Search for electromagnetic transitions between
12C-
12C cluster states in
24Mg (*)
F. HAAS(1), A. ELANIQUE(1), R. M. FREEMAN(1), C. BECK(1), R. NOUICER(1) D. L. WATSON(2), C. JONES(2), R. COWIN(2), P. LEE(2) and Z. BASRAK(3)
(1) Institut de Recherches Subatomiques, IN2P3-CNRS/Université Louis Pasteur
B.P. 28, F-67037 Strasbourg Cedex 2, France
(2) Department of Physics, University of York - Heslington, York Y01 5DD, UK
(3) Rudjer Boskovic Institute - HR-10001 Zagreb, Croatia
(ricevuto il 4 Agosto 1997; approvato il 15 Ottobre 1997)
Summary. — The superdeformed states in heavy nuclei with A 60 are
characterized by their gamma decay pattern. In light nuclei, this signature is still missing especially for the cluster states formed in light heavy-ion reactions. The aim of the present experiment was thus to search for g-ray transitions between 101and
81resonant states formed in the12C +12C reaction. A bombarding energy of E lab4
32.9 MeV has been chosen to populate a known and isolated 101 resonance. The
experiment has been carried out in a triple coincident mode (fragment-fragment-g) with the outgoing binary fragments detected in two position-sensitive Si detectors and the g rays in the 4p array Château de Cristal. A few events have been observed which we attributed to the g-ray transitions we searched for. This would be the first time that such transitions have been seen and, under certain assumptions, a radiative partial width of (1.2 6 0.4) 3 1025has been deduced for the 101resonant state.
PACS 25.70.Ef – Resonances.
PACS 23.20.Lv – Gamma transitions and level energies. PACS 27.30 – 20 GAG38.
PACS 01.30.Cc – Conference proceedings.
1. – Introduction
Clustering in nuclear physics is strongly connected with the shapes and deformations of nuclei. A large fraction of the experimental and theoretical activity in nuclear physics over the last ten years has been devoted to the study of the
(*) Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.
deformation of nuclei under fast rotation. In the mass region A C150, the existence of superdeformed states, with shapes corresponding to a 2:1 axis ratio, had been predicted and were finally discovered in 1986 in the nucleus 152Dy [1]. Since then a remarkable large amount of results in this field have been published and are compiled in a recent issue of Nuclear Data Sheets [2]. This compilation shows that up to now 150 superdeformed bands have been discovered in four distinct mass regions A C80, 130, 150 and 190. In fact, in some cases, a rather detailed spectroscopy of the “second well” could be performed with, for example, the observation of six different superdeformed bands in the same nucleus152Dy. Concerning deformed nuclei, one should also mention that about 45 fission shape isomers are known in the mass region A 4230 to 245 [2]. The experimental identification of the superdeformed bands relies on their gamma “signature”: a long cascade of accelerated E2 g transitions between the members of a same band.
In light nuclei with A E60 where one would like to connect the cluster states with superdeformed states, the experimental results are rather meagre. Of course in some cases like 20Ne (16O + a) and 18O (14C + a), the existence of a cluster states is well established and relies on the observation of accelerated intraband E2 and E1 transitions, respectively. Concerning the “heavy” cluster states in light nuclei, since 1960 tens of “light” heavy-ion systems have been studied and hundreds of excitations functions measured. Genuine resonances have certainly been observed and we have been able to specify the best conditions for their observation [3], but their structure and the connection between resonances and heavy cluster states could not be firmly established. One of the main reasons is because the gamma “signature” mentioned before is still missing!
For example, the formation of cluster states in 24Mg is well supported by a large number of experimental results pointing to the existence of 12C-12C states in this light nucleus. In particular, the pronounced resonances found in the12C +12C cross-sections of the elastic, inelastic and fusion channels are frequently interpreted in terms of different rotational bands of the superdeformed dinuclear complex. Unfortunately, this explanation is not unique and is still much debated. One unquestionable experimental signature to confirm the existence of such a dinuclear system would be the observation of enhanced E2 g-ray transitions connecting these deformed rotational cluster states. However, the corresponding short-lived resonances are located at relatively high excitation energies well above the particle decay threshold. In fact, even with the enhancement of the radiative width (Gg) due to the large deformation of the system
and anticipating a large decay g-ray energy of 6–7 MeV (Eg5 dependence), Gg is still
expected to be much smaller (C1025–1026) than the particle decay width (G) requiring extremely clean experiments to be performed.
Up to now, only upper limits of Gg/G have been reported for transitions between
states corresponding to the Jp
4 141 and 121 resonances in 12C +12C [4]. These negative results reflect probably both the complex nature of the Jp4 141resonance at
Ec.m.4 25.5 MeV and the different configurations of the two resonances. For these reasons, we have decided to perform our experiment at lower bombarding energies and to search for g-ray transitions between the well-known and isolated 12C +12C 101 resonance [5] at Ec.m.4 16.45 MeV (which has a large Gc carbon decay width) and the
12
C +12C fragmented 81 resonances. These resonances range over the center-of-mass energy interval from Ec.m.4 8.85 to 12.98 MeV corresponding to eventual g-ray transition energies from 7.6 to 3.5 MeV.
2. – Experimental set-up and data reduction
In the present experiment, rare events are searched for and this requires an experimental device allowing for complete identification of the reaction products and also the use of a high detection efficiency 4 p 2g multidetector like the Château de Cristal. A self-supporting carbon target of 20 mg/cm2thickness was bombarded with a 12C beam provided by the Orsay Tandem accelerator. A beam energy of E
lab4 32.9 MeV has been chosen to populate a 101resonance which has been previously observed in the elastic channel [5]. The beam intensity (20 nAe) was limited by the counting rate in the
g array. The charged-particle reaction products were detected in two 500 mm thick Si
Fig. 1. – Mass spectra m3 and m4 of the 12C +12C binary reaction channels at Elab4 32.9 MeV.
Position Sensitive Detectors (PSD) located on either side of the beam axis. The PSDs had an active area of 15 mm 3 45 mm and subtended angles between ulab4 17 7 to 507 and 2647 to 2317, respectively. Coincident g rays were detected in the 74 BaF2 counters of the Château de Cristal, each of them has an hexagonal shape with R410 cm and h 415 cm. The PSDs were mounted in a 35 cm diameter scattering chamber located inside the BaF2shell. Each PSD provides energy E and position u signals for each detected fragment. The coincidence signal between the two fragments served to trigger the Château de Cristal, an event being validated if at least one of the BaF2’s was hit. Twofold fragment-fragment (F-F) and triple or manifold F-F-g coincidences have been stored for subsequent analysis.
The data analysis is based on binary reaction kinematics and allows the masses of the reaction products and the reaction Q value to be determined. Figure 1 displays typical mass spectra obtained in the present work.
The total efficiency of the Château de Cristal has been determined from g rays with energies Eg4 1.63, 2.61 and 4.44 MeV corresponding to the transitions 20Ne 21K 01,
20Ne 41
K 21(a fusion channel) and12C 21
K 01(inelastic channel), respectively. This efficiency is equal to 50 % and is almost constant for Eg between 1 and 5 MeV.
3. – Results and discussions
We will now report on the results obtained for the three main exit channels 20Ne + a, 16O +8Be and 12C +12C of the 12C +12C reaction at E
lab4 32.9 MeV. It is interesting to mention that all the data have been recorded in about five days of beam time.
3.1. The 20Ne + a channel. – At the low incident energy of the experiment, the 12C +12C reaction is dominated by the20Ne + a fusion channel. By choosing m
44 4 (see fig. 1) for this particular channel, the deduced reaction Q value depends only on parameters from the most backward PSD detector in which the energy and position of the a particles are better resolved than those of the 20Ne heavier partner. The corresponding Q value spectrum is shown in fig. 2 and presents about ten well-resolved structures for 20Ne excitation energies between 0 and 12.1 MeV. In the figure, the indicated identifications are based on previous studies on the20Ne spectroscopy [6]. In this nucleus, the threshold energy corresponding to the16O + a decay is located at 4.73 MeV. Thus, all states at excitation energies above C6 MeV, observed in our experiment as binary channels (see fig. 2), are non-natural parity states. We have observed the main decay of these states but the energy resolution of the BaF2 detectors was not sufficient to establish detailed decay schemes. It would be very interesting to study these 20Ne states, located at 6 to 7 MeV above the a decay threshold and which still have large radiative partial widths, by using the now available high efficiency, high-resolution Ge g arrays. Such studies should give us more information on a clustering in20Ne and also on the electromagnetic transition selection rules in this self-conjugate nucleus.
3.2. The 16O +8Be channel. – The reaction Q-value for this a transfer channel has been obtained from the two fragment energies. The corresponding spectrum is represented in fig. 3 and shows all bound states of16O up to an excitation energy of 7.12 MeV. The unbound states at 8.87 ( 22) and 11.03 ( 31) MeV are also seen because they are non-natural parity states.
Fig. 2. – Reaction Q-value of the12C(12C, a)20Ne reaction at E
lab4 32.9 MeV. The spectrum has
been obtained with the fragment-fragment coincidence condition.
In the two channels just discussed, we have not performed an extensive search for the eventual and very weak g-ray transitions of Eg4 6 to 7 MeV connecting the
12C +12C resonant states. The main reasons for this are, in the20Ne + a case, the rather large number of20Ne excited states in the region of interest and, in the16O +8Be case, the strong ground state g transitions of the 16O 6.13, 6.92 and 7.12 MeV states which have energies close to those of the g rays we are looking for. We will now present the results for the12C +12C channel which is much better suited for such a search than the two previous channels.
3.3. The12C +12C channel. – The main result of our experiment is presented in fig. 4 which shows the distribution of fragment-fragment-g coincidences in a Q-value vs. Eg
diagram. This spectrum has been obtained by setting narrow gates on the BaF2timing and mass spectra and by imposing a g-ray multiplicity constraint Mg4 1 . As will be
shown later, this condition was crucial in order to suppress the contribution of events coming from the13C isotope contained in the carbon target. The reaction Q-value was inferred from the summed energy of the two 12C fragments. Three groups of events with Q 40, 2 4.44 and 2 8.88 MeV are clearly apparent, they correspond to the elastic, inelastic (21, 4.44 MeV) and mutual excitation binary exit channels. Events for which the observed energy in the particle and g-ray detectors is equal to the beam energy
Fig. 3. – Reaction Q-value of the12C(12C,8Be)16O reaction at E
lab4 32.9 MeV. The spectrum has
been obtained with the fragment-fragment-g condition.
(within the particle energy and g photo peak resolutions) will fall between the two straight dashed lines (Q 42 Eg6 1.1 MeV) shown in the figure. In particular, the
events of interest, i.e. those for which the 101
K 81 transitions are followed by the elastic break up of the 81states, are expected to fall inside the parallelogram. Thus the window we have chosen corresponds to a Q-value running from 2 6 to 2 7.5 MeV.
We are looking for rare events, so we have to understand as much as possible all events present in the spectrum of fig. 4. The events with EgC 3.5 2 4.5 MeV observed
close to Q C2 3 MeV and to Q between 2 7 and 2 8 MeV arise presumably from the 13C(12C, 13C)12C reaction populating the low-lying states in 13C between 3 and 4 MeV and the 4.44 MeV 12C state. Indeed, the kinematics of the 12C +13C and 12C +12C exit channels are quite similar. Other events with Q between 2 10 and 2 11.5 MeV and Eg
between 6 and 7 MeV are related to the three-body process 16O* + a + a which simulates the kinematics of the12C +12C reaction. In this process, the two a particles are detected in the PSDs and the remaining energy goes undetected in the recoil of16O along the beam axis direction. This recoil energy can be readily calculated to be 4.4 MeV irrespective of the state of16O which is excited. The corresponding measured
g-ray energies come from the excited states between 6 and 7 MeV in 16O. The events with Q 40 are pure random events.
Fig. 4. – Reaction Q-value of the12C(12C,12C)12C reaction at E
lab4 32.9 MeV vs. the fragment g-ray
energies Eg. The spectrum has been obtained with the fragment-fragment-g coincidence condition
and a g multiplicity Mg4 1 condition (see text).
To show how the multiplicity condition affects the events, we have plotted in fig. 5 the projection of the events within the band Q 42 Eg6 1.1 MeV on the Q-value axis for
different Mg conditions: Mg4 1 (a), Mg4 2 (b) and Mg4 all (c). It follows from the
Fig. 5. – Reaction Q-value spectra obtained after projection of the events between the two straight lines (see fig. 4) and with different Mgmultiplicity conditions. Spectra a), b) and c) correspond to
dramatically but also that the events between Q 42 7 to 2 8 MeV disappear completely. A contribution arising from the detection of both 4.44 MeV photons is visible in the mutual excitation line of fig. 4. The Mg4 1 condition implies that both
photons have been detected in the same BaF2. As the total efficiency of each detector is roughly 1%, applying the Mg4 1 condition reduces the intensity in this region by two
orders of magnitude. This is the factor by which we have been able to suppress any contribution from the12C +13C mutual excitation exit channels.
From the discussion above, it has been demonstrated that events shown in the 2D diagram of fig. 4 are quantitatively understood. Furthermore, the region of interest contains 7 counts which we quite confidently ascribe to the process we are looking for,
i.e. the g transitions between the 101 and 81resonant states in the 12C +12C system. From the present measurements, we deduce a mean value g-ray energy for these transitions of EgC 6.9 MeV.
For the resonant state, the ratio of the number of g rays emitted to the number of decays into two12C nuclei in their ground states is given by
Rexp4 Ng( F-F-g) Ng( 21, F-F-g) 3 N( 2 1, F-F) N( 01, F-F) 3 1 e , where
– e is a relative geometrical correction factor between inelastic channels with
Q 42 6.9 and 2 4.44 MeV, respectively;
– N( 01, F-F) and N( 21, F-F) are the yields in the elastic ( 01) and inelastic ( 21) channels for a common detection angular range (uc.m.4 577 to 987) and the coincidence condition fragment-fragment (F-F);
– Ng( 21, F-F-g) is the yield in the inelastic ( 21) channel corresponding to the
coincidence condition fragment-fragment-g (F-F-g) and to the 21region of the Q vs. E
g
band defined by Q 42 Eg6 1.1 MeV (see fig. 4);
– Ng(F-F-g) 47 as shown before.
We finally obtain for Rexpa value of (1.2 6 0.4) 3 1025, where the given error is only statistical.
We will now establish the relationship between R and the radiative partial width of the 101 resonant state. R is the ratio, after corrections for the fragment and g detectors efficiencies, of the events corresponding to the formation of the 101state, its
g decay to the 81state and the12C +12C decay of the 81state (process A) to the events corresponding to the formation of the 101state and its12
C +12C decay (process B). R can be written in the form:
R 4 (Gc/GT) 101 3 (Gg/GT)10 1 3 (Gc/GT)8 1 (Gc/GT)10 1 3 (Gc/GT)10 1 ]process A( ]process B( ,
where Gc is the 12C +12C decay widths of the 81and 101states, GT their total widths and Gg the radiative width of the 101K 81 transition. From this expression of R, we
obtain (Gg/GT)10 1 4 R 3 (Gc/GT) 101 (Gc/GT)8 1 .
The partial Gc/GT widths of the 81 and 101 states are not very well known and we simply will suppose that they are equal. In this case, we have
(Gg/GT)10
1
4 Rexp4 ( 1.2 6 0.4) 3 1025
and Gg( 101K 81) 44.8 6 1.6 eV with GT4 400 keV reported in the literature (see ref. [5] and also the references given therein).
For an E2 transition and a mean g-ray energy of 6.9 MeV, the corresponding reduced width Sg is given by: Sg4 Gg(E2 ) /GW(E2 ) 490630 W.u. For a light nucleus like 24Mg, this E2 strength of the 101 resonant state can be considered as strongly accelerated. In fact, as mentioned before, the resonant states are strongly fragmented and only three 81 states are included in the investigated Q-value interval (2 7.5 to 2 6 MeV), whereas a total number of nine 81resonant states in12C +12C are reported in the literature between Ec.m.4 8.85 and 12.98 MeV [7]. If we assume that all 81states should be equally fed, the preceeding Sg strength has to be multiplied by a factor of
about three (SgC 270 W.u.).
This transition strength is in good agreement with the pioneering theoretical calcu-lations of Chandra and Mosel [8] who have studied the molecular configurations and high spin properties of24Mg by means of the cranking-Strutinsky method using a two-center shell model for the shell model part of the calculations. These authors have predicted a special stable 12C-12C molecular configuration in 24
Mg with a separation distance R 4 4.5 fm which corresponds to a quadrupole moment Q0of 181.5 fm2and, for a 101K 81 transition in a K 40 rotational band, to a reduced Sgtransition strength of 269 W.u.
4. – Conclusion and perspectives
Gamma rays from the three binary20Ne + a,16O +8Be and12C +12C channels of the 12
C +12C reaction have been studied at a bombarding energy of Ec.m.4 16.45 MeV corresponding to a 101 resonance. In the 12C +12C channel, there is evidence for
g-decay between the 101resonant state and 81resonant states around E
c.m.4 9.6 MeV followed by elastic break-up. A radiative partial width (Gg/GT)10
1
4 (1.2 6 0.4) 3 1025 has been deduced and corresponds to strongly accelerated E2 transitions which are quite consistent with a12C-12C cluster configuration of the 101and 81 resonant states in24Mg.
Finally, we would like to draw from the present work proposals for few new experiments to be performed:
– measurements in a systematic and consistent way of the carbon and other cluster widths of12C +12C resonances in general and of the 81and 101resonances, in particular;
– for the resonances studied in this work and also for resonances at energies closer to the Coulomb barrier, measurements of complete g distributions between the initial resonant state and the final fragmented resonant states to deduce the total radiative strength. This implies good resolution and efficiency for both fragment and g detectors;
– search for g transitions between the pronounced and narrow well-known resonances in the24Mg +24Mg and 28Si +28Si systems. Such experiments will however be quite difficult because of the complexity of the fragment Q-value spectra due to the prolific mutual inelastic excitations.
R E F E R E N C E S
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