application/xml11Be continuum studied through proton scatteringA. ShrivastavaY. BlumenfeldN. KeeleyT. ZerguerrasT. AumannD. BazinM. ChromikG.M. CrawleyT. GlasmacherK.W. KemperF. MaréchalD.J. MorrisseyT. NakamuraA. NavinE.C. PollaccoD. SantonocitoB.M. SherrillT. SuomijärviM. ThoennessenE. TryggestadR.L. VarnerElastic and inelastic scatteringRadioactive ion beamCoupled channels calculationsPhysics Letters B 596 (2004) 54-60. doi:10.1016/j.physletb.2004.06.070journalPhysics Letters BCopyright © 2004 Elsevier B.V. All rights reserved.Elsevier B.V.0370-26935961-219 August 20042004-08-1954-60546010.1016/j.physletb.2004.06.070http://dx.doi.org/10.1016/j.physletb.2004.06.070doi:10.1016/j.physletb.2004.06.070http://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/

Journals

S300.3

PLB21165S0370-2693(04)00936-010.1016/j.physletb.2004.06.070Elsevier B.V.Experiments

Fig. 1

Energy vs. angle scatter plot measured for recoiling protons in coincidence with (a) 11Be and (b) 10Be. The calculated kinematic line for the 11Be ground state is shown as the solid curve in (a). Calculated kinematic lines for the 1.78 MeV (dotted curve), 3.41 MeV (solid curve) and 5.24 MeV (dashed curve) resonant states of 11Be are shown in (b).

Fig. 2

Excitation energy spectrum for 11Be inelastic scattering measured at 64 MeV/A, integrated over the total centre of mass angular range of 15 to 35 degrees. The background contribution arising from 12C is denoted by the shaded area.

Fig. 3

Angular distribution data for quasi-elastic (a) and inelastic scattering to the 0.5–3.0 MeV bin (b) and 3.0–5.5 MeV bin (c).The curves are the result of CDCC calculations as indicated in the figure (see text). Both the resonant (r) and non-resonant (nr) contributions and their sum are shown as individual curves in (b).

Table 1

States populated in the Be11(p,p′) reaction [2,5,18,19]. E* denotes the excitation energy. Spin assignments in brackets are unconfirmed experimentally. The suggested dominant structures are mostly those of Liu and Fortune [19]

E* (MeV)JπSuggested dominant structuregs1/2+Be10(0+)⊗(s1/2)0.3201/2−Be10(0+)⊗(p1/2)1.778(5/2+)Be10(0+)⊗(d5/2)2.67(3/2−)Be10(0+)⊗(p3/2)3.41(3/2−)Be9(3/2−)⊗(sd)0+23.89(3/2−)

[19]

Be10(2+)⊗(s1/2)(5/2−)

[2]

3.963/2−Be9(3/2−)⊗(sd)2+25.2511Be continuum studied through proton scattering

Shrivastava

aradhana@apsara.barc.ernet.in

Blumenfeld

Keeley

Zerguerras

Aumann

Bazin

Chromik

G.M.

Crawley

Glasmacher

K.W.

Kemper

Maréchal

D.J.

Morrissey

Nakamura

Navin

E.C.

Pollacco

Santonocito

B.M.

Sherrill

Suomijärvi

Thoennessen

Tryggestad

R.L.

Varner

aInstitut de Physique Nucléaire, IN2P3-CNRS, F-91406 Orsay, FrancebNuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, IndiacNational Superconducting Cyclotron Laboratory, Michigan State University, East Lansing, MI 48824, USAdDepartment of Physics, Florida State University, Tallahassee, FL 32306, USAeDepartment of Physics and Astronomy, University of South Carolina, Columbia, SC 29208, USAfDSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette, FrancegPhysics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA1

Present address: DSM/DAPNIA/SPhN, CEA Saclay, F-91191 Gif-sur-Yvette, France.

Permanent address: GSI, Planckstrass 1, D-64291 Darmstadt, Germany.

Permanent address: IRES, F-67037 Strasbourg, France.

Permanent address: Department of Physics, Tokyo Institute of Technology, 2-12-1 0-Okayamy, Meguro, Tokyo, Japan.

Present address: INFN-Laboratorio Nazionali del Sud, Via S. Sofia 44, 95123 Catania, Italy.

Editor: V. Metag

Abstract

Elastic and inelastic proton scattering on 11Be were measured in inverse kinematics up to a 11Be excitation energy of 7 MeV. Continuum discretised coupled-channels (CDCC) calculations using a Be10(0+)+n cluster model of 11Be are able to explain the elastic scattering data. However, for the inelastic scattering angular distributions for 11Be excitation energy bins of 0.5–3 and 3–5.5 MeV the CDCC calculations under-predict the data, indicating the presence of contributions due to the deformed and active 10Be core to the 11Be breakup process.

PACS

25.60.-t25.40.Cm25.40.Ep

Keywords

Elastic and inelastic scatteringRadioactive ion beamCoupled channels calculations

The 11Be nucleus has been the object of considerable interest since the inversion of the p1/2 and s1/2 orbitals predicted by Talmi and Unna [1] leading to a 1/2+ ground state was confirmed by the measurements of Alburger et al. [2]. In addition, the transition strength from its Jπ=1/2+ ground state to its 1/2− first excited state located at 320 keV excitation energy is the strongest among the lighter nuclei [3,4]. However, recent interest in 11Be has centred on its nature as the archetype of a one-neutron halo nucleus. The halo nature of 11Be was established by reaction cross section [5] and momentum distribution measurements [6,7]. Higher lying states in 11Be are particle unbound resonances, which makes the measurement of their strength particularly challenging. There are various calculations that predict the presence of a large amount of transition strength located just above the particle emission threshold [8]. This low energy strength, dubbed the “soft mode”, is expected to be a generic property of neutron halo nuclei due to the very weak binding energy of the halo neutron(s). Calculations by Fayans et al. for 11Li and 11Be [8] indicate that the angular distributions corresponding to different multipolarities peak around 1.5 MeV in excitation energy and at forward angles in (p,p′) scattering. More recent calculations show that the coupling of the soft mode to core excitation is weak, and it resembles more a non-resonant single particle excitation than a particle hole collective mode like giant resonances [9]. Experimentally, such low energy strength has been observed in 11Be through Coulomb excitation using a Pb target [10,11], where it was attributed to non-resonant E1 strength. No evidence for the excitation of resonant states was observed in this Coulomb excitation study.The objective of the present work is to investigate the unbound states in 11Be by nuclear excitation, specifically through (p,p′) scattering. The advantage of nuclear scattering is that all multipolarities will contribute, while Coulomb scattering strongly favours L=1. While the continuum of several light neutron-rich nuclei has been investigated by proton scattering [12,13], this is the first such study for 11Be. The results are analyzed with the help of continuum discretised coupled-channels calculations [14] employing a simplified two-body cluster model of 11Be, which is considered to consist of an inert Be10(0+) core plus a valence neutron.The experiment was performed in inverse kinematics. A pure secondary beam of 11Be with an intensity of ∼105 pps at an energy of 63.7A MeV was produced at the National Superconducting Cyclotron Laboratory at Michigan State University by bombarding a 1100 mg/cm2 Be production target with a 13C beam accelerated to 100A MeV in the K1200 cyclotron. The fragments were analysed using the A1200 fragment separator [15] and the resulting beam was purified by passage through a 300 mg/cm2 Al wedge. The 11Be beam was scattered from a CH2 target, 1 mg/cm2 thick. An array of eight telescopes, each of 5×5 cm2 active area, described in Ref. [16], was used to measure the kinetic energy and angle of the recoiling protons, from which the excitation energy and centre of mass scattering angles were subsequently deduced from two-body kinematics. Each telescope was composed of a 300 μm thick Si strip detector with 16 vertical strips (3 mm wide) backed by a 500 μm thick PIN diode detector and a 1 cm thick stopping CsI detector read out by 4 photodiodes. The telescopes covered a laboratory angular range of 68° to 85°, corresponding to 10° to 42° in the centre of mass frame for elastic scattering. A 1 MeV threshold had to be set for the strip detector trigger to cut the noise, effectively limiting the centre of mass angular range to angles larger than 15°. Particle identification in the telescopes was performed by a ΔE–E measurement for particles traversing the strip detector, and by time of flight for the lowest energy particles. The beam spot size on target was approximately 6 mm FWHM. Incident beam tracking could not be used since the performance of the cathode readout drift chambers, installed for this purpose, deteriorated during the experiment.Such an experiment necessitates a careful tagging of the reaction channel in order to obtain background free spectra. Therefore, in coincidence with the recoil protons, the scattered fragments were detected in the S800 spectrometer equipped with its standard detection system [17]: a pair of position sensitive cathode readout drift chambers for trajectory measurements followed by a multi-segmented ion chamber and two large plastic scintillators. The combination of these measurements furnished unambiguous Z and A identification of the fragments. Two magnetic field settings of the spectrometer were used to detect 11Be and 10Be fragments, respectively. In the first case one gates on bound final states of 11Be, i.e., elastic scattering and inelastic scattering to the 1/2− 320 keV state. In the second case, inelastic scattering to unbound states up to the 2n emission threshold (7.3 MeV) can be measured. It was checked by a simulation that in the latter case all 10Be fragments corresponding to 11Be scattering angles of less than 40° in the centre of mass frame lay in the large acceptance of the S800, 7° horizontally by 10° vertically. To evaluate the background arising from the 12C present in the CH2 target, a separate measurement of inelastic scattering was made with a 12C target of thickness 2.7 mg/cm2. As will be shown later, this contribution is very small.

Fig. 1

(a) displays an energy vs. angle scatter plot obtained for protons recoiling into the telescopes centred at 80° in coincidence with 11Be identified after analysis in the S800. After kinematical transformation, the FWHM of the corresponding peak was found to be 1.4 MeV, mainly due to the energy resolution. The main contributions to this resolution are the beam spot size, the strip width and the absence of a vertical position measurement in the strip detectors. Therefore, elastic and inelastic scattering to the 320 keV state could not be separated. The uncertainty due to the beam spot size in the energy and angle resolution is 1 MeV and 1.1°, respectively. An attempt was made to detect the 320 keV γ rays from the decay of the 1/2− state by placing 68 BaF2 detectors of the ORNL-TAMU-MSU array adjacent to the reaction chamber. Unfortunately, the γ-ray data collected did not have meaningful statistical accuracy. A similar plot for protons measured in coincidence with 10Be fragments in the S800 is shown in Fig. 1(b) along with kinematic curves calculated for three known unbound resonant states of 11Be. Fig. 2

shows the excitation energy spectrum for 11Be inelastic scattering, which exhibits a broad peak culminating around 2 MeV, followed by a slowly decreasing tail. This peak can be attributed to the excitation of the Jπ=5/2+ state known to be located at 1.78 MeV. Once again, the energy resolution did not allow observation of well separated peaks. The data taken with the carbon target were analyzed using the same procedure and normalized to the same number of beam particles and equivalent carbon thickness as for the CH2 target. The resulting spectrum is shown as the shaded histogram in Fig. 2, and it can be concluded that the carbon contribution to the data is very small.

We define quasi-elastic scattering as the sum of elastic scattering and inelastic scattering to the bound excited state at E*=320 keV. The quasi-elastic scattering angular distribution is shown in Fig. 3

(a). Each point corresponds to an angular width of 0.8° in the laboratory, corresponding to a width of 1.5° to 1.56° in the centre of mass frame for the angular range of 10° to 42°. The inelastic scattering distributions (for reactions leading to 10Be in the final state) are displayed in Fig. 3(b) and (c). Due to the relatively poor energy resolution, two regions of excitation energy were selected. The first bin, from 0.5 to 3.0 MeV, is centred around the known resonance E*=1.778 MeV, with bin size equal to E*±2σ (σ=0.6 MeV from the quasi-elastic scattering data). This bin also includes a large part of the 2.67 MeV state. The second bin, ranging from 3.0 to 5.5 MeV, should contain other higher energy resonant states according to the list of known states in 11Be shown in Table 1

, compiled from [2,5,18,19]. Both bins will also contain contributions from non-resonant breakup. The error bars shown are statistical and take into account the errors on the carbon target data which have been subtracted. The systematic error is approximately 10%, mainly due to the uncertainty in the target thickness, while the incident beam particles were counted individually with a drift chamber placed at the entrance of the target chamber.

Calculations were carried out using a cluster-folding model [20] of 11Be within the framework of the continuum discretised coupled-channels (CDCC) formalism. The 11Be nucleus was assumed to have a two-body cluster structure with an inert Be10(0+) core and a valence neutron (n). As 10Be is known to be deformed with a strongly coupled 21+ state at 3.37 MeV the use of the inert core model may be considered questionable. However, we believe that it is justified on two counts. Firstly, while contributions from the 21+ state of the 10Be core can be important in giving the correct ground state spin-parity for 11Be, most measurements and structure calculations agree that the main configuration (approximately 70%) of the 11Be ground state is Be10(0+)+n[11,21,22]. The few calculations available for the excited states also suggest that the 0.32 MeV 1/2− and 1.78 MeV 5/2+ states are mostly of this configuration [23–25]. Secondly, a more sophisticated calculation that included the effects of core excited states would necessitate an extensive structure calculation to provide the large number of spectroscopic amplitudes required for the different contributions to the bound and resonant excited states and the Be10+n continuum in order to be physically meaningful. Such a calculation would be extremely difficult, and before embarking on this task the sensitivity of the data to excited core configurations needs to be established. If the simple inert core model is able to describe the data for excitation to the continuum there is little to be gained from more sophisticated calculations.Couplings to the bound 1/2− state at an excitation energy of 320 keV and the resonant states at excitation energies of 1.275 and 2.166 MeV above the Be10+n threshold of 0.504 MeV (assumed to have spin-parity of 5/2+ and 3/2−, respectively) and the L=0,1,2 non-resonant continuum were included. All allowed couplings between excited states were also included. The Be10+n binding potential was of Woods–Saxon form, with the geometry of Dasso et al. [26,27]. A spin–orbit component with the same geometry as the central part and a well depth of 4.39 MeV was also included. The well depth of the central part of the potential was adjusted to obtain the correct binding energy in the case of the bound states or a resonance at the correct energy for the resonant states. The Be10(0+)+n continuum was discretised into a series of bins in momentum space, the two lowest momentum bins being of width Δk=0.16 fm−1 and the two highest momentum bins of width Δk=0.14 fm−1, where ℏk is the momentum of the Be10+n relative motion. This binning scheme was adopted in order to match the cuts used to extract continuum excitation cross sections for 11Be from the data. It was suitably modified for the L=1, J=3/2− and L=2, J=5/2+ continuum to avoid double counting with the two resonant states while maintaining the match to the “experimental” binning scheme. The two resonant states were also treated as bins, of widths equivalent to 0.2 and 0.4 MeV for the 5/2+ and 3/2− states, respectively. All partial waves up to ℓ=30 were included and the matching radius was set equal to 150 fm. The Be10+n wave functions were averaged over the width of the bins and were not normalised to unity. The cluster-folding model for Be11+p scattering requires optical potentials for Be10+p and n+p scattering at 10/11 and 1/11 of the 11Be beam energy, respectively, as input. The Be10+p potential parameters were obtained from the CH89 parametrization of Varner et al. [28], while the p+n parameters were derived from a fit to the scattering data of Ref. [29], yielding parameters V=84.0 MeV, R=1.24 fm and a=0.30 fm for a standard real Woods–Saxon potential.The calculations were performed using the code FRESCO [30], version frx008. The results are compared with the quasi-elastic data in Fig. 3(a). Since these data represent the sum of the cross sections for scattering to the ground and first excited states of 11Be, the sum of the calculated cross sections for these processes, shown by the solid curve, is compared with the data. The dot-dashed curve denotes the calculated cross section for excitation of the 0.32 MeV 1/2− state. Despite the large B(E1;1/2+→1/2−) for this excitation the cross section is negligible in comparison with the elastic scattering, due to the low charge product of the system which makes the Coulomb excitation cross section very low. In order to obtain good agreement between the calculations and the quasi-elastic data it was necessary to renormalise the CH89 potential used for the Be10+p component of the cluster-folded potential by factors of 0.75 and 1.8 for the real and imaginary parts, respectively. Such a renormalisation is reasonable, as a similar procedure was found to be necessary to describe (p,p) data for many other light weakly bound nuclei [31].The inelastic scattering angular distributions are compared to the CDCC calculation for the 11Be excitation energy (E*) bin from 0.5–3.0 MeV in Fig. 3(b) and the E* bin from 3.0–5.5 MeV in Fig. 3(c). Fig. 3(b) shows contributions from resonant and non-resonant breakup. A comparison of the measured and calculated angular distributions shows that the shape of the data is best matched by the calculated L=2 angular distributions, both resonant and non-resonant, although the magnitude is under-predicted by the sum of all the contributions.Over the measured angular range the non-resonant and resonant L=2 breakup channels contribute approximately equally to the calculated cross section, that for the 2.67 MeV resonance being negligible and for the L=0 non-resonant continuum only significant for angles smaller than approximately 17°. The non-resonant E1 contribution is dominant for angles smaller than about 20°, the resonant and non-resonant L=2 and non-resonant L=1 cross sections contributing approximately equally to the total for angles greater than this. Thus, the calculated L=1 non-resonant breakup behaves like the predicted “soft dipole” mode. Nevertheless, Fig. 3(b) indicates that over the angular range where data are available a considerable amount of breakup strength is missing from our calculation. This missing strength may most likely be ascribed to processes not included in our calculation, i.e., those including an excited 10Be core. As the data were measured in coincidence with a 10Be, contributions from other possible clustering modes, e.g., those with a 9Be core, may be ruled out. Test calculations found that the L=3 non-resonant continuum made a negligible contribution to the breakup cross section. Further support for this conclusion comes from a recent analysis of the Be10(d,p)Be11 transfer reaction [32], which selectively populates the Be10(0+)⊗n configuration and showed evidence, in addition to a high energy continuum, for only one sharp state above 2 MeV, located at 3.4 MeV, and which moreover was weakly populated. This implies that the missing strength in this bin cannot be ascribed to other resonant states not included in the calculation. Also a QRPA analysis of 11B(7Li, 7Be)11Be charge exchange reaction [33] indicates that the strength distribution at excitation energies above 2 MeV is very likely produced by core excitation.In Fig. 3(c), the same comparison is made for the higher excitation energy bin, 3 MeV ⩽E*⩽5.5 MeV. Here the CDCC calculation strongly under-predicts the data and does not describe the shape of the observed angular distribution. This discrepancy is most probably due to the omission of the resonant states built on the 10Be 21+ excited state (see Table 1) and core excitation contributions to the non-resonant continuum. Thus, we find that over the angular range for which data are available simple Be10(0+)+n breakup is not the dominant process contributing to the observed cross section for the 3 MeV ⩽E*⩽5.5 MeV bin.An alternative possible cause for the discrepancy between the calculated and measured breakup could be a failure of the CDCC method to give the correct absolute magnitude for the breakup cross section. While it is impossible to definitely rule out this possibility, the CDCC method is able to describe coincidence breakup data for other nuclei where core excitation may be neglected, e.g., 6Li [34], 7Li [35] and the deuteron [14].In summary, we have obtained data for the Be10+n continuum of 11Be by means of (p,p′) scattering for the first time. Continuum discretised coupled-channels calculations based on an inert Be10(0+) core plus a neutron in single particle orbits show significant contributions from the 1.78 MeV resonant and L=2 non-resonant states to the 0.5⩽E*⩽3 MeV bin. However, the calculation under-predicts the data. This is probably due to contributions from configurations involving excited states of the 10Be core to the Be10+n continuum, both resonant and non-resonant, of 11Be not included in the calculation. The same could be true for the data corresponding to the 3⩽E*⩽5.5 MeV bin, which are considerably under-predicted by the calculation. The detection of a 10Be in coincidence with the recoiled proton rules out contributions from other clustering modes as the cause of the discrepancy. Therefore, the current data strongly suggest that core excitation makes a significant contribution to the Be10+n breakup of 11Be, although further, more sophisticated calculations and higher resolution data will be required to confirm this conjecture.

Acknowledgments

The authors are grateful to Dr. I.J. Thomson for providing technical help related to the FRESCO code. This work was partially supported by the National Science Foundation under Contract Nos. PHY-95-28844 and NSF 1334-678-22.

References

[1]

Talmi

UnnaPhys. Rev. Lett.

1960

469

[2]

D.E.

Alburger

Phys. Rev.

136

1964

916

[3]

D.J.

Millener

Phys. Rev. C

1983

497

[4]

Nakamura

Phys. Lett. B

394

1997

[5]

Tanihata

Phys. Lett. B

206

1988

592

[6]

Anne

Phys. Lett. B

304

1993

[7]

J.H.

Kelley

Phys. Rev. Lett.

1995

Aumann

Phys. Rev. Lett.

2000

[8]

S.A.

Fayans

Phys. Lett. B

292

1992

239

S.A. Fayans, private communication

[9]

Sagawa

Z. Phys. A

351

1995

385

[10]

Nakamura

Phys. Lett. B

331

1994

296

[11]

Palit

Phys. Rev. C

2003

034318

[12]

A.A.

Korsheninnikov

Phys. Rev. Lett.

1997

2317

[13]

Lagoyannis

Phys. Lett. B

518

2001

[14]

Austern

Phys. Rep.

154

1987

125

[15]

B.M.

Sherrill

Nucl. Instrum. Methods Phys. Res. B

1992

298

[16]

Maréchal

Phys. Rev. C

1999

034615

[17]

Bazin

Nucl. Instrum. Methods Phys. Res. B

204

2003

629

[18]

Ajzenberg-Selove

J.H.

KelleyNucl. Phys. A

506

1990

[19]

G.-B.

Liu

H.T.

FortunePhys. Rev. C

1990

167

[20]

Buck

A.A.

PiltNucl. Phys. A

280

1977

133

[21]

Fortier

Phys. Lett. B

461

1999

[22]

J.S.

Winfield

Nucl. Phys. A

632

1998

[23]

Vinh MauNucl. Phys. A

592

1995

[24]

Nunes

I.J.

Thompson

R.C.

JohnsonNucl. Phys. A

596

1996

171

[25]

Bhattacharya

KrishanPhys. Rev. C

1997

212

[26]

C.H.

Dasso

Phys. Rev. C

1999

539

[27]

Diaz-Torres

I.J.

ThomsonPhys. Rev. C

2002

024606

[28]

R.L.

Varner

Phys. Rep.

201

1991

[29]

Boukharouba

Phys. Rev. C

2001

014004

[30]

I.J.

ThompsonComput. Phys. Rep.

1988

167

[31]

M.D.

Cortina-Gil

Phys. Lett. B

401

1997

[32]

F. Delaunay, et al., Proceedings of the 41st International Winter Meeting on Nuclear Physics, Bormio, Italy, 2003

[33]

Cappuzzello

Phys. Lett. B

516

2001

[34]

Signorini

Phys. Rev. C

2003

044607

[35]

Rusek

Phys. Rev. C

2003

014608