INTERMEDIATE STRUCTURE ASPECTS OF THE REACTION 12C(16O, α)24Mg

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INTERMEDIATE STRUCTURE ASPECTS OF THE REACTION 12C(16O, α)24Mg

J. Gastebois

To cite this version:

J. Gastebois. INTERMEDIATE STRUCTURE ASPECTS OF THE REACTION 12C(16O,α)24Mg.

Journal de Physique Colloques, 1971, 32 (C6), pp.C6-57-C6-62. �10.1051/jphyscol:1971608�. �jpa- 00214826�

JOURNAL DE'.PHYSIQUE Colloque C6, supplkment au no 11-12, Tome 32, Novembre-Dkcembre 1971, page C6-57

INTERMEDIATE STRUCTURE ASPECTS OF THE REACTION 12C(' 60, a ) 2 4 M g

J. GASTEBOIS

DCpartement de Physique NuclCaire C . E. N. Saclay, France

Rksum6. - Des structures globales, corrkl6es entre elles, ont ete observees dans les fonctions d'excitation de la reaction lZC(l60, a)24Mg, conduisant a des Ctats de 24Mg jusqu9B 22 MeV d'excitation. L'existence d'etats intermediaires dans 28Si, ayant un spin BlevC, ou une structure particuliere, de type quasi molkulaire ou B plusieurs agregats, est discutee.

Abstract. - Gross, correlated structures have been observed in the excitation functions of the reaction ^12C(l60, a)24Mg, lcading to a number of states, up to 22 MeV excitation in 24Mg.

The possible occurrence of intermediate states in 28Si, having high spin or a particular structure, quasi molecular, or of sevcral-a-cluster type, is discussed.

The heavy ion beams available from Van de Graaff tandem accelerators since around 10 years have allowed the experimental study of complex systems, such as 12C

+

+

+

of the first results is the observation, by Almqvist and coll. in 1960 [I], of resonances in the elastic scattering of 12C by 12C, at incident energies around the Cou- lomb barrier. This phenomenon was then attributed to a repulsive effect due to the Pauli principle, as the two ions approach each other. At higher incident energies, the measurements of excitation functions for both the elastic channel and the alpha-particle emission channels do not reveal any cross correlation, and were successfully described as statistical fluctuation phe- nomena [2], [3].

Concerning the ¹⁶⁰

+ 12c

In that last case, the incident energy range corresponds to excitation energies between 26 and 35 MeV in the compound nucleus "Si, and their measurements were limited to final states i n 2 4 ~ g of lip to 6.44 MeV excitation. The theoretical analysis of the data leads to a coherence width of

-

The study of that reaction (160

+

+

Pennsylvania group [7] and by the Yale group [8], as reported here in Pr. Middleton's and Pr. Bromley's talks. A new aspect of the problem is given by the results that we have obtained in Saclay [9]. Our study was suggested by the comparison of two spectra, shown on figure 1 and figure 2.

Figure 1 shows a spectrum obtained in bombarding a 12C target with an 1 6 0 beam at 50.67 MeV, and looking at alpha particles emerging at O,,, = 150. One observes the same kind of selection as in [7], but the relative intensities are somewhat different. For instance, the peak corresponding to the 15.15 MeV level is quite strong, and was very weak in Middleton's experiment. The same remark applies to levels around 20 MeV excitation in 24Mg. For comparison, Mid- dleton's experiment - using an incident 12C beam

-

would have correspond to a slightly lower incident energy for an incident 160 beam - only 48 MeV -

and t o backward angles in our experiment.

Figure 2 shows a similar result for a slightly higher incident energy - 52.67 MeV instead of 50.67 MeV -

That corresponds to a small difference of 860 keV in the C . M. system. New levels have shown up while others have almost disappeared. The cross sections for the 15.15 and 16.55 MeV levels, which were the highest ones at the previous energy, have considerably de- creased. One gets an idea of that decrease in looking at the ratio of the peaks over the continuous back- ground. This background is mainly due to three-body reactions, and its differential yield has been found roughly constant within that energy range. So, the main conclusion is the very fast variation of cross sections with incident energies.

Then we decided to explore a wide region of incident energies - between 45 and 59 MeV lab. - above the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971608

J. GASTEBOIS OUTGOING A L W -PARTICLE ENERGY ( M e V )

E h = 50.67 MeV

EXCITATION ENERGY IN ( M U )

FIG. 1. - Experimental spectrum obtained at @lab.

-

OUTGOING MFiiA WRTICLE ENERGY ( M e V )

1500

2 W Z

5 6

'2

%

8 _m I, t

EXCITATION ENERGY IN 2 4 ~ 9 ( M eV)

FIG. 2. - Experimental spectrum obtained at 0lab.

-

INTERMEDIATE STRUCTURE ASPECTS OF THE REACTION 12C(J60, a)24Mg one already explored by Halbert and coll. [5], [6] and

extending the final state spectrum up to -- 25 MeV iqgZ4Mg.

In order to somewhat smooth out the statistical fluctuations, we used a rather thick target

-

-

-

These are excitation functions for 10 final levels in 24Mg, each one corresponding to measurements at 52 different energies.

''c 1160, N 0 ' ~ ~

FXCITAllON FUNCTIONS

l X C l l A l l O N ENERGY IN

..

3.6 8 . 0

"

,

. ,.

FIG. 3. - Excitation functions of the reaction 1'C(160, a)"Mg for 10 levels, at Blab.

-

Data corresponding to 2 4 ~ g ground state and first excited state have not been obtained, due to too small cross-sections. The observed bumps have usually a width of 300 to 400 keV. One can see a clear corre- lation between the curves corresponding to the 8.12 MeV level ^- 6' member of the ground state rota- tional band - and t o the 11.88 MeV level - spin and parity are unknown. The 13.18 MeV level is the 8' member of the ground state rotational band, but the corresponding curve does not look like the two previous ones. The curves corresponding to the 15.15 MeV and 16.55 MeV levels have their maxima and minima at the same energies in the middle part of the energy range.

In order to see whether there is or not an underlying gross structure, we have averaged these results over 1 MeV (C. M.). We then got the curves shown in figure 4.

'Zr. ('Cc,oc12"*

CXClTAilOh FUNCTIONS AVERASED WER IMtV

FIG. 4. - Excitation functions of the reaction 12C(160, a)24Mg, for 10 levels, at Blab. = I j n , averaged over 1 MeV.

One clearly sees a wide structure on most curves.

The widths of such bumps are between 1 and 2 MeV.

There is again a clear correlation between curves corresponding to the 8.12 MeV and 11.88 MeV levels, together with the 20.91 MeV level. Two wide bumps appear at the same energies. And, in their upper part, the 15.15 and 16.55 MeV curves exhibit the same behaviour.

I must mention that anomalies are also observed in the elastic channel, as well as in two inelastic channels, as shown in figure 5.

The angles are around 1300 C. M. One sees a deep minimum in the elastic scattering, together with a bump in each inelastic curve. Some correlation seems to exist between the position of these anomalies, and some of those observed in the alpha-particle excitation functions, and one must point out that the observed widths are again between 1 and 2 MeV.

Now, to get an idea of the physical reasons of such phenomena, we will try t o review different arguments.

First of all, we have to remember the statistical fluctuations observed by Halbert and coll. [5], [6] at lower incident energies, for excitation energies in 28Si lower than 35 MeV, and for only the six lowest states in 24Mg. We are forming "Si between 36 and 41 MeV excitation. It is reasonable to expect a coherence width slightly larger than the one they got, i. e. larger than 120 keV. In fact, Stokstad and coll. [lo], from Yale, have measured excitation functions with a thin target, for C. M. energies between 20 and 21.5 MeV, and they have observed a width of about 200 keV. So we are quite far from the 1 to 2 MeV width of the gross structure. The probability for chance occurrence of such a wide bump in one given excitation function is not negligible. According to a calculation done by P. P. Singh and coll. [ll], it is about 0.3. But the probability to observe a bump in two different curves, and at the same energy, is reduced to about 3 x

EXCITATION ENERGY IN *%i ( MeV)

3 8 39 4 0 d l

I t I I 1 1

I

FIG. 5. - Excitation function of elastic and inelastic scatte- ring of 1 6 0 from I 2 C . The outgoing I 2 C particles were detected

a t @lab. = 15O.

So, we cannot explain the gross structure within the framework of the S-matrix formalism used to analyze statistical fluctuations.

But one has to be very careful. Indeed, according to Moldauer [12], if one uses the R-matrix formalism, in connection with the fact that we are dealing with strongly absorbed particles in both entrance and exit channels, then the probability to observe widths several times larger than the individual level width can be much higher. In other words, when the trans- mission coefficients are well described by a sharp cut-off model, we may select a few states in the com- pound system, each one having a well defined total angular momentum, and being associated with a well defined partial wave in the incident channel. And Moldauer concludes that these states can be observed as wide intermediate resonances of well defined spin and parity, occurring at the same energy in several exit channels. That possibility has been already pointed out by Halbert and coll. [ 5 ] , [6], as an attempt to explain the anomaly that I have previously mentioned.

Unfortunately, that formalism does not allow to calculate the spin and parity of these states, and not even their energy. Are they, for instance, high spin states ? Indeed, the L-values available in the entrance channel allow to build spin values up to -- 14 units

in the compound system. One could then suggest that 38 MeV in 28Si is an energy close to the yrast line for spin J = 14, which means a region where the density of J ⁼ 14 levels is low. So these levels, when they are formed, would show up as isolated resonances. And as shown by T. D. Thomas [13] at least for heavier nuclei, there is a large increase of alpha-particle emission near the yrast line. So they would decay toward high spin states in 24Mg.

Moreover, one has to explain other experimental results, such as the following, shown in figure 6. This spectrum has been obtained by Middleton and coll. [I41 and shows the alpha-particle spectrum at 7 1/20 (lab.) for the reaction ^{1 4}

+

+

+

Furthermore, the available L-values may be somewhat lower than in ^{1 6 0}

+

EXCITATION ENEROY I MeV1

DISTANCE ALONG PLATE I c m l

FIG. 6. - Experimental spectrum of the reaction '4N(14N, x)24Mg obtained at E ~ s b . = 28 MeV (courtesy of

R. Middleton et a].).

Others results have also been obtained in Saclay, by Mme Conjeaud and coll. [15]. They looked at reactions such as 12C i- 24Mg + a

+

''C

+

incident energies as well as available angular momenta are quite similar to the ¹⁶⁰

+-

+

Then we feel that some argument is missing, and that the differences observed between all these reac-

INTERMEDIATE STRUCTURE ASPECTS OF THE REACTION 12C(160, a)2JMg C6-61

tions may be due to differences in the structure of configuration of lZC. Here, quantitative calculations the colliding nuclei. are lacking so far. So, let us assume that:

Let us try, first, to describe the reaction 1 6 0

+

u

+

-

9 MeV. So their kinetic energy decreases by the same amount, from its value 22 MeV, down to 13 MeV.

This is too small an energy to break an ^l60 nucleus into 4 alpha particles - one needs.

-

but high enough for the breaking of the 12C nucleus into 3 alpha-particles - one needs only -- 7.3 MeV.

So the ¹⁶⁰ nucleus would not see a 12C nucleus as a whole, but rather 3 loosely bound alpha clusters, each one having a kinetic energy between 1 and 2 MeV.

Such an entrance channel could have a large overlap with an intermediate state described as three alpha- clusters around an 1 6 0 ground state core. The exis- tence of such kind of doorway state has been already suggested by Michaud and Vogt [16] in 1969, as a way to explain the close spacing of the cr molecular states >> observed in I2C-12C elastic scattering just below the Coulomb barrier. But, in that case, not enough energy is available to break up a 12C nucleus into three alpha clusters.

The existence of rather simple intermediate states has also been predicted in the framework of the two center shell model, applied by K. Pruess and W. Grei- ner [17] to ion-ion collision. They note that when the interaction time is of the same order of magnitude as the typical nucleon orbital time, then only a few nucleon transitions are allowed to take place during the collision. So the configurations that can be reached are those which differ from the elastic configuration

- described by the two center shell model - by only a few nucleon excitations. These configurations can be observed as doorway states strongly coupled not only to the elastic channel, but also to non-elastic channels whose configurations are closest to the one of the doorway state. In that theory, it is just the time which prevents the formation of a more or less statistical compound nucleus. An immediate consequence of the model is that the existence of such doorway states depends sensitively on the ratio of collision energy to nucleon binding energy, and is then strongly shell dependent. Unfortunately, four nucleon cluster states do not seem to be favoured in any obvious way.

Concerning the structure of possible intermediate states around 38 MeV in 2 8 ~ i , a description is propo- sed by Arima and coll. [18], in the framework of the quartet model. They, calculated that the lowest three quartet configuration must occur around 30 MeV in 28Si. Of course, a lot of other three quartet configu- rations can be built at higher excitation energies, and their selection in 12C bombardment would be determined by the overlap with the (1 s ) ~ (I p)4 (1 p)4

1. we are looking at the lowest three quartet confi- guration in 28Si.

2. among all the three configurations available around 38 MeV in "Si, the maximum overlap with the incident channel is obtained for that previous one.

Then, as shown in figure 7, Arirna and coll. [18]

have calculated that the energy of that configuration

- 3 quartets raised from the (2 s, 1 d) shell to the (2 p, 1 f) shell - decreases when one goes to heavier nuclei. That would explain the negative results obtai- ned for the reactions 12C

+

+

+

+

+

t

FIG. 7. - The excitation energies E* of quartet states are plot- ted as a function of mass number for the even-even N = Z nuclei from 12C to s2Fe. The circles denote states with quartets excited from the (0 p) to the (0 d, 1 s) shell, the triangles denote states with quartets excited from the (0 p) to the (0 f, 1 p) shells, and the squares denote states with one quartet excited from the (0 p) to the (0 f, 1 p) shells. A solid line connects states in which one quartet of a particular type is excited, and the dash- dot line connects states in which three quartets of a type are excited. Only states with at most three quartets excitcd from one major shell to the next major shell are plotted, and states with only one quartet excited from the (0 p) to the (0 f, 1 p)

shells are plotted.

C6-62 J. GASTEBOIS

excited by the electromagnetic field than 1 6 0 , s o that the description of the entrance channel must include some superposition of several excited states.

In conclusion, I might say that the study of reac- tions induced by heavy ions could be a way t o find new kind of doorway states and new simple structures in nuclei, namely those where certain multi-nucleon correlations have t o be provided by the entrance channel t o make up a finite width of the doorway into this channel. But one obviously needs many more experimental results as well as further theoretical calculations, namely numerical studies of concrete experimental cases.

Note added in proof. - It is quite remarkable that all excitation functions drop around 23 MeV incident C . M. energy, and exhibit n o more structure for ener- gies higher than 24 MeV. A very similar behaviour is observed in the excitation functions of 1 6 0 - 1 6 0

elastic scattering [19], for incident C. M. energies around 32-34 MeV. It is of interest to note that both

phenomena could be explained in a very similar way, if we suppose that the intermediate structure is d u e to doorway states consisting of a n ¹⁶⁰ core inter- acting with 3 alpha-clusters - in the ¹⁶⁰

+

or 4 alpha-clusters - in the 1 6 0

+

-

+

+

-

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Phys. Rev. Letters, 1960, 4, 515.

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