Observation of bound excited states in 15B

Abstract

The structure of the A/Z = 3 nucleus 15B has been investigated using the in-beam
g\gamma
-spectroscopy technique with a fragmentation reaction of a 36S beam on a 9Be target at 77.5
MeVA{\rm MeV}\cdot A
. The fragments were identified and selected by their energy loss and time of flight using the SPEG spectrograph.
g\gamma
-ray energies and intensities have been measured in coincidence with the projectile-like fragments. From this information as well as from the
gg\gamma\gamma
-coincidence relationships a level scheme is proposed for 15B up to the neutron separation energy. The experimental results have been interpreted using shell model calculations in the psd valence space. Effects of the weakly bound nature of the valence neutrons have been observed.

Full text

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DOI 10.1140/epja/i2004-10078-8
Eur. Phys. J. A 22, 5–8 (2004)
THE EUROPEAN
PHYSICAL JOURNAL A
Letter
Observation of bound excited states in15B
M. Stanoiu1, M. Belleguic1, Zs. Dombr´ adi2,a, D. Sohler2, F. Azaiez1, B.A. Brown3, M.J. Lopez-Jimenez4,
M.G. Saint-Laurent4, O. Sorlin1, Yu.-E. Penionzhkevich5, N.L. Achouri6, J.C. Ang´ elique6, C. Borcea7, C. Bourgeois1,
J.M. Daugas4, F. De Oliveira-Santos4, Z. Dlouhy8, C. Donzaud1, J. Duprat1, S. Gr´ evy6, D. Guillemaud-Mueller1,
S. Leenhardt1, M. Lewitowicz4, S.M. Lukyanov5, W. Mittig4, M.G. Porquet9, F. Pougheon1, P. Roussel-Chomaz4,
H. Savajols4, Y. Sobolev5, C. Stodel4, and J. Tim´ ar2
1Institut de Physique Nucl´ eaire, IN2P3-CNRS, F-91406 Orsay Cedex, France
2Institute of Nuclear Research, H-4001 Debrecen, Pf. 51, Hungary
3NSCL, Michigan State University, East Lansing, MI 48824-1321, USA
4GANIL, B.P. 55027, F-14076 Caen Cedex 5, France
5FLNR, JINR, 141980 Dubna, Moscow region, Russia
6Laboratoire de Physique Corpusculaire, F-14050 Caen Cedex, France
7IFIN-HH, P.O. Box MG-6, 76900 Bucarest-Magurele, Romania
8Nuclear Physics Institute, AS CR, CZ-25068, Rez, Czech Republic
9CSNSM, IN2P3-CNRS and Universit´ e Paris-Sud, F-91405 Orsay Campus, France
Received: 4 May 2004 / Revised version: 2 September 2004 /
Published online: 19 October 2004 – c ? Societ` a Italiana di Fisica / Springer-Verlag 2004
Communicated by J.¨Ayst¨ o
Abstract. The structure of the A/Z = 3 nucleus
spectroscopy technique with a fragmentation reaction of a
The fragments were identified and selected by their energy loss and time of flight using the SPEG spectro-
graph. γ-ray energies and intensities have been measured in coincidence with the projectile-like fragments.
From this information as well as from the γγ-coincidence relationships a level scheme is proposed for15B
up to the neutron separation energy. The experimental results have been interpreted using shell model
calculations in the psd valence space. Effects of the weakly bound nature of the valence neutrons have been
observed.
15B has been investigated using the in-beam γ-
36S beam on a
9Be target at 77.5 MeV · A.
PACS. 25.70.Mn Projectile and target fragmentation – 23.20.Lv γ transitions and level energies – 27.20.+n
6 ≤ A ≤ 19 – 21.60.Cs Shell model
The structure of very neutron-rich nuclei came into
the focus of interest, because some novel structural ef-
fects are expected in some of these exotic nuclei. Among
others, the structure of neutron-rich boron isotopes at-
tracted attention in the last decade mainly because the
odd-proton boron nuclei represent weakly bound systems.
In the early experimental studies of heavy boron nuclei,
their ground-state properties were primarily investigated.
By measuring an increased interaction cross-section in rel-
ativistic nuclear reactions [1], the existence of a neutron
skin or halo could be demonstrated also in the15B isotope
with A/Z = 3. The increased neutron radius is considered
as a typical consequence of the weak binding and of the
large neutron excess. These features, typical for drip line
nuclei, may have consequences also on other properties of
nuclei, like the energies of the excited states.
ae-mail: domb@atomki.hu
Concerning the excited states in15B, several unbound
states could be revealed by use of multi-nucleon trans-
fer reactions [2]. According to preliminary reports, γ-rays
indicating the existence of bound excited states were ob-
served in15B from in-beam γ-ray spectroscopy with frag-
mentation reactions [3,4].
Theoretical predictions on the structure of neutron-
rich boron nuclei are different from one approach to
another. For instance, the antisymmetrized molecular-
dynamics model (AMD) [5] suggests a transitional, de-
formed structure for15B, while shell model calculations
predict a much smaller value of the moment of inertia
which can be associated with a more moderate deforma-
tion [6,7].
We have developed the method of in-beam γ-ray spec-
troscopy of projectile fragmentation reaction in GANIL in
order to study the structure of neutron-rich nuclei [8,9].

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6The European Physical Journal A
This method has been applied to investigate several nu-
clei in the region of the N = 28 shell closure like the
45,46Ar [10],43,45Cl [11], and40,42,44S nuclei [12] via frag-
mentation of the48Ca beam. The fragmentation of the36S
beam has been applied to obtain information on the sub-
shell closures at N = 14,16 [13]. In the same set of data
we could extract information on the bound excited states
of14,15B. In the present paper we report on the results
obtained on the structure of these nuclei.
A36S16+beam of 77.5 MeV · A energy and 15 enA
intensity was fragmented on a9Be target of 2.77 mg/cm2
thickness. The emerging15B fragments were detected by
the SPEG magnetic spectrometer. Ionization and drift
chambers, as well as a plastic scintillator were placed at
its focal plane, which provided data on the energy loss,
total energy, and time of flight of the fragments. The frag-
ments were identified by use of a standard ∆E–time-of-
flight method. The time of flight was taken from the tim-
ing signals in the plastic scintillator with respect to the
cyclotron radio frequency. It was corrected from the po-
sition of the fragments in the focal plane of the SPEG
spectrometer to obtain a better time resolution and sub-
sequently a better identification of the nuclei. Altogether
43 different isotopes have been identified in the experi-
ment. We have collected 6 · 105 14B and 9 · 104 15B nuclei
in the spectrograph.
The γ-rays emitted in flight by the excited fragments
were detected by the 74 BaF2detectors of the “Chateau
de crystal” and 4 hyper pure Ge detectors of 70% relative
efficiency. The BaF2crystals were mounted symmetrically
above and below the target at a mean distance of 21 cm
covering about ∼ 80% of the total solid angle. The spec-
tra obtained in the BaF2 detectors situated at forward
angles (smaller than ∼ 40◦) were found to contain a large
background due to fast neutrons emitted in break-up reac-
tions. These spectra were not used in the analysis in order
to improve sensitivity by raising the signal-to-noise ratio
in the γ-ray spectra. As the detectors were closely packed,
the γ-rays could easily scatter from one to another. To de-
crease the background caused by the scattered γ-rays we
used the array in anti-Compton mode, by rejecting all the
events where at least 2 neighboring detectors have fired
at the same time. Due to the relatively high efficiency of
the BaF2array of about 20% at 1.3 MeV, for the stronger
transitions, γγ-coincidence techniques could be exploited.
The Ge detectors were placed at about 16 cm from the
target at the most backward angles of 162◦and 145◦with
respect to the beam direction. The total efficiency of the
Ge spectrometer was ∼ 0.12% at about 1300 keV.
The γ-ray spectra were corrected for the Doppler shift
caused by the large fragment velocity (v/c = 0.34). For a
raw Doppler correction the beam speed and the geomet-
ric detector positions were used. Two corrections were ap-
plied to this transformation: first, a mass-dependent cor-
rection was used, which takes into account that the av-
erage speed of the fragments depends on the number of
nucleons removed. According to the reaction theory, the
energy transfer has a linear mass dependence. To deter-
mine the parameters of the linear function, we fitted a
010002000
Eγ (keV)
30004000
0
40
80
120
654(5)
Counts
14B
Fig. 1. The γ-ray spectrum of
36S beam obtained by use of Ge detectors is shown.
14B from fragmentation of a
line to the energies of γ-rays known precisely from previ-
ous studies. Second, to compensate for the statistical un-
certainty in the speed of a given isotope arising from the
statistical nature of energy transfer in the fragmentation
reaction, the information on the momenta of the fragments
provided by the SPEG spectrograph was applied similarly
to the correction used in the time-of-flight method. Using
these corrections, we applied a slightly mass-dependent
internal energy calibration and in this way corrected for
the systematic errors caused by different geometrical un-
certainties. As a result, the energies of 30 known lines in
the 200–3700 keV energy region of 17 different isotopes in
the A = 10–32 mass region were reproduced with less than
4 keV RMS deviation by use of the Ge detectors. There-
fore, a 4 keV systematic error was assigned to their energy
determination. For the BaF2 array, less peaks could be
used for internal calibration due to the lower energy reso-
lution. The energy of 14 transitions in the 900–3700 keV
energy region has been reproduced within a 26 keV RMS
deviation for the BaF2setup.
The quality of the Doppler correction influenced also
the resolution of the spectrometers especially for the BaF2
array, where spectra from a wide angular range were
added. After the above corrections a full width at a half-
maximum (FWHM) of ∼ 38 keV was obtained at the γ-
ray energy of ∼ 1500 keV in the Ge detectors and a 12%
energy resolution was achieved with the BaF2array.
As a typical γ spectrum, we show the Ge spectrum of
14B in fig. 1. In the spectrum we can see a single γ line at
654 ± 5 keV. The energy of the first-excited state in this
nucleus was adopted as 740 ± 40 keV [14]. In the γ spec-
trum there is no sign of a transition corresponding to the
decay of a state with that energy. On the other hand, the
two energies slightly overlap at the 2σ confidence level,

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M. Stanoiu et al.: Observation of bound excited states in15B7
0200040006000
0
100
200
300
400
500
600
12001800
0
10
Eγ (keV)
1306(43)
Counts
1460
1329(12)
1401(21)
15B
(
)
+46
-80
Fig. 2. γ-ray spectrum of15B by use of BaF2 detectors. In the
insert the same spectrum measured by Ge detectors is shown.
which allows the assumption that these states are the
same. In this case, using the energy values given above
and the 1/σ2weights, the energy of the first-excited state
in14B is 655±5 keV. The two states, in principle, may also
be different due to the different excitation mechanisms ap-
plied in the two studies, although, no other bound excited
state is expected from the psd shell model.
The γ-ray spectrum of15B produced by the BaF2de-
tectors is shown in fig. 2. The spectrum measured by the
Ge detectors is presented as an inset. In the Ge spectrum
of15B a stronger line is present at 1329 keV and there is
an indication for a weaker one at 1401 keV. Due to the
low resolution of the BaF2detectors, these two lines are
seen as a single wide peak in the BaF2spectrum. Knowing
the width of peaks from the systematics of single peaks of
other nuclei, the two lines could be resolved. Their en-
ergies were fitted as 1306 ± 43 and 1460+46
tively. The uncertainties of the energies come from the
uncertainty of the energy calibration (26 keV), the statis-
tical uncertainties of the peak positions (28 and 38 keV,
respectively) and a systematic error caused by the possi-
bility of using different shapes for the background below
the peak. The energies are especially sensitive to the po-
sition where the background is reaching the high-energy
tail of the peak. The deviation of the mean energies de-
duced from the two spectrometers for the higher-energy
γ-ray may suggest that the background has been slightly
underestimated in the fit, which is expressed via the asym-
metric uncertainty of the energy value. The adopted value
of the γ-ray energies can be obtained by use of the energy
values from both types of detectors and the 1/σ2weight-
ing factors (assuming σ = (46 + 80)/2 = 63 keV for the
1460 keV line) at Eγ = 1327(12) and 1407(20) keV. It
−80keV, respec-
02000
Eγ (keV)
4000
0
20
40
60
80
100
1327+
Counts
1407
Gate: 1327+1407 keV
15B
Fig. 3. γγ-coincidence spectrum of15B gated on the 1327 and
1407 keV transitions.
is worth pointing out that the observation of a peak at
∼ 1.35 MeV has been reported in two other experiments
using in-beam γ-ray spectroscopy with double-step frag-
mentation reactions [3,4]. Counting statistics of the BaF2
array was sufficient to extract some information on γγ-
coincidences. By gating on the 1327 + 1407 keV doublet,
it was found that the two lines of the doublet are in coin-
cidence with each other as can be seen in fig. 3. This situa-
tion is confirmed also by the coincidence spectra of ref. [3].
As the intensity of the 1327 keV transition is stronger
than the 1407 keV one, it is assigned to the decay of
the first-excited state to the ground state. The weaker
1407 keV transition is placed on top of the 1327 keV es-
tablishing another state at 2734(32) keV excitation energy.
This state is situated just below the neutron separation
energy of 2770(30) keV [15]. The proposed level scheme
together with the results of the theoretical calculations is
shown in fig. 4.
The ground-state spin and parity of15B were deter-
mined by Sauvan et al. [16] as 3/2−in agreement with
the theoretical expectations. All the theories predict a
5/2−spin-parity value for the first-excited state. This
state can be assigned to the experimentally observed state
at 1327 keV. Among the theoretically predicted low-lying
states, the 7/2−one is expected to feed the 5/2−state via
an M1 transition with higher intensity than a decay to the
ground state through an E2 transition. On the other hand,
the decay of the other possible bound state with spin 1/2 is
expected to feed the ground state with higher intensity via
a high-energy M1 transition branch, and a lower-energy
E2 transition to the 5/2 state would be weaker. Thus, on
the basis of its decay properties the level at 2734 keV may
be a candidate for the theoretical 7/2−state. Using these
tentative assignments, the different theoretical predictions
are compared with each other and with the experimental
results in fig. 4.
The common point in predictions of the different mod-
els is that all of them expect a ground-state band with the
spin sequence 3/2−, 5/2−and 7/2−. This is very likely,
due to the coupling of a p3/2proton hole to the 2+excited

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8The European Physical Journal A
WBT SM
B
WBT* SM AMDExp.
3/2−
15
3/2−
5/2−
7/2−
1/2−
3/2−
0
1630
3020
3950
3900
3/2−
5/2−
7/2−
3/2−
1/2−
9/2−
0
1251
2608
3170
3577
3681
5/2−
3/2−
1/2−
7/2−
5/2−
3/2−
0
1500
2470
3070
3300
630
0
3480
2734
1327
1327 100(9)
1407 41(14)
Fig. 4. Proposed level scheme of
their energies and relative intensities with uncertainties are
given. The results of the shell and AMD model calculations
are included in the right part of the figure. The unbound ex-
perimental state at 3480 keV is taken from ref. [2].
15B. Along the transitions
state in16C, which has an almost pure neutron configu-
ration [17]. As a matter of fact, this coupling produces a
multiplet of negative-parity states with a spin sequence go-
ing from 1/2 to 7/2. The shell model calculation using the
WBT interaction [7] agrees more with the experimental
spectrum than the AMD model. However, the experimen-
tal spectrum is compressed by about 10% as compared
to shell model theory. A similar feature has also been ob-
served in the16–20C isotopes [18]. It can be traced back
to the weakly bound nature and consequently to the rela-
tively large radii of these nuclei [1], as compared to those
for which this interaction was developed. The matrix ele-
ments of the two-body interaction are approximately in-
versely proportional to the squared radius. Therefore, a
simple method for compensation of the effects of weak
binding is to reduce the two-body matrix elements. In this
region, a renormalization of the matrix elements of the sd
shell interaction by a factor of 0.75 was appropriate. The
renormalized interaction is called the WBT* interaction.
Using this modified interaction, the calculated energies of
the members of the ground-state band of15B give a nice
agreement with the experiment, as is shown in fig. 4.
Summarizing our results, we have observed bound ex-
cited states in15B for the first time. Comparing the ex-
perimental energies with those obtained from shell model
calculations it was found that the ground-state band is
more compressed than the calculated one, which could be
interpreted as a consequence of the weakly bound nature
of the valence neutrons in this very neutron-rich nucleus
(A/Z = 3).
The experiment using in-beam γ spectroscopy with fragmen-
tation reactions benefits from the availability of
kindly provided by our colleagues from DUBNA, and from the
smooth running of the accelerator by the GANIL crew. This
work has been supported by the European Community con-
tract No. HPRI-CT-1999-00019, and also from OTKA T38404,
T42733, T46901, PICS(IN2P3) 1171, INTAS 00-00463, RFBR
N96-02-17381a, GA ASCR A 1048 102, and NSF PHY-0244453
grants, as well as from Bolyai J´ anos Foundation.
36S isotope
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