondary beam was performed event-by-event by means of the time-of-flight (TOF)–ΔE method using a 1-mm thick plastic scintillation counter located 180 cm upstream of the target. The 12Be beam had a typical intensity of 4×105 particles per second and a purity of 97%. The momentum acceptance of RIPS was set to ±0.5% at the first focal plane. The incident and outgoing energies of the beam were determined as 42.9 MeV/nucleon and 22.6 MeV/nucleon, respectively. Two sets of parallel plate avalanche counters (PPACs) were placed upstream of the target to record the positions and angles of the projectiles incident upon the target. Another PPAC was mounted 30 cm downstream of the target. These three PPACs yielded the scattering angles of ejectiles.The experimental setup around the secondary target is schematically shown in Fig. 2. Outgoing particles were identified by means of the ΔE–E–TOF method using a plastic scintillator hodoscope located 86 cm downstream of the target. The hodoscope with an active area of 24×24 cm2 consisted of a 2-mm thick ΔE plane and a 5-mm thick E plane. In order to eliminate γ rays coming from the hodoscope, a thick lead shield was placed around the target.De-excitation γ rays from the in-flight excited 12Be were detected by two clover-type Ge detectors in which four crystals of about 55 mm diameter and 70 mm length resided. The detectors were set at polar angles of 150° with respect to the beam direction in the laboratory frame. The distance from the target to each clover detector was 30 cm. The solid angles of the detectors led to the Doppler broadening of about 25 keV for the 2.1-MeV γ rays from the 21+ state. On the other hand, the energy spread due to the change of the beam velocity was about 150 keV. Hence, the solid angle was small enough to distinguish γ rays emitted outside and inside the target in the energy spectrum.Fig. 3 shows a γ-ray energy spectrum measured by the clover detectors when the incident and the outgoing particles were identified as 12Be. Accidentally coincident γ-rays were subtracted using the TOF of γ rays. The peak around 1.7 MeV represents the Doppler-shifted 2.1-MeV line of the 21+→0g.s.+ transition, while the peak around 2.2 MeV corresponds to the 2.7-MeV line of the 1−→0g.s.+ transition. The lineshapes of the 2.1 and 2.7 MeV peaks are clearly different from each other, indicating their different lifetimes. In particular, the flat 1− peak exhibits a much shorter lifetime than the passing-through time of 14 ps as a consequence of almost all de-excitation γ rays being emitted inside the target.The 12Be beam was found to contain the isomeric 02+ state with a mean-life of 331(12) ns [22] populated by the fragmentation reaction [7]. The state decays to the ground state via either the E0 transition of e+/e− pair creation by 80%, or the cascade E2 transitions of 02+→21+→0g.s.+ by 20% [7]. The cascade transitions would contribute to the energy spectrum of the 21+→0g.s.+ transition. In the present experiment, the amount of isomeric ratio was determined as 5±2% at the production target by measuring the yield of pairs of 511-keV γ rays with an array of 32 NaI(Tl) scintillators of 12×6×6 cm3 mounted around the secondary target.The mean-life of the 21+ state, τ2+, was determined by analyzing the lineshape of the measured energy spectrum. We performed Monte Carlo simulations to obtain the lineshape for the assumed transitions. Then, we fitted the simulated lineshapes together with an assumed background to the observed spectrum.The simulation was made using the GEANT code [23] as follows. We have included the shapes of the clover detectors and the geometry of the experimental setup. The measured detection efficiencies for 661, 1172, and 1333-keV γ-rays emitted from standard sources placed on the upstream surface of the gold target were reproduced by the simulation within 4% of the measured values. Note that the absorption of the γ rays by the target, measured with the sources on the downstream surface of the target, was also reproduced within the 4% discrepancies.The simulations were then applied to the two transitions through which γ rays were emitted from the energy-degrading excited particles. The transitions were the 21+→0g.s.+ and the 1−→0g.s.+ transitions. Here, both the excited states were assumed to be directly populated by inelastic scatterings. The slowing down of the 12Be beams in the gold target was simulated using the formula of Hubert et al. [26]. We estimated the uncertainty of the stopping power as ±1.5% from the discrepancies between the calculated and experimental stopping powers of gold targets for 16O beams of 20–95 MeV/nucleon [27]. The simulation also used experimentally obtained angular and spatial distributions of the projectiles and the ejectiles. Excited 12Be beams were generated in the target, taking into account the energy dependence of the excitation cross section. In the case of the 0g.s.+→21+ excitation, the change of cross section was calculated to be 10% using the couple channel code ECIS79 [24] with an optical model parameter set [25]. Note that the resultant τ2+ was found to be unchanged even without the energy dependence of the cross section. De-excitation γ rays were emitted isotropically from the excited nuclei according to a given mean-life. For the case of the 1− state, τ1− was fixed to 1.9 fs as obtained from the B(E1) value of 0.051(13) e2fm2[6]. The Doppler shifts of the γ rays were calculated from the velocity of the beam at de-excitation.In addition to the aforementioned transitions, the contribution by the cascade transition from the isomeric 02+ state to the 21+→0g.s.+ transition was also simulated. For this purpose, γ rays from the 21+ state were generated uniformly along the beam trajectory with an intensity determined from the measurement without the target as mentioned above.Simulated lineshapes for the transitions and a background were fitted to the experimental energy spectrum from 1.3 to 3.0 MeV. For the 21+→0+ transition, simulated lineshapes assuming τ2+=1.0∼4.0 ps with 0.5 ps step were used to fit the spectrum to obtain χ2 value as a function of τ2+. The background was assumed to have an exponential shape. In the fitting, we used the respective absolute excitation energies and cross sections of the 0g.s.+→21+ and the 0g.s.+→1− excitations as free parameters. A lineshape assuming τ2+=2.5 ps is presented in Fig. 3, showing good agreement with the experimental spectrum.The reduced χ2 values as a function of τ2+ are presented in Fig. 4(a). The smallest χ2 value was obtained at τ2+=2.5 ps through fitting a parabolic curve to the χ2 distribution. The statistical error was determined as 0.7 ps in 1σ. The lineshapes for τ2+=1.1 ps (best fit −2σ) and 3.9 ps (best fit +2σ) are presented with the experimental data and the best-fitted lineshape in Fig. 4(b). The lineshape is sensitive to the mean-life of a few ps as shown in the figure. On the other hand, for the mean-life of the 1− state, only the upper limit was determined as 1.5 ps at the 84% confidence level, suggesting that the lower limit to which the present method can be applied is about 1 ps.The systematic errors were due to the uncertainty of the estimated isomer contribution (3%), the uncertainty of the stopping power (4%), and the geometrical ambiguity (6%). In addition, assuming a linear function for the background shape changes the mean value of τ by 6%. The respective uncertainties of the beam velocities which originated from the momentum acceptance of the RIPS and the multiple scattering in the target are 0.5% and 0.6%, which were negligibly small. The total systematic error was determined to be 10% by taking quadratic sum of these values. The resultant mean-life was determined as τ2+=2.5±0.7(stat)±0.3(syst) ps.Note that the cross sections were obtained from the fitting as 74.5±5.8 mb and 55.0±5.3 mb for the inelastic scattering of the 0g.s.+→21+ and 0g.s.+→1− excitations, respectively, in good agreement with the values measured with a 208Pb target [6]. The contribution of the cascade transition to the 21+→0+ peak was determined to be 7%. The respective excitation energies of the two states were determined to be 2.107±3 and 2.693±5 MeV, being in line with the values reported in Refs. [22] and [6].The measured τ2+ corresponds to a B(E2;↓) value of 8.0±2.2±0.8e2fm4, or 4.9±1.3±0.5 in Weisskopf units (W.u.). The present B(E2;↓) value is larger than 1.9 and 3.4 W.u. for the N=8 nuclei 14C and 16O [28]. In Fig. 5, the B(E2;↓) values for even–even beryllium and carbon isotopes around 12Be are presented. Unlike the carbon isotopes which exhibit a steady decrease in the B(E2;↓) values, the B(E2;↓) value of 12Be is almost same as that of 10Be [29] even when the neutron number is 8. These systematics support the claim that the magicity at N=8 is considerably deteriorated for 12Be.As mentioned earlier, information on both Mp and Mn is important for a more complete understanding on the structure of this nucleus. In the earlier work on 12Be [5] where the deformation length of proton inelastic scattering was obtained as δpp′=2.00±0.23 fm, the Mn value was deduced by incorporating results of shell model calculations. In the present case where both the B(E2;↓) value and the δpp′ are available, we can determine Mp and Mn experimentally. The obtained B(E2;↓) value leads to Mp=6.3±0.9 fm2, which is almost equivalent to Mp=6.6±0.1 fm2 for 10Be, suggesting that the “core” part remains unchanged from 10Be to 12Be. On the other hand, one can obtain Mn value using the following equation [15]:(1)MnMp=13(δpp′δem(1+3NZ)−1).δem, which stands for the deformation length of the charge distribution, is calculated to be 2.40±0.34 fm using the equation δem=4π/(3eZR)5B(E2;↓). Note that the errors of δem and Mp were defined by the quadratic sum of the statistical and systematic errors. We deduced Mn=10.1±1.4 fm2. This value is rather close to Mn=9.5 fm2 obtained in Ref. [5], and is about two times larger than Mn=3.8 fm2 and 3.9 fm2 for the other N=8 nuclei 14C [28,30] and 16O [28,31], respectively. The large Mn value for 12Be clearly indicates the disappearance of the magic number N=8 at the extremely neutron-rich 12Be.It should be noted that the radial dependence of proton and neutron transition densities are assumed to be identical in Eq. (1). A theoretical calculation [32] predicts the radial dependences to differ largely from each other. A recent microscopic coupled channel (MCC) analysis on the proton inelastic scattering data [5] that uses the calculated transition densities has yielded a larger Mn value than that assuming the same radial dependences [33]. To determine the Mn value and to discuss the importance of the radial dependences quantitatively, an MCC analysis which takes into account the present B(E2;↓) value is awaited.In summary, the B(E2;↓) value of 12Be has been determined through the lifetime measurement of the first excited state applying the DSAM to the inelastically excited 12Be beam. The obtained B(E2;↓) value was found to be larger than those for the N=8 nuclei 14C and 16O, and close to that for 10Be even though the excitation energy of the 2+ state decreases. In the framework of the empirical model, the almost same proton matrix elements for 10,12Be indicate the unchanged core in 12Be. 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