fulltext

Resonances in the

C(

C,

Be

)

O reaction and rotational

states in

Mg

)

M. LATTUADA(1)(2), E. COSTANZO(1)(2), A. CUNSOLO(1)(2), A. FOTI(1)(2)

S. ROMANO(1)(2), C. SPITALERI(1)(2), A. TUMINO(1)(2)

D. VINCIGUERRA(1)(2)and M. ZADRO(3)

(1) Istituto Nazionale di Fisica Nucleare, L.N.S. and Sezione di Catania - Catania, Italy (2) Universit`a di Catania - Catania, Italy

(3) Rudjer Boˇskovi´c Institute - Zagreb, Croatia

(ricevuto il 3 Agosto 1997; approvato il 15 Ottobre 1997)

Summary. — The results of a set of experiments on the12C+12C!8Beg :s:

+16O

excitation function between 20 and 36 MeV c.m. beam energy are summarized and discussed. A set of 1 MeV wide resonances shows up in the energy range investigated, all of them following the rotational rule with a coefficient of inertia consistent with a

,16O,configuration.

PACS 25.70.Ef – Resonances. PACS 21.60.Gx – Cluster model. PACS 27.30 –20A38.

PACS 01.30.Cc – Conference proceedings.

1. – Introduction

When speaking of12C+12Cresonances, the starting point is often the historical data

by Almqvist et al. [1], first evidence for intermediate width resonances in heavy-ion colli-sions, interpreted as due to the formation of a dinuclear system in rotational states. Since then a lot of experimental and theoretical work has been done on quasi-molecular reso-nances in light-medium ion collisions (see, for example, ref. [2, 3]). Special attention has been devoted to the12C+12Csystem, which is still able to show unexpected features.

The data showed here are connected with recent experimental evidences on the excitation function of the12C+12C ! 12C(0+2)+12C(0+2) ! 6reaction around 32.5 MeV c.m.

energy, which in a first interpretation were considered as an indication of the formation of a linear-chain state in24Mgat 46.4 MeV [4].

( 

)Paper presented at the 174. WE-Heraeus-Seminar “New Ideas on Clustering in Nuclear and

Atomic Physics”, Rauischholzhausen (Germany), 9-13 June 1997.

two ’s, the so-called configuration, at an energy close to the energy of the Wuosmaa resonance, thus suggesting the possible competition of24Mg decay into many channels with different degrees of deformation.

From these indications it seemed to us interesting to study the excitation function of another exit channel of the12C+12Cinteraction, which could be related to theD1

config-uration, namely the8Beg :s:

+16Og :s:one.

2. – Experiments and data analysis

Several experiments were performed in different times and with different detection setups, using12C beams accelerated by the SMP Tandem Van de Graaff of Laboratorio Nazionale del Sud, Catania, and natural C targets of thickness ranging from 100 to 300

g/cm2.

All the experiments were performed by using silicon Position Sensitive Detectors (PSD) arranged in different ways. Some of the data showed here were collected by iden-tifying16O by means of ionization chambers placed in front of PSDs. In this case the wide

8_{Be first excited state gives some background under the ground state peak and the}

exci-tation energy spectrum is complicated by the presence of peaks due to the exciexci-tation of both8Be and16O (the last one under the threshold for-decay). Other data were taken

by identifying8Beg

:s:ions by means of the same telescopes. In this case it was the locus

in theE-
E plane corresponding to the 2-particle detection of a8Beg

:s:ion near the Z =3locus. Lithium ions produced in the12C+12Cinteraction have low energy and do

not overlap the events due to the simultaneous detection of the-particles produced by

the decay of8Beg

:s:, at least when the recoil

16Oion is left at the lower excited states. Then

the8Bespectrum is cleaner, but there is again a limitation in the16Oexcitation energy.

A third way of measuring the final state under consideration consisted in the coincident detection of each of the two-particles emitted by8Beby each of the two halves of a Dual

PSD (DPSD). The8Beis clearly identified from the relative energy spectrum of the two

-particles, as it is shown in fig. 1. In this case the whole accessible16Oexcitation spectrum

is unambiguously measured (fig. 2). In the last two cases detection efficiency has been calculated and data have been corrected accordingly. Of course, in both cases, efficiency for detection of higher excited states of 8Beis very poor, because of the much larger

gs

Fig. 1. –-relative energy spectrum as measured by means of a Dual Position Sensitive Detector.

A first experiment [11] was performed at three energies on the top and on both sides of the 32.5 MeV resonance. The result could not be taken as evidence of the resonance but was consistent with its shape. Also the angular distributions showed the same feature of the ones reported in ref. [4] and needed the contribution of several Legendre polynomials to be described. Nevertheless the dominance of spin 16 could be deduced from those data, in agreement with the value deduced in ref. [4].

These results showed that the24Mgexcited around 46 MeV could decay both into the

12C(0+2)+12C(0+2)and into the8Be+16Osystems with a much higher cross-section in

Fig. 2. – Typical16O excitation spectrum deduced from the detection of8Beg

:s:by means of a Dual

Fig. 3. – Excitation function of the12C(12C;8Beg :s:

)16Og

:s:reaction averaged over the c.m. angular

range between73 

and106 

.

the latter case. This difference may be understood as due to the mismatch of 6 units (10 againstLgraz=16) of angular momentum for the first case compared with the almost full

matching in the case of8Beg :s:

+16Og :s:.

Further measurements were then performed in the 27 to 36 MeV c.m. energy range with steps of a few hundreds keV [12] . The data confirmed that a resonance at 32.5 MeV is actually present also in this exit channel, but its width turned out to be a factor 4 less than in the12C(0+2)+12C(0+2)channel, as it was in the meanwhile found by the Strasbourg

group [9] from the reanalysis of old data. Another surprising result of our experiment was the presence of a second peak around 28.7 MeV with the same width.

Extension of the experiment down to 20 MeV c.m. energy [13] showed that these two peaks were not isolated and revealed a very structured excitation function with a number of intermediate width peaks.

The full excitation function measured in all these experiments is reported in fig. 3. The data from different runs are normalized separately and they show a fair internal consistency.

One of the necessary conditions to say that a resonance is associated with a quasi-molecular configuration is the possibility of finding an unique value of the angular mo-mentum for such a resonance, or at least a value of the angular momo-mentum which is dom-inant. Note that, since both final nuclei have spin zero in our case, their relative angular momentum is just the spin of the emitting nucleus.

One way to assign the spin to a resonance consists in comparing the periodicity of the angular distribution on resonance with the periodicity of single Legendre polynomials. We applied this method, but also we checked the results in the region of 20 to 30 MeV, where the peaks are superimposed to a remarkable background, by making use of another approach able to bring a deeper information.

gs

Fig. 4. – Comparison among the excitation functions integrated over small intervals around the angles where Legendre polynomials of orderLvanish (L=12;14;16;18).

of the argument and in some cases these zeroes are well separated. From our data we could extract the excitation functions in small angular ranges around the zeroes of Leg-endre polynomials of order 12 to 18, which is the range of the expected24Mgspins at such

excitation energies. If a peak is dominated by a value J of the angular momentum, it is expected to disappear (or to be strongly depressed) in the excitation function integrated around the angle for which the Legendre polynomial of orderJ has a zero (fig. 4).

Such kind of analysis brings to assignment of a dominant spin value to each of the 6 structures present in this region of excitation energy. Furthermore it suggests the pres-ence of a resonance around 26.5 MeV which is not clearly seen in the integrated excitation function.

These results together with those obtained on the same reaction at lower energies by other authors [14-17] are summarized on theEc

:m:vs.

J(J+1)plane of fig. 5 and show

a fair consistency with the linear rule typical of rotational bands. Note that a correspon-dence between these states and states excited in some inelastic channels of the12C+12C

reaction can be found [13]. Around 25 MeV, the energy where a broad resonance was ob-served by Rae and Keeling [18], we find a less dominant peak. The same value 14 of spin is assigned by our analysis. The difference in cross-sections may be due to the different angular ranges explored in the two experiments.

The slope coefficient (90 keV) deduced by a linear fit to our data gives a moment of

inertia of the system which is just the one calculated for a D1 configuration.

The correlation among different final states of this reaction leading to different exci-tations of the16O



Fig. 5. – _cm vs. plot of the intermediate width resonances found in the excitation function of the12C+12C!8Beg

:s: +16Og

:s:reaction. The present data are reported together with previous

data available in the literature.

unresolved doublets around 6 MeV(0+;3 ,

)and 7 MeV(2+;1 ,

). At excitation energies

larger than 7 MeV the large background due to the opening of three-body channels pre-vents the extraction of reliable information from the excitation functions.

No clear correspondence has been found between the resonances present in these ex-citation functions and those relative to the ground state (fig. 6). On the other hand the contribution of states with different spins and different configurations makes the interpre-tation of these structured exciinterpre-tation functions harder. One can speculate that the known 4p-4h configuration of the 6.05 MeVO+state well fits with a picture where one of the

in-teracting12C ions picks up onefrom the other

12_{C. In this case, at least the resonances}

in the first doublet excitation function might be understood as due mainly to this compo-nent of the doublet. Unpublished data by Lee et al. [19] seem on the contrary to be in favour of a larger contribution of the3

,

state to the peak in this energy range. 3. – Conclusions

In conclusion, the excitation function of the12C+12C ! 8Beg :s:

+16Og

:s:reaction

between 20 and 36 MeV c.m. energy shows a set of resonances which can be related to the decay of24Mg states associated with the so calledD1configuration. The 32.5 MeV

resonance is also present and probably represents the upper excited state having such configuration. A value around 16 is indeed predicted as limit for the angular momentum of theD1configuration [5].

In spite of the large experimental information now available on the decay of24Mg at 46.4 MeV into many channels, a consistent interpretation is still lacking. The formation of a linearchain invoked to describe some of the characteristics of the12C(0+2)+12C(0+2)

exit channel is inadequate when less deformed nuclei are produced as for example16Oor

even12C(3 ,

1). And the recent results on the presence of a resonance at the same energy

also in transfer reaction channels involving non-nuclei [10] open new question marks in

gs

Fig. 6. – Comparison of the excitation function of the12C(12C;8Beg :s

:)16Oreactions between 20

and 30 MeV for the ground state and the first two doublets of the recoil16O.

Moreover Baye and Herschkovitz [20], following the evolution of a system of two

-particles (the simplestlinear chain), found the disappearance of the configuration in

less than210 ,22

s and predicted even shorter lifetimes for longer chains, which casts doubts on their observability.

The Cranked Cluster Model has been recently revised by Rae and Merchant [21]. In the interaction of the two12C, both can be excited to their3

,

state to form a24Mgstate.

Different ways of breaking up of this configuration lead to different final states, among which the16O+8Bechannel is also predicted. Following this approach the resonance has

to be seen as an entrance channel effect which populates a special state, whose evolution can lead to a number of exit channels according to the different ways of breaking up.

It is worth mentioning also the improvement of the Band Crossing Model by the Kyoto group [22] with the introduction of a density dependent potential with realistic12Cnucleon

density. The change of mass distribution and thus of moment of inertia with increasing angular momentum generates a crossing of many12C



-12C 

bands with the elastic molec-ular one, allowing for prediction of resonances in the corresponding exit channels. The complexity of the experimental information now available requires the extension of these calculations to configurations other than the12C



-12C 

one, in order to get an unified de-scription of the formation and decay of these resonances.

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