arXiv:nucl-ex/0510048v1 16 Oct 2005
Structure of12Be: intruder d-wave strength at N=8
S.D. Pain,1, ∗W.N. Catford,1,2N.A. Orr,2J.C. Ang´ elique,2N.I. Ashwood,3V. Bouchat,4N.M. Clarke,3N.
Curtis,3M. Freer,3B.R. Fulton,5F. Hanappe,4M. Labiche,6J.L. Lecouey,2R.C. Lemmon,7D. Mahboub,1A.
Ninane,8G. Normand,2N. Soi´ c,3, †L. Stuttge,9C.N. Timis,1J.A. Tostevin,1J.S. Winfield,1, 2and V. Ziman3
1Department of Physics, University of Surrey, Guildford, GU2 7XH, UK
2Laboratoire de Physique Corpusculaire, ENSICAEN et Universit´ e de Caen, IN2P3-CNRS, 14050 Caen Cedex, France
3School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK
4Universit´ e Libre de Bruxelles, CP226, B-1050 Bruxelles, Belgium
5Department of Physics, University of York, Heslington, York, YO10 5DD, UK
6Electronic Engineering and Physics, University of Paisley, High Street, Paisley, Scotland, PA1 2BE, UK
7CCLRC Daresbury Laboratory, Daresbury, Warrington, Cheshire, WA4 4AD, UK
8Insitut de Physique Nucl´ eare, Universit´ e Catholique de Louvain, Louvain-la-Neuve, Belgium
9Institut de Recherche Subatomique, IN2P3-CNRS/Universit´ e de Louis Pasteur, BP28, 67037 Strasbourg Cedex, France
(Dated: February 4, 2008)
The breaking of the N=8 shell-model magic number in the12Be ground state has been determined
to include significant occupancy of the intruder d-wave orbital. This is in marked contrast with all
other N=8 isotones, both more and less exotic than12Be. The occupancies of the 0¯ hω νp1/2-orbital
and the 1¯ hω, νd5/2intruder orbital were deduced from a measurement of neutron removal from a
high-energy12Be beam leading to bound and unbound states in11Be.
One of the principal aims of present day nuclear struc-
ture research is to understand the evolution of shell struc-
ture with increasing asymmetry in the neutron-to-proton
ratio.In this context the N=8 isotonic chain, which
spans from22Si via the doubly magic N=Z16O to the
two-neutron halo system11Li and the unbound10He, is of
considerable interest. Indeed, the N=8 shell closure, that
is clearly evident close to stability, disappears amongst
the lightest of these nuclei. In particular, the halo struc-
ture of11Li is enhanced by a strong ν(1s1/2)2intruder va-
lence neutron configuration . Similarly, recent experi-
ments [2, 3, 4, 5] have confirmed earlier work [6, 7, 8, 9]
in which it was concluded that the12Be ground state
is formed from both the “normal” closed shell ν(0p1/2)2
valence configuration and the intruder ν(1s0d)2configu-
rations. The factors producing these intruder configura-
tions appear to include a reduction in the p−sd shell gap
as the dripline is approached, an increase in the monopole
pairing energy and deformation . The deformation is
also believed to be related to the tendency towards alpha-
particle clustering  in the Be isotopes.
for configuration mixing involving the ν(1s1/2)2and
ν(0p1/2)2valence neutron configurations in the ground-
state , model predictions indicate that a substantial
ν(0d5/2)2admixture (∼30-50%) should also be present
[10, 12, 13, 14, 15]. In the experiment of Navin et al.,
11Be core fragments in either the Jπ= 1/2+ground state
or the bound 320 keV 1/2−excited state were detected
. These states have large overlaps with the pure single-
particle states ν(1s1/2) and ν(0p1/2) respectively [16, 17].
The measurement of ref.  was, however, not sensitive
to the ν(0d5/2)2component as the removal of a 0d5/2
neutron leaves11Be in the ν(0d5/2) single-particle state
high-energy single-neutronremoval (or
12Be has provided direct evidence
(Ex = 1.78 MeV, Γ = 100 keV) [16, 18], which is un-
bound to neutron emission and decays to10Be(g.s.)+n.
It is thus necessary to design an experiment to detect
both the10Be fragment and the neutron and then to re-
construct their relative decay energy from the measured
momenta. This was the approach adopted in the present
work. Further, to assist comparisons with theory and the
earlier work, the ability to detect11Be in the first excited
state (via the 320 keV gamma-ray) was included.
A secondary beam of12Be (∼5000 pps) was prepared
using the LISE3 spectrometer at GANIL and the reaction
of a 63 MeV/nucleon18O beam on9Be. The average12Be
beam energy was 39.3 MeV/nucleon at the centre of the
carbon secondary reaction target (183 mg/cm2).
beam purity was 95% with the remaining 5% being6He
and15B. Owing to the poor emittance of the secondary
beam, the spot size on target was ∼10mm diameter and
the incident ions were tracked event-by-event using two
position-sensitive drift chambers located upstream of the
carbon target. The point of impact was thus determined
∼1 mm at the target. The measured time-of-
flight through the LISE spectrometer allowed the12Be
ions to be selected uniquely event-by-event from the rest
of the beam particles and also provided a measure of the
energy with a resolution of 1.6% (FWHM).
All charged particles emerging from the carbon tar-
get close to zero degrees, including the unreacted beam,
were recorded in a telescope subtending ±9◦in the hor-
izontal and vertical planes. This was composed of two
50×50 mm2500 µm thick silicon strip detectors to mea-
sure the energy loss (∆E1,2), followed by a 4×4 array of
16 CsI stopping detectors (E) 25 mm thick . The tele-
scope array was calibrated using “cocktail” beams con-
taining all relevant isotopes of Be, with several spectrom-
eter settings to span the energies of interest. Using ∆E1,2
and E, all observed isotopes of H, He, Li, Be and B were
clearly resolved. The silicon detectors also provided ver-
tical and horizontal position measurements, which were
combined with the drift chamber data to determine the
scattering angle with a resolution 0.7◦(FWHM).
Coincident γ-rays were recorded using 4 NaI detectors
mounted around the target at angles of ±45◦and ±110◦
to the beam, with a total absolute photopeak efficiency
of 3.5% for detection of Doppler-shifted 320 keV γ-rays.
Neutrons were detected using the DEMON array of
91 liquid scintillator modules  located between 2.4 m
and 6.3 m downstream of the carbon target and spanning
angles out to 32◦. The neutrons were distinguished
from γ-rays using standard pulse-shape discrimination
and their energies (En) were derived via the time-of-flight
with a resolution ∼5%. Neutrons with En ≤ 15 MeV,
originating from the target, were excluded in the analysis.
In addition to the measurements with the carbon tar-
get, data were also acquired with no target. This de-
termined the background arising from12Be beam parti-
cles that passed through the target and reacted in the
telescope. Such events gave a degraded energy signal
and could be misidentified as11Be or10Be. As in previ-
ous experiments , the target-out measurements were
made with the beam energy lowered to account for the
average energy loss in the target. The background from
reactions in the telescope precluded an accurate measure-
ment of the yield to the11Be ground state . For the
excited states, however, coincident detection of a γ-ray
or neutron reduced substantially the background (down
to 50 and 60 % of the target-in data for the bound and
unbound states respectively).
The background subtracted, Doppler corrected γ-ray
spectrum, measured in coincidence with11Be ions in the
telescope, is shown in Figure 1. The cross section for pro-
duction of the 1/2−state in11Be (see Table I) was ex-
tracted after taking into account the experimentally mea-
sured γ-ray detector efficiencies, attenuation in the target
and the relativistic focussing of γ-rays in the laboratory
frame (β ≃ 0.28c). The cross section measured here at
39.3 MeV/nucleon is compatible with the value measured
previously at 78 MeV/nucleon with a Be target , as
interpreted below using an eikonal reaction model. The
longitudinal momentum distribution of the11Be*(1/2−)
fragments was also measured, giving a FWHM of 137(21)
MeV/c, in agreement with the value ∼150 MeV/c esti-
mated from ref. .
Kinematic reconstruction of unbound states in11Be
was performed from the measured momenta of coincident
10Be ions and neutrons. The procedure was verified 
by reconstructing the well known ground state resonance
of7He from6He + n coincidences. The relative energy
(Erel) spectrum for10Be + n, after background subtrac-
tion, is shown in Figure 2. This has been corrected for
the intrinsic efficiency of the DEMON detectors but not
for the geometrical acceptance. A peak is clearly evident
0 100 200 300400
FIG. 1: Background subtracted, Doppler corrected γ ray en-
ergy spectrum, in coincidence with11Be fragments following
the reaction of12Be (39.3 MeV/nucleon) on a carbon target.
The full line is the result of a Gaussian fit, with an exponen-
tial background. From this, the cross section shown in Table
I was deduced for11Be in the first excited (1/2−) state.
at ∼ 1.3 MeV, corresponding to the decay of the 1.78
MeV (5/2+) state in11Be. There is also another peak
apparent near 2.2 MeV, corresponding to decay of the
2.69 MeV (3/2−) state . The very narrow peak near
threshold is compatible with decay from a state at ∼4.0
MeV in11Be to the first 2+state in10Be at 3.37 MeV.
The ground state branch of this decay corresponds to the
peak at Erel∼3.5 MeV; its inclusion improves the fit, but
the magnitude of neither peak is well defined by the data
for this ∼4.0 MeV state. However, good candidates exist
for such a state in11Be [18, 24].
The detection efficiency for neutrons from11Be* decay
is determined in part by their laboratory angular distri-
bution, which in turn depends on the decay energy to
10Be + n and also the spread in momentum induced by
the initial neutron removal from12Be. Detailed simu-
lations were performed , including the effects of the
geometric acceptance of the neutron detector array, the
energy and angular straggling of charged particles, the
energy loss in the target, and the divergence and energy
spread of the beam. The effects of the telescope resolu-
tion and efficiency were also included, along with the ab-
sorption of neutrons by the telescope (a 10% effect ).
The momentum spread arising from the neutron removal
was determined from the measured angular distribution
of neutrons from the very low energy decay of11Be*(4.0
MeV) to10Be*(2+, 3.37 MeV) + n (cf. Figure 2), where
the neutron momentum distribution was dominated by
that of the11Be* before decay. The detection of a fast
neutron (En>15 MeV) from the breakup of12Be, mea-
sured in coincidence with a10Be from the subsequent
decay of11Be* was also simulated.
Simulations were performed for the decay of the un-
bound states in11Be below 4 MeV (isotropically in the
Total Efficiency (%)
FIG. 2: (color online). Relative energy spectrum of10Be +
n (lower panel) where the solid points represent the exper-
imental data. The histogram depicts the result of the full
simulation; the line-shapes of the individual components of
the simulation are shown (see text). The 1.78 MeV state in
11Be is clearly visible at Erel ≈ 1.3 MeV (Sn = 0.50 MeV).
The resolution in Erel varies as a0E1/2(where a0 is a con-
stant), and at 1 MeV is ∼400 keV (FWHM). The upper panel
depicts the simulated array efficiency.
11Be rest frame), including the decay from the ∼4 MeV
state to the 2+state in10Be, and also the detection
of neutrons diffracted from12Be in coincidence with a
10Be core. The simulated events were analyzed in the
same manner as the experimental data. The resulting
Erelline-shapes (Fig. 2) were least-squares fitted to the
experimental distribution and, using the detection effi-
ciency determined from the simulations (Fig. 2, upper
panel) the cross sections for the different states were de-
termined. As a consistency check, the11Be transverse
momentum distribution (from10Be+n), and the neutron
reconstructed from the simulated events, and in both
cases the agreement with experiment was very good. The
simulated “hit” efficiency for neutrons was checked and
agreed with the value determined by fitting and integrat-
dΩto within 1%.
The cross section extracted for the production of the
1.78 MeV 5/2+state is included in Table I, along with
that for the 2.69 MeV 3/2−state and the bound 1/2−
state. The estimated uncertainties include contributions
from statistical fitting plus uncertainties in the efficiency
corrections, target thickness and background subtrac-
dΩin coincidence with10Be were
tion. The cross section for diffractive breakup to produce
a bound11Be (either 1/2+or 1/2−) and a fast neutron
was also extracted and was 46 ± 10 mb.
The measured neutron removal partial cross sections
from12Be can be interpreted in terms of spectroscopic
factors using a reaction model. The spectroscopic fac-
tors listed in Table I are, except for the 1/2+state, the
ratio of the experimental (σexp) to the eikonal model par-
tial cross section (σsp). For the 1/2+state, the measure-
ment of diffractive breakup of12Be to the two bound
11Be states has been used, with the 1/2−contribution
being subtracted according to its theoretical diffraction
cross section (see Table I) and the spectroscopic factor of
0.44±0.08found here. Note that the uncertainties quoted
for Sexpin Table I do not include any contribution arising
from the assumptions in the reaction calculation, where
for example two-step processes are not included, and it
is estimated that this implies an additional uncertainty
of up to 20% (which is consistent with ref. ).
The present reaction analysis follows closely the
eikonal model of Refs. [3, 26].
matrix was computed from the target density and the
JLM effective nucleon-nucleon interaction . The usual
real and imaginary part scale factors (λV = 1.0, λW =
0.8) were applied to the optical potential. The matter
densities for12C and10Be were of harmonic oscillator
and Gaussian form, respectively, with rms radii of 2.4 fm
and 2.28 fm. For the 1/2+, 1/2−and 5/2+(particle)
transitions, (10Be+n) composite core-target S-matrices
were constructed from those of10Be and the neutron .
In the (unbound) 5/2+case, a separation energy of 0.01
MeV was used to compute the S-matrix. For the 3/2−
(hole) state, a Gaussian (mass 11) core density of rms ra-
dius 2.54 fm was used, representative of the size of12Be.
The removed-nucleon single-particle overlaps were taken
as eigenstates of Woods-Saxon potentials, with geometry
r0=1.25 fm and a=0.7 fm, and with depths adjusted to
the physical separation energies for each final state.
Our observation of the 5/2+state in knockout from
12Be is the first direct experimental evidence for a sig-
nificant d-wave intruder component in any N=8 isotone.
Barker  first pointed out that the observed lowering
of the 1s1/2and 0d5/2neutron orbitals in11Be should
lead to strong admixtures of both these orbitals in the
ground state of12Be and concluded [6, 7] that as little
as 20-40% of the12Be ground state might comprise the
0¯ hω ν(0p1/2)2configuration. For11Li, this model also
successfully predicted a strong 1s1/2strength admixture
in the ground state.
The (1s0d)2contribution to the12Be ground state was
deduced in an indirect fashion by Fortune et al.  in the
light of their measurements of τ1/2and E(2+
[8, 28]. Indeed, according to subsequent psd-space shell
model calculations, the β-decay from the12Be ground
state is quenched to an extent that places an upper limit
of 35% on the 0¯ hω component of the wavefunction .
The neutron-target S-
TABLE I: Cross sections for states in11Be produced via neutron removal from12Be on a carbon target at 39.3 MeV/nucleon
(present work) compared with reaction calculations and previous work at 78 MeV/nucleon on9Be. Uncertainties for Sexp are
experimental only (for comparison, ref.  values have been adjusted to remove the assumed 20% theory uncertainty).
0.42 ± 0.05
0.37 ± 0.07
[0.56 ± 0.18]b
0.44 ± 0.08
0.48 ± 0.06
0.40 ± 0.06
32.5 ± 6.1
30.3 ± 4.0
22.6 ± 4.1
auncertainties do not include contribution from theoretical model of reaction mechanism, estimated to be ±10-20%.
btotal σexp not measured, but σdiff = 46 ± 10 mb for 1/2+and 1/2−together and Sexp deduced from this (see text).
The12O-12Be Coulomb energy difference also supports
shell breaking of this order .
The magnitude of shell breaking observed in the
present work can be quantified by comparing with theory.
Table I includes spectroscopic factors (WBT2) based on
the shell model calculations reported in ref. , which
correspond to a mixing of 32% 0¯ hω (0p8) and 68% 2¯ hω
to the value 2.0 that would be expected in the sim-
plest picture.These values are scaled by 0.8 to give
WBT2′(which is consistent with other knockout work
) and this reproduces the present experimental re-
sults very well. Also listed for comparison, the EXC2
values from a 3-body model including10Be core excita-
tion  give good agreement with the present work while
reproducing other features of12Be.
Recently, Iwasaki et al. inferred the disappearance of
the N=8 shell gap in12Be from both the deformation
length derived from inelastic proton scattering to the 2+
state , and the low energy and large B(E1;0+→ 1−)
for the 1−
1state . Their deductions agreed in detail
with the psd shell model calculations [13, 29], concluding
that the 0p1/2and 1s1/2orbitals are effectively degener-
ate for12Be, just as they are in11Be.
Consistent theoretical results are obtained using nu-
clear field theory , which predicts both the presence
of large ν(0d5/2)2strength in12Be and its absence in11Li,
in agreement with Barker  and with a recent theoreti-
cal analysis  of11Li reaction data . It is interesting
to note that the early work of Barker  also predicted
a low-lying 0+
recently been observed, at 2.24 MeV .
Thus, the neutron shell breaking observed at N=8 for
12Be, but not14C, is similar to the breaking of N=20
for32Mg but not34Si. In each case, when the proton
j>orbital is full, the neutrons are magic. When protons
are removed, the full j<orbital for neutrons is no longer
magic, the next shell intrudes and deformation results.
In conclusion, one-neutron removal cross sections from
12Be to the 0.32 MeV (1/2−) and 1.78 MeV (5/2+) states
in11Be have been measured. From these and eikonal
The sum of these is close
2state at 2.35 MeV in12Be which has only
model calculations, spectroscopic factors were deduced.
These indicate strong breaking of the N=8 magic number
in12Be, including a significant d-wave component. This
is distinct from other N=8 isotones and is the first direct
experimental confirmation of the predictions of a number
of structure models.
The authors wish to acknowledge the support provided
by the technical staff of LPC and GANIL. Partial sup-
port through the EU Human Mobility programme of the
European Community is also acknowledged.
∗present address: Rutgers University, c/o Physics Divi-
sion, Oak Ridge National Laboratory, TN 37831-6354.
†present address: Rudjer Boˇ skovi´ c Institute, Bijeniˇ cka 54,
HR-10000 Zagreb, Croatia
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