Neutron knockout of 12Be populating neutron-unbound states in 11Be
William A. Peters, T. Baumann, B. A. Brown, J. Brown, P. A. DeYoung, J. E. Finck, N. Frank, K. L. Jones, J.-L. Lecouey, B. Luther, G. F. Peaslee, W. F. Rogers, A. Schiller, M. Thoennessen, J. A. Tostevin, K. Yoneda
AAPS/123-QED
Neutron knockout of Be populating neutron-unbound states in Be W. A. Peters,
1, 2, 3, ∗ T. Baumann, B. A. Brown,
2, 3
J. Brown, P. A. DeYoung, J. E. Finck, N. Frank,
2, 3, † K. L. Jones, ‡ J.-L. Lecouey, § B. Luther, G. F. Peaslee, W. F. Rogers, A. Schiller, ¶ M. Thoennessen,
2, 3
J. A. Tostevin, and K. Yoneda ∗∗ Department of Physics and Astronomy, Rutgers,State University of New Jersey, Piscataway, NJ 08854, USA. Department of Physics & Astronomy, Michigan State University, East Lansing, MI 48824, USA National Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USA Department of Physics, Wabash College, Crawfordsville, IN 47933, USA Department of Physics, Hope College, Holland, MI 49423, USA Department of Physics, Central Michigan University, Mt. Pleasant, MI 48859, USA Department of Physics, Concordia College, Moorhead, MN 56562, USA Department of Physics, Westmont College, Santa Barbara, CA 93108, USA Department of Physics, Faculty of Engineering and Physical Sciences,University of Surrey, Guildford, Surrey GU27XH, U.K. (Dated: October 23, 2018)Neutron-unbound resonant states of Be were populated in neutron knock-out reactions from Be and identified by Be–n coincidence measurements. A resonance in the decay-energy spectrumat 80(2) keV was attributed to a highly excited unbound state in Be at 3.949(2) MeV decaying tothe 2 + excited state in Be. A knockout cross section of 15(3) mb was inferred for this 3.949(2) MeVstate suggesting a spectroscopic factor near unity for this 0 p / − level, consistent with the detailedshell model calculations. PACS numbers: 29.38.Db, 29.30.Hs, 24.50.+g, 21.10.Pc, 21.10.Hw, 27.20.+nKeywords: neutron decay spectroscopy, neutron-unbound states in Be Several recent experiments have mapped the levelstructure of Be. Hirayama et al. [1] observed the β -delayed neutron decay from polarized Li, identify-ing neutron-unbound levels in Be and assigning spinand parity to each. Previous neutron knockout experi-ments have identified additional levels, and highlightedsignificant mixing with sd -shell states [2, 3]. We alsoreport on neutron-unbound excited states in Be popu-lated by neutron knockout from Be and investigated byin-beam neutron-decay spectroscopy. These data showa resonance at a decay energy of 80(2) keV indicatingpopulation of the known 3 / − state at 3.949(2) MeV in Be decaying to the first 2 + state in Be via neutronemission. The uncertainty of the measured energy forthis state is significantly improved over the previous ac-cepted value [4]. The measured knock-out cross sectionof 15(3) mb implies a spectroscopic factor near unity forthis 3 / − state.The reports of Hirayama et al. [1], Aoi et al. [5], ∗ Electronic address: [email protected] † Currently at Department of Physics, Augustana College, RockIsland, IL 61201, USA ‡ Currently at Department of Physics & Astronomy, University ofTennessee, Knoxville, TN 37996, USA § Currently at Laboratoire de Physique Corpusculaire, ENSICAENIN2P3, 14050, Caen, Cedex, France ¶ Currently at Department of Physics & Astronomy, Ohio Univer-sity, Athens, OH 45701, USA ∗∗ Currently at RIKEN Nishina Center, Wako, Saitama 351-0198,Japan and Morrissey et al. [6] from β -decay of Li, noted ex-cited states in Be including (1.778 MeV)( J π = 5 / + ),(2.690 MeV)( J π = 3 / − ), and (3.949 MeV)( J π = 3 / − )that are also observed in this work. Additionally, Navin et al. [3] demonstrated the importance of sd intruderstates to understanding the structure of Be by usingneutron-knockout reactions from Be to populate the1 / + and the 1 / − states in Be. These levels from ν (1 s / ) and ν (0 p / ) valence neutron configurationsin Be were found to be populated with nearly equalprobability. This significant shell-level mixing with the sd -shell, the subsequent fragmentation of simple single-particle strengths [7, 8], α -particle clustering, and re-sulting deformation, contribute to the disappearance ofthe eight-neutron magic shell gap in Be. Pain et al. further identified a possible resonance at approximately3.5 MeV decay energy. They also observe a narrow reso-nance near zero due to a state (or two states) in Be atabout 4 MeV excitation energy that subsequently decayvia neutron emission to the first excited 2 + state of Beat 3.368 MeV, but these paths could not be well definedby their data because of limitations in their experimen-tal setup. We employed the neutron-knockout techniqueof References [2, 3] using the Modular Neutron Array(MoNA) [9, 10]. Figure 1 displays the level scheme forthe low-lying energy levels in Be and Be including theneutron decay energies seen in the present experiment.The experiment consisted of a primary beam of O accelerated to 120 MeV/nucleon with the CoupledCyclotron Facility [12] at the National Superconduct-ing Cyclotron Laboratory; this beam impinged onto a a r X i v : . [ nu c l - e x ] A p r Be + n Be3869501 a a EE decaydecay aa J π + + + - + - + - - FIG. 1: (Color online) Be level scheme up to 4 MeV includ-ing the first two states in Be. The neutron decay energiesobserved in this experiment to the Be ground state or firstexcited state are labeled. Energies are given in keV alongwith known spin and parity assignments. ( a denotes valuesderived in the current work incorporating the recently remea-sured separation energy from Ref. [11]). / cm Be production target. The secondarybeam of 90 MeV/u Be, produced by fragmentation, wasseparated with the A1900 fragment separator [13] uti-lizing a 750 mg / cm acrylic achromatic wedge degraderinstalled at the dispersive image. The average intensityof the Be beam was about 60,000 particles per second,with a momentum spread of ± .
5% and a purity of over99%.The secondary beam was directed onto a 102 mg / cm Be reaction target. Charged particles were deflectedby the large gap Sweeper magnet [14, 15] and the neu-trons were detected by MoNA [9, 10]. The setup and thecharged-particle detectors after the Sweeper magnet aredescribed in Figure 4 of Ref. [9]. Additionally, a steelblocker was installed in front of the first CRDC to pro-tect it from the low-momentum tail of the unreacted Bebeam.The energies of the neutrons were calculated from theflight time between a timing detector in front of the re-action target and MoNA, located at zero degrees andpositioned 8.2 m from the reaction target. Their anglesrelative to the beam axis were assigned by the first in-teraction point in MoNA. Timing the arrival of the light at each end of neutron detector bars yields a horizontalposition with a standard deviation of 3 cm. The verticaland longitudinal position resolution is 5 cm (one half thebar width and height of 10 cm) [9, 16].The directions of the charged particles behind theSweeper magnet were measured by two Cathode ReadoutDrift Chambers (CRDCs). The position resolution of theCRDCs was 1.5 mm in the horizontal dispersive plane.The energy and emission angle of each fragment at thereaction target was calculated using a transformation ma-trix constructed from the measured magnetic field mapsof the Sweeper [17] using the beam physics code package cosy infinity [18, 19]. The elemental identification ofthe charged fragments was based on energy loss in a plas-tic scintillator downstream of the two CRDCs. Isotopicseparation of the beryllium nuclei was based on the mea-sured horizontal angle determined by the two CRDCsand the fragment flight time between the timing detec-tor at the target to the d E scintillator as in Ref. [20].The results presented below are based on events witha neutron in coincidence with a Be fragment. Thiscoincidence gate yields a clean neutron spectrum withlittle background. The decay energy can be determinedby subtracting the mass of the decay products from theinvariant mass of the neutron–fragment system as de-scribed in Ref. [21]. The neutrons are moving near beamvelocity (90 MeV in the current experiment) and are for-ward focused. This results in a neutron acceptance of60% for decay energies less than 2.5 MeV. The resolu-tions described above propagate through the invariant-mass equation and broaden the resolution of the decayenergy as the square-root of the energy; from a standarddeviation of 75 keV at 300 keV, to 200 keV for a decayenergy of 1500 keV [16].The decay energy spectrum is shown in Fig. 2 and twoprominent peaks are indicated, one produced by a low-energy decay (less than 100 keV), and the other withan energy of 1.28 MeV. The overall shape of the spec-trum is similar to the decay energy spectrum presentedin Ref. [2]. A detailed simulation of the data, as de-scribed below, further indicates the presence of a broadresonance with decay energy of 2.19 MeV.Monte Carlo simulations were performed which incor-porated the geometric acceptances and measured reso-lutions of the neutron and charged particle detectors.The resonances were modeled by Breit-Wigner distri-butions. For the simulation shown in Fig. 2, the res-onant energies of Be*(1.778 MeV) (dot-dashed line)and Be*(2.690 MeV) (dashed line) and their widths(100 keV and 200 keV) were kept constant at the valuesreported in Ref. [4] along with the proportional intensi-ties of the two as reported by Pain et al. in Ref. [2].For the third low-decay-energy peak (dotted line), theenergy, width, and relative population with respect tothe other two resonant level were free parameters. Abackground distribution due to non-resonant neutronsand neutrons from the direct diffractive breakup chan-nel of Be was included with a Maxwellian distribu-
FIG. 2: Decay energy spectrum from Be–neutron coinci-dence data. The simulation (solid line) is the sum of three res-onances with decay energies of 80 keV (dotted line), 1.28 MeV(dot-dashed line), and 2.19 MeV (dashed line). In addition,a non-resonant background component (double-dot dashedline) was included. The insert shows a separate fit to thelow energy range with higher fidelity, confirming only one lowenergy peak at 80 keV. tion, √ E exp( − E/E ), where E was a free parameter(see Ref. [22] concerning modeling of non-resonant back-ground). The magnitude and E parameter of the back-ground (double-dot dashed line) were also treated as freeparameters, the final best-fit curve with E = 5.0 MeVwas nearly identical to the background curve of Ref. [2].The angle and position distributions of the incoming Bebeam used in the simulation were adjusted to reproducethe angle and position distributions of the fragments inthe charged particle detectors.Due to a technical failure of the beam counting mon-itor, it was not possible to extract the cross section di-rectly from the experiment. The overall normalizationto extract the cross section of populating the low-energypeak was done by scaling relative to the cross sectionsreported by Pain et al. [2]. Since the beam energy(39 MeV/nucleon) was much lower than the present ex-periment (90 MeV/nucleon), the reported cross sectionsof Pain et al. were scaled to account for the reductionof knockout cross sections with faster beams. This wasdone by calculating the single particle cross sections foreach state at both energies using the same Eikonal re-action model [23] that was used in Ref. [2]. The singleparticle cross section ratio for the former to current beamenergies is 0.62 for all three states observed: Be*(1.778& 2.690 & 3.949 MeV). The reported cross sections forthe 1.778 MeV and 2.690 MeV states were then scaledby this factor of 0.62 (keeping the relative magnitudesconstant) and the cross section of the low-energy peakwas determined. The decay energy of the low-energy peak was found tobe S n = 80(2) keV as shown in the inset of Fig. 2 with across section of 15(3) mb. Systematic uncertainties, dueto various beam parameters that fit the measured dis-tributions recorded in the charged-particle detectors, ac-counts for the limited resolution of fitting the decay widthleading to an upper limit of 40 keV that is consistent withthe accepted value of 15 keV [4]. The uncertainty of thecentroid of the peak is much less affected and a χ analy-sis yields a 2 keV standard deviation for the uncertaintyof the 80 keV value. By adding the measured value ofthe first excited 2 + state in Be at 3.36803(3) MeV [24]and the recently improved neutron separation energy of501.3(6) keV [11], this neutron decay energy correspondsto an excitation energy of 3.949(2) MeV in Be, and im-proves the uncertainty of the currently adopted energyof this state (the second 3 / − state at 3.956(15) MeV inRef. [4]. The present value is below the value measuredby Hirayama et al. for this state, 3 . +0 . − . MeV, from Li beta decay [1]. The lack of evidence for a resonancebelow 80 keV shows that the Be*(3.887) state, decay-ing to the 2 + in Be, is not measurably populated in thepresent knockout reaction.The large measured cross section of 15(3) mb for theneutron decay of Be*(3.949) is similar in magnitude tothe cross sections for populating Be*(1.778 and 2.69),as reported in Ref. [2]. The reported cross sections forpopulating these two states, after scaling by the sin-gle particle cross section ratio (0.62) for the differentbeam energies, are 19(3) and 14(3) mb, respectively. Theknockout reaction model calculation [23] yields a singleparticle cross section of 31.4 mb to populate the second3 / − state in Be. Haigh et al. [25] measured the decaybranching from this 3.949 MeV state to both the groundstate (with a decay energy of 3.45 MeV that is outside thegeometric acceptance of our setup) and to the 2 + excitedstate (the 80 keV channel we measured) of Be with atwo-neutron pickup reaction ( O, O) on Be. Their re-sults show that the branching to these two channels isequal. Earlier work by Hirayama et al. [1] also mea-sured the branching ratio (with large uncertainties) from Be*(3.949) following the beta decay of Li. Therefore,our measured cross section to the first excited state in Be is doubled to get the total single-neutron knockoutcross section from Be to the Be*(3.949) state. Thistotal production cross section of 30(6) mb leads to a spec-troscopic factor of 1.0(2) when compared to the reactionmodel calculation [23]. This value is about twice the ob-served spectroscopic factor of the lower-lying states in Be measured in Refs. [2, 3], supporting the interpreta-tion for the character of this 3 / − state as predominantlysingle-particle, likely due to hole correlations in the 0 p / orbital.The experimental results can be compared to calcula-tions in the p -shell with the WBP Hamiltonian [26] thatinclude up to two particles excited into the sd -shell [27].The wavefunction for the Be 0 + ground state is cal-culated to comprise 31% 0 (cid:126) ω with p -shell configurations TABLE I: WBP Hamiltonian [26] theoretical calculations for the first three 3 / − states in Be. Energies, spectroscopic factors,and their wavefunctions are calculated for the p -shell including up to two particles excited into the sd -shell [27].E ∗ Th. E ∗ Exp. Spec. factors Wavefunction components(MeV) (MeV) from Be g.s. to Be 0 + to Be 2 + (cid:126) ω % 2 (cid:126) ω %1.76 2.69 1.576 0.155 0.461 73 272.80 3.949 0.693 0.0012 0.215 19 814.24 ? 0.033 0.0053 0.221 70 30 and 69% 2 (cid:126) ω with two nucleons excited into the into the sd -shell. The calculated energies of the first two 3 / − states are about 1 MeV too low compared to their mea-sured values; and experimental energy of a third 3 / − state is not known, but calculated to be 4.24 MeV. Thefirst 3 / − state in Be is produced by one nucleon re-moval from the 0 (cid:126) ω component of the Be ground statewith an observed spectroscopic factor of 0.40(6) [2] thatis significantly smaller than the calculated value of 1.576.The second 3 / − state in Be (81% 2 (cid:126) ω ) is produced byone-nucleon removal from the 2 (cid:126) ω component of the Beground state. The experimental spectroscopic factor re-ported herein of 1.0(2) is in reasonable agreement withthe calculated value of 0.69. See Table I for more details.The decay widths are calculated by Γ = C S Γ sp wherethe spectroscopic factors C S and the single-particle de-cay widths Γ sp are calculated by Eq. 3F-51 in [28] usingthe experimental Q values. The single-particle l = 1 de-cay width for the decay of the first 3 / − to the Be0 + ground state ( Q = 2.19 MeV) is 1.5 MeV. Combinedwith the spectroscopic factor of 0.155, the resulting de-cay width of 0.23 MeV is in good agreement with the ex-perimental value of 0.20(2) MeV [4]. The single-particle l = 1 decay width for the decay of the second 3 / − Be*(3.949) state to the two decay channels, Be 2 + ( Q = 0.080 MeV) and 0 + ( Q = 3.448 MeV), are 0.020and 4.0 MeV, respectively. Combined with the calculatedspectroscopic factors; 0.22 for the 2 + channel and 0.0012for the 0 + channel, the decay widths are 4.4 and 4.8 keV,respectively. The large variation in spectroscopic factorsis due to interference between the various 0 (cid:126) ω and 2 (cid:126) ω wavefunction components of the decaying 3 / − state andthe 0 + or 2 + states in Be. The total experimentalwidth is 15(5) keV [4] and, for equal branching ratios[25], the experimental partial widths would each be halfthat; around 7(3) keV. The agreement between exper-iment and theory is surprisingly good, given the smallspectroscopic factors involved.We note that a general feature of analyses of nucleonknockout reactions is that measured cross sections aresmaller than those calculated using the Eikonal modelwith shell-model spectroscopic factors. This empiricalbehavior is shown, for example, in Figure 6 of Ref. [29].The observed reduction factors, R s , show a systematicdependence on the asymmetry of the neutron and protonseparation energies from the projectile ground state, ∆ S .In the present case, of weakly-bound neutron removalfrom Be, the neutron separation energies to the Be ground state and 3.949 MeV excited state correspond to∆ S of −
20 MeV and −
16 MeV, respectively. These ∆ S ,and the measured reaction systematics, suggest R s valuesof close to unity in the present work.The non-observation of the 3.887 MeV state, decayingpreferentially to the 2 + state in Be by 14 keV, indi-cates that this state is not strongly populated by singleneutron removal from Be or two-neutron transfer [25].This interpretation is also consistent with the results ofthe three-proton stripping reaction from N [22] thatpopulated Be*(3.887) but not Be*(3.949), where thelikelihood of exciting neutrons to higher sub-shells ex-ists. This 14 keV decay channel was also observed inRef. [30] that selectively populated the 3.887 MeV and3.949 MeV states by two-proton and two-neutron trans-fer reactions, respectively. Finally, in another MoNA ex-periment populating unbound states in Be by the non-selective reaction of direct fragmentation from Ca, neu-trons decaying from both excited states near 4 MeV tothe 2 + state in Be were observed [20]. The similaritiesbetween the setups for that experiment and the presentsupports our interpretation of the selectivity of the single-neutron knockout from Be to Be*(3.949). However,as noted earlier, we cannot rule out the possibility thatthe Be*(3.887) state is populated and subsequently di-rectly decays predominantly to the ground state of Beby 3.38 MeV neutron decay.In summary, the resonance observed through neutron-decay spectroscopy measurements of the neutron-unbound excited states in Be at a decay energy of80(2) keV indicates the population of the known second3 / − state at 3.949(2) MeV in Be decaying to the 2 + state in Be via neutron emission. The inferred crosssection for this decay branch of 15(3) mb implies a spec-troscopic factor near unity for this 3 / − state, consistentwith shell model calculations.W.A.P. thanks S. Pain, D. Bardayan, and F. Nunesfor fruitful discussions. The MoNA project was madepossible by funding from the National Science Founda-tion under Grants PHY-0110253, PHY-0132367, PHY-0132405, PHY-0132434, PHY-0132438, PHY-0132507,PHY-0132532, PHY-0132567, PHY-0132641, PHY-0132725, PHY-0758099 , PHY-0098800, and by supportfrom Ball State University, Central Michigan University,Concordia College, Florida State University, Hope Col-lege, Indiana University at South Bend, Michigan StateUniversity, Millikin University, Westmont College, West-ern Michigan University, and the National Superconduct-ing Cyclotron Laboratory. This work was also supportedby the NSF grant PHY-06-06007 and by the United King- dom Science and Technology Facilities Council (STFC)under Grant No. ST/F/012012/1. [1] Y. Hirayama, T. Shimoda, H. Izumi, A. Hatakeyama,K. P. Jackson, C. D. P. Levy, H. Miyatake, M. Yagi, andH. Yano, Phys. Lett. B , 239 (2005).[2] S. D. Pain, W. N. Catford, N. A. Orr, J. C. Angelique,N. I. Ashwood, V. Bouchat, N. M. Clarke, N. Curtis,M. Freer, B. 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