$^{12}$C+$^{16}$O sub-barrier radiative capture cross-section measurements

Abstract

We have performed a heavy ion radiative capture reaction between two light
heavy ions, $^{12}$C and $^{16}$O, leading to $^{28}$Si. The present experiment
has been performed below Coulomb barrier energies in order to reduce the phase
space and to try to shed light on structural effects. Obtained $\gamma$-spectra
display a previously unobserved strong feeding of intermediate states around 11
MeV at these energies. This new decay branch is not fully reproduced by
statistical nor semi-statistical decay scenarii and may imply structural
effects. Radiative capture cross-sections are extracted from the data.

Full text

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arXiv:1107.1124v1 [nucl-ex] 6 Jul 2011
12C+16O sub-barrier radiative capture cross-section measurements
A. Goasduff1,2,a, S. Courtin1,2, F. Haas1,2, D. Lebhertz3, D.G. Jenkins4, C. Beck1,2, J. Fallis5, C. Ruiz5, D. A. Hutcheon5,
P.-A. Amandruz5, C. Davis5, U. Hager5, D. Ottewell5, and G. Ruprecht5
1Universit´ e de Strasbourg, IPHC, 23 rue du Loess 67037 Strasbourg, France
2CNRS, UMR7178, 67037 Strasbourg, France
3GANIL, CEA/DSM-CNRS/IN2P3, Bd Henri Becquerel, BP 55027, F-14076 Caen Cedex 5, France
4Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom
5TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T 2A3 Canada
Abstract. We have performed a heavy ion radiative capture reaction between two light heavy ions,12C and
16O, leading to28Si. The present experiment has been performed below Coulomb barrier energies in order to
reduce the phase space and to try to shed light on structural effects. Obtained γ-spectra display a previously
unobserved strong feeding of intermediate states around 11 MeV at these energies. This new decay branch is
not fully reproduced by statistical nor semi-statistical decay scenarii and may imply structural effects. Radiative
capture cross-sections are extracted from the data.
1 Introduction
The isotope28Si can be considered as a key nucleus to un-
derstand the coexistence between mean field effects and
cluster structures. Indeed different structures coexist in its
excited states even at low excitation energies. Recent anti-
symmetrized molecular dynamics (AMD) calculations for
28Si [1] have shown that cluster structures such as12C-
16O or24Mg-α may have large contributions for normal-
deformed and superdeformed states, respectively. By us-
ing the heavy-ion radiative capture (HIRC) mechanism in
which the compoundnucleus decays solely by γ-ray emis-
sion we have investigated the12C-16O cluster structure in
28Si. Moreover this mechanism will directly populate28Si
at energies where the calculated nuclear matter densities
have similar asymmetries as the12C+16O reaction [2].
Theexcitationfunctionof12C+16Oexhibitsnarrowres-
onances [3] around the Coulomb Barrier (VB∼ 7.8 MeV).
These resonancesare correlatedin all reactionchannelsin-
cludingtheHIRC.BayeandDescouvemont[4]haveshown,
using GCM calculations, that for the similar system12C+
12C,severalobservedresonancescanbeinterpretedinterms
of molecular resonances. Although HIRC is a rare process
compared to the dominant fusion-evaporationchannels (n,
p, α), γ-decay will favourably populate states with large
structural overlaps with the entrance-channel thus allow-
ing us to try to identify the possible cluster states.
2 Experiment
OurexperimentalprogramisfocusedonthestudyofHIRC
in the12C+12C and12C+16O [5,6] systems. The present
ae-mail: alain.goasduff@iphc.cnrs.fr
12C(16O,γ) reaction has been performed at the TRIUMF
facility (Vancouver, Canada). A16O ISAC beam has been
used at two resonant energies down to 15% below VB(Elab
= 1.07 and 0.96 AMeV) on high purity (99.9%)12C thin
(50 µg.cm−2) targets. The DRAGON recoil separator has
been used at 0◦to select the28Si recoils. We have used
the BGO array to record the γ-rays in coincidence with the
heavyrecoilsidentifiedinaDSSSDplacedattheDRAGON
focal plane.
3 Results and discussion
3.1 γ-ray decay
Fig. 1 displays the highest energy γ-ray in each γ-event
recorded in the BGO array in coincidence with the28Si
for the two studied energies. Both spectra show the same
global structure. Concerning the region above 17 MeV, the
direct transition to the ground state (g.s.) contributes to the
bump above 20 MeV but due to the response function of
the spectrometer and the deviation out of 0◦of the recoils
inducedbyhighenergyγ-rayemissionveryfewrecoilsen-
terDRAGON. Thefeedingofthe2+
resonances is also observed (Eγ0∼ 21 MeV) at both ener-
gies. Forthe lowest energywe also have a γ-line around18
MeV correspondingto the feeding of the 4+
Concerning the low energy part of the spectra, the de-
cay of the two first excited states of the28Si can be identi-
fied (Eγ0= 1.78 and 2.84 MeV). The decay of the prolate
head band 0+
around 5 MeV but this line does not correspond to a sin-
gle state decay. We observe also the decay of the 3−
g.s. which contributes to the γ-line at 6.8 MeV, a direct
1(1.778MeV)fromthe
1(4.617 MeV).
3(6.690 MeV) to the 2+
1contributes to the line
1to the

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(MeV)
0
γ
E
05 1015 2025
Normalized Counts
0
20
40
60
80
100
120
140
160
= 6.6 MeV
c.m.
E
= 7.2 MeV
c.m.
E
Fig. 1. Highest energy γ-ray spectra in coincidence with28Si for
the12C+16O reaction at Ec.m.= 6.6 MeV (dashed line) and Ec.m.=
7.2 MeV (full line). Spectra are normalized to the same integral.
decay from the resonance is also observed for the two en-
ergies. It has been shown at higher energies [5] that this
first state of negative parity in28Si is crucial to understand
the γ-spectra.
Due to the low resolution of the BGO γ-array and the
large number of states in28Si around 10 MeV, the large
bumpbetween10and15MeVwithcorrespondtothefeed-
ing of intermediate states around 8-13 MeV cannot be dis-
cussed in terms of the feeding of particular states. More-
over in this region the transitions from the resonances and
the subsequent decays to the g.s. are quite close in en-
ergy. This previously unobserved γ-flux at these reaction
energies has to be linked to what has been observed at
higher energies (Ec.m= 8.5, 8.8 and 9.0 MeV) [5], where
the bump was around 14 MeV. Taking into account that
in our previous experimental campaign the28Si was pop-
ulated at higher excitation energies (E∗∼ 25.3, 25.6 and
25.8 MeV), than in the present experiment (E∗∼ 23.3 and
23.9MeV),theobserveddifferencesonthebumpcentroids
are only resulting from the differences in entrance-channel
energies.
) h
l (
02468 10
(%)
fusion
σ
/
lσ
0
5
10
15
20
25
= 6.6 MeV
c.m.
E
= 7.2 MeV
c.m.
E
Fig. 2. Spin distributions normalized to fusion cross-sections ob-
tained by CCFULL [8] calculations for the two studied energies:
red triangles correspond to Ec.m.= 6.6 MeV and blue squares to
Ec.m.= 7.2 MeV.
(MeV)
0
γ
E
05 10 15 2025
Normalized Counts
0
50
100
150
200
/ndf = 13.24
2
χ
= 6.6 MeV
c.m.
E
(MeV)
0
γ
E
05 10 15 2025
Normalized Counts
0
50
100
150
/ndf = 9.01
2
χ
= 7.2 MeV
c.m.
E
Fig. 3. Highest energy γ-ray spectra in coincidence with28Si for
Ec.m.= 6.6 MeV (full line) Ec.m.= 7.2 MeV (full line) compared
to fully statistical decay (red dashed line) using the spin distri-
butions given in Fig. 2. Simulation spectra are normalized to the
data integrals.
In order to fully understand the decay pattern of the
resonances and see if we have a structural effect which
will favourably feed particular states, we compared our γ-
spectra to GEANT simulations with different conditions
in the entrance-channel.All simulations include 68 known
boundor quasi boundstates of28Si between0 and 13 MeV
andtheirγ-decays.Abovetheparticlethreshold(∼10MeV
for the lowest one, in this case α+24Mg) we have selected
states with a large Γγcomparedto particle emission. To es-
timate the branching ratios of the entrance-channelto each
of these states we have used Weisskopf estimates and the
reported average strengths of electric and magnetic transi-
tions in28Si [7]. In this self-conjugate nucleus (Tz = 0),
some particular selection rules on isospin apply for L=1,
∆T=0 transitions: E1 are forbidden and M1 strengths are
reduced by a factor of 100. As we use an entrance-channel
with T = 0 in all simulations, these rules will strongly in-
fluence the obtained γ-spectra.
Wehavefirstsimulatedafullystatisticalscenario,which
consists of a spin distributionin the entrance-channel.Spin
distributionsforthetwostudiedenergiesaregiveninFig.2.
These distributions are the results of coupled-channel cal-
culations, performed with the CCFULL code [8], and are
obtained by adjusting the diffuseness parameter (a =0.57
and 0.55 for Ec.m.=6.6 and 7.2 MeV) in order to reproduce
the fusioncross-sectionsfrom[11] andgiveninFig. 7. The
two curves are normalized to the calculated fusion cross-
sections. Below VB, phase space is reduced and spin dis-
tributions are quite narrow and centered at low spin (2+)

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FUSION11
compared to what was obtained at higher energies for the
12C+16O reaction [5].
Simulated spectra (dashed lines) are given in Fig. 3
along with experimental data (full lines). For the two ener-
gies we globally reproducethe γ-spectrum shape. Indeed a
large bump between 11 and 15 MeV dominates the spec-
trum. However lookinginto the details we see that this sta-
tistical scenariois unableto reproducethe intensities ofthe
different transitions between the low-lying states. Another
discrepancy concerns the high energy part of the simula-
tions where the direct feedingof the two first excited states
isoverestimated.Concerningtheintermediateregionofthe
spectra the bump is better reproduced for the highest en-
ergy. For the lowest energy, the fully statistical model has
too large branching ratios to states lying below 10 MeV.
(MeV)
0
γ
E
05 101520 25
Normalized Counts
0
50
100
150
200
Experimental
= 1J
= 2J
-
π
+
π
Fig. 4. Highest energy γ-ray spectrum for Ec.m.= 6.6 MeV (full
line) compared to decay scenarii with two different spins in the
entrance-channel: 1−(red dashed line) and 2+(red dotted line).
Simulations spectra are normalized to the data integral.
As the studied energies correspond to resonant ener-
gies, we used another scenario which consists of a unique
spinintheentrance-channel.Asthespindistributionsgiven
in Fig. 2 show that entrance-channel spins greater than 5?
have very small contributions to the fusion cross-sections,
we limit the discussion here to entrance spins less or equal
to 4?. Fig. 4 displays the simulation results for resonances
Jπ= 1−and 2+and their comparison with the lowest en-
ergy data. As for the first scenario, we see that we overall
reproduce the shape of the spectrum with the negative par-
ity entrance spins, even if the bump seems to be shifted.
Again this is due to too large branching ratios to states ly-
ing below the fed states in the experiment and has to be
interpreted in terms of structural effects. In the case of a
positive parity resonance the large γ-flux going directly to
the g.s. and the 2+
MeV and gives rise to a completely different γ-spectrum.
In order to have a objective criterion to compare simu-
latedandexperimentalspectraweusedtheso-calledχ2test
of homogeneity. Evolution of the χ2versus the resonance
spinforthetwostudiedenergiesis giveninFig.5.Looking
at the two curves on Fig. 5, we observe a kind of oscilla-
tion between even and odd spins. This can be understood
1depletes the region around Eγ0= 12
) h
(
resonance
J
01234
/ ndf
2
χ
0
5
10
15
20
25
= 6.6 MeV
c.m.
E
= 7.2 MeV
c.m.
E
Fig. 5. χ2variation as a function of the spin of the entrance-
channel, red triangles correspond to Ec.m. = 6.6 MeV and blue
squares to Ec.m.= 7.2 MeV.
by the fact that for the even spins, corresponding to posi-
tive parity in the entrance-channel,decays to the low-lying
states of positive parity are mainly achieved by E2 transi-
tions which are not slowed down by any selection rules in
this nucleus.
(MeV)
0
γ
E
05 1015 20 25
Normalized Counts
0
50
100
150
Experimental
-
= 3
= 2
π
J
J
+
π
Fig. 6. Highest energy γ-ray spectrum for Ec.m.= 7.2 MeV (full
line) compared to decay scenarii with two different spins in the
entrance-channel: 3−(red dashed line) and 2+(red dotted line).
Simulations spectra are normalized to the data integral.
For the highest energy for which results are given in
Fig. 6 the same discussion can be held. The difference is
that a Jπ= 3−resonance in the entrance-channel repro-
duces the data better than a Jπ= 1−. But as for the lowest
energy, data are better reproduced with entrance-channel
odd spins. Branching ratios to negative parity states from
annegativeentrancespinareexpectedtobefavoredagainst
branching ratios to positive parity states in resonance γ-
decay. This is partially reproduced by the semi-statistical
scenario. We already stressed the importance of particu-
lar negative states such as the 3−
tive parity state, at higher energies. As the phase space is
reduced due to the reduction of the bombarding energy,
1which is the first nega-

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EPJ Web of Conferences
this particular decay may be more important in the two
explored energies than in our previous experimental cam-
paign.
3.2 Radiative capture cross-section
The previously unobserved large feeding of intermediate
states around 11 MeV allows us to reevaluate the radiative
capture (RC) cross-section measured in Ref. [10].
σRC=
Nr
Nt· Ni· Ta
·
1
ǫdet
· 1024
,
(1)
in which the cross-section, σRC, is given in barn. Nr, Nt
and Nicorrespond, respectively, to the number of28Si re-
coils observed at DRAGON focal plane (±10%), the num-
ber of12C atoms/cm2(±10%) in the target and the number
of incident16O per second (±10%). Tadenotes the time
with beam on target reduced by the data acquisitions dead
time (8 and 17 % for the lowest and highest explored en-
ergies, respectively) and is known with an error of ±5%.
ǫdetstands for the detection efficiency which takes into ac-
count the DSSSD detection efficiency (96.2 ± 0.1%) [9],
the28Si8+charge state fraction which corresponds at both
energies to 35% and finally the acceptance and the trans-
port efficiency of DRAGON. This third parameter can be
extractedusingtheGEANTsimulationswiththebestagree-
ment with data and corresponds to 32% (resp. 36%) for
Ec.m.= 6.6 MeV (resp. 7.2 MeV). The error on the accep-
tance and the transport through DRAGON is of the order
of 15%.
(MeV)
c.m.
E
6.57 7.588.59
(mb)
fus
σ
-1
10
1
10
2
10
3
10
b)
µ
(
RC
σ
-1
10
1
10
2
10
3
10
fus
σ
σ
RC
7.8 MeV
≈
B
V
Fig. 7. RC cross-sections (blue filled circles) along with fu-
sion cross-sections (red crosses) [11]. Error bars for the fusion
cross section correspond to the size of the red crosses. RC cross-
sections above VBare from a previous study [5].
The obtained cross-sections are given in Fig. 7 along
with data from our previous study [5] above VB(Ec.m=
8.5, 8.8 and 9.0 MeV) and fusion cross-section at these en-
ergies extracted from [11]. For the two recently explored
energies RC cross-sections are lower than 1 µb. Further-
moreexcitationfunctionslopesshowthatRC cross-section
tends to decreasefaster than the fusioncross-sectionbelow
VB. Indeed at Ec.m.= 9.0 MeV RC cross-section represents
∼ 10 × 10−5of the fusion cross-section, this ratio falls to
∼ 2 × 10−5for the two energies discussed in this paper.
4 Conclusion
We have performed a heavy ion radiative capture reaction
between two light heavy ions,12C and16O, leading to28Si
at two resonantenergies below VB. Obtained γ-spectra dis-
play a previously unobserved strong feeding of interme-
diate states around 11 MeV at these energies. This new
decay branch has to be compared to the feeding of the
same region observed at higher energies, in order to ob-
tain the evolution of the direct feeding of the different28Si
known states from the entrance-channel. As the new de-
cay branch can not be fully reproduced by statistical nor
semi-statistical decay scenarii this may be the signature of
structural effects. With the upcoming new scintillator gen-
eration, such as the PARIS project [12], a sufficient res-
olution will be achieved in order to disentangle the feed-
ing of intermediate states around 11 MeV contained in the
large bump. New Monte-Carlosimulations with other con-
ditions such as calculated branching ratios with a cluster
model for the entrance-channelhave to be tested to see if a
better agreement with the data can be achieved.
GEANTsimulationshavebeenusedtoextracttheDRA-
GON spectrometer acceptance which is crucial to obtain a
value for the radiative capture cross-sections. If new decay
scenarii can reach better agreement with data, error bars
on capture cross-section will be reduced. This will lead to
a better understandingof the fusion reactionbelowVBand,
more particularly, for astrophysical energies where new
resonances have been observed mainly in the neighbour-
ing12C+12C system in the vicinity of the Gamow window
[13].
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