APH N.S., Heavy Ion Physics 2 (1995) 269-277 HEAVY ION PH Y SIC S ~ Akad~m|ai Kiad£

Cluster Effects in the Angular Distribution of Alphas Scattered from 34S

M.Brenner 1, K.-M. K~illman 1, Z. M•233 2, T. Vertse 2 and L. Zolnai 2

1/~bo Akademi University, FIN-20500 Turku, Finland ~Institute of Nuclear Research of the Hungarian Academy of Sciences H-4001 Debrecen Pf. 51, Hungary

Received 10 October 1995

Abst rac t . The addition of a resonance scattering contribution to the shape elastic scattering improves the fit in analysing experimental angular distribu- tions. Spins from 7 to 10 h characterize the resonances, which have a dominant influence on the six analysed angular �91 of 12.80 to 20 MeV alpha particles elastically scattered from 34S. The relation between the energy of the resonances and their spin compares well with the results from alpha scattering from 28Si. As in the scattering from silicon, the occurrence of a dominating spins supports the assumption that they belong to cluster states formed when alpha particles hit the target nuclei.

1. I n t r o d u c t i o n

In a recent paper [1] we have reported on the angular distributions of a-particles elastically scattered from 34S. For the optical model description Saxon-Woods and squared Saxon-Woods form factors were applied. Five energies, 12.80, 14.56, 16.34, 18.13 and 20.00 MeV were chosen in the most used energy region of the two sim- ilar 103 cm isochronous cyclotrons of our laboratories. Later studies of excitation functions of a-particles elastically scattered from ~ssi [2] and 34S [3] revealed a struc- ture of narrow resonance like peaks. The height of the peaks and the small yield between them make the Ericsson fluctuation unlikely to explain their appearance. The angular distributions measured at the peaks gave quite interesting information about the nature of the resonance like Structures observed in the scattering from sil- icon. From the angular distributions a single angular momentum I of the scattered particles could be determined at most of the peaks, by fitting the distribution in the backward region, by squared Legendre polynomials. The/-values agreed with the angular momenta of a-particles captured by 2sSi in the (6Li,d) reaction on Si

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270 M. Brenner et al.

targets and subsequently emitted to leave the Si nucleus in its ground state [4,5]. These findings have led to the assumption that the peaks ate fragments of alpha cluster states in a2S [6]. Another possible interpretation is the formation of solitonic states, which yield a richness of resonances [7,8].

The measurements of the angular distribution of a-partides elastically scattered from 2sSi showed that the angular momentum at strong resonance like peaks in- creases with the bombarding energy. If the peaks really ate due to single resonance states, the spins J of the states would be the same as the measured angular mo- mentum I. Ir was observed that the spins ate the same within a broad energy region. When the energy is increased, there follows a region with peaks of the next higher spin and opposite parity mixed with the first mentioned. Increasing the en- ergy further, there appears a new region of constant spin, now of the same parity but two units higher and so on [2].

In our previous study of the scattering from 34S [1] no attention was paid to the angular momentum of the scattered a-particles. The angular distributions, however, resemble qualitatively in the backward direction the squared Legendre- polynomials. We have therefore considered that a reanalysis of the distributions could yield angular momenta to be compared with the results of [2]. Furthermore, the adding of a resonant scattering amplitude to the shape elastic scattering from the optical potential, can improve the fits. which at some energies were quite bad in our previous work [1].

2. T h e E x p e r i m e n t a l D a t a

A s a target of only sulphur is unstable under the exposure to a beam of a few nanoamperes, sulphur compounds or some stabilizing material have to be used in the target. Traditionally sulphur-silver targets have been used [9]. The high electron density of silver, however, reduces the energy of the beato in the target considerably, resulting in a poor energy resolution. In taking the data we used a sulphur--silver target enriched in S4S. An excitation curve was measured at 14 MeV and compared to one obtained with a sulphur-germanium target [3]. The peak at 14.06 MeV was quite broad and low with the silver stabled target as compared to the curve obtained with the germanium based target. The experimental data therefore present the angular distributions as average over energy regions from 0 to 80 keV below the energy of the beato. The energy is nevertheless given as the energy of the incoming analysed beam. A measurement of the angular distribution a t a 14.06 MeV peak was analysed as well in addition to the distributions at 12.80, 14.56, 16.34, 18.13 and 20.00 MeV of our first study [1]. For a presentation of the experiment, we refer to that paper.

Cluster Effects in the Angular Distribution of Alphas Scattered from a4S 271

3. The Analysis of the Angular Distributions

We assume that the elastic scattering cross-section is an incoherent sum of a com- pound nucleus part ~cJv and another part obtained asa coherent sum of the amp- litudes of the shape elastic cross-section a@t and the resonance scattering ate, :

o" -trcN q- [El(aopt,! q" ares,l)] 2. (I)

This is ah approach which has been applied before e.g. to cross-sections at isobaric proton resonances.

To ¡ our experimental di¡ cross-sections measured at angles within the range 20 ~ to 173 ~ (lab.angle), we used the optical model program FITOPTIC of [10], in which the resonant contributions of the forro

kr~/2 eip~.. P,(cosO) (Er,, - ~)) ~- irl2 (2)

were added. Here Pre, allows for an adjustment of the phase angle with respect to the amplitude of the shape elastic scattering. In our earlier study we applied optical model description to the scattering frorn 34S without including the resonant term of Eq.(2) [1]. For a presentation of the optical model parameters and the search routine for the evMuation we refer to that work.

The appearance of only one or at most two angular momentajusti¡ the follow- ing approximation, to be used in the analysis of the angular distributions of alpha particles elastically scattered from 34S. The scattering angle enters only in the Le- gendre polynomials. The sum of several contributing resonances represented by the forro of Eq.(2) may thus be written in the same form. The sum of the resonance amplitudes can be considered as the amplitude of a single resonance, which effect is equivalent to that of the many contributing resonances. The amplitude of this single resonance is added to the amplitude of the shape elastic scattering.

If we further put E = Eres for the equivalent resonance, the contribution of the resonances is still given by the forro (2), but the meaning of the parameters ra , I' and Pre~ should be changed. In the ¡ we have used r a / I ' and Pre, as two free parameters in addition to the optical model parameters to be varied. For a single resonance r a _~ r. When only the elastic channel is open then r~ = r. Ir should be mentioned that we cannot apply this relation to the widths Fa and r of the equivalent resonance since they ate formed from many resonances with unknown parameters.

The experimental points were fitted by minimizing the X2-values. In the calcu- lations the two resonance parameters r a / r and Pre8 were varied in discrete steps by hand, while the adjustment of the optical parameters [1] V, W, a v and aw was made automatically by the search routine. Low X2-value curves as candidates for the best fit were plotted and the best des'criptions were found by eye. The parameters of the best ¡ ate given in Tables la and lb. Fig.1 is a matrix, the elements of which are the fitted angular distributions. The rows from above correspond to the bombarding energies 12.80, 14.06, 14.56, 16.34, 18.13 and 20.00 MeV.

272 M. Brenner et al.

Table la . The parameters of the best fits, Saxon-Woods + resonance

Eo V rv av W rw aw l F a / F P,-,s (MeV) (MeV) (fm) (fm) (MeV) (fin) (fm) 12.80 132.29 1.55 0.678 10.32 1.55 1.245 8 0.16 2.0 14.06 150.38 1 . 5 5 0.437 13.68 1.55 0.289 8 0.20 3.0 14.56 150.75 1.55 0.603 14.55 1.55 0.031 7 0.16 1.9 16.34 133.57 1.55 0.581 14.25 1.55 0.059 7 0.10 0.4 18.13 144.37 1.55 0.497 11.59 1.55 0.309 9 0.07 1.5

10 0.12 0.2 20.00 137.40 1.55 0.570 17.00 1.55 0.510 9 0.08 1.0

Table lb . The parameters of the best fits, squared Saxon-Woods + resonance

Ea V rv av W rw aw l r a / r Pre8 (MeV) (MeV) (fm) (fm) (MeV) (fm) (fin) 12.80 198.46 1.37 1.308 12.12 1.75 0.896 8 0.10 2.4 14.06 200.48 1.37 0.990 10.16 1.75 0.623 8 0.22 3.0 14.56 199.85 1.37 1.397 10.68 1.75 0.714 7 0.06 1.0 16.34 195.76 1.37 1 .295 11.79 1.75 1.116 7 0.03 1.1 18.13 199.74 1.37 1.219 11.84 1.75 0.735 9 0.18 0.5

10 0.13 3.0 20.00 196.80 1.37 1.298 13.07 1.75 1.021 9 0.02 1.2

From the left the columns correspond to the Saxon-Woods (S-W), (S-W)+resonance, squared Saxon-Woods (S-W)2and (S-W)2+resonance.

4. Comments upon the Fits

The followin8 comments upon the goodness of the fit~ enlight~ the significance of the experimental result& The angular distributions are discussed energy by en- ergy. Some of the commenting sentences are l�91 by it�91 which ate used for re~erences.

1~.80 M e V. a) The curves in which reson�91 were �91 gire a good fit in the backward angle re$ion from 120 ~ up, whereas the sole (S-W) and (S-W) 2 give a very poor fit in th�91 region, b) There is only one spin value that gives �91 good fit, i.e. the spin of the resonance to be added is un�91 At this energy the spin value is 8. c) The curves with resonances added give a good fit in the forward direction up to 100 ~ . d) The (S-W)2+resonance gives �91 resonable fit in the intermediate region, 100~ ~ as well. There the experimental points are too low but their error b�91 touch the calcul�91 curve, e) In the intermedi�91 region the (S-W)+resonance is worse, as the experimental points are below the calcul�91 curve. J) The sole (S-W) and (S-W) 2 curves differ by �91 considerable �91 from the experimental points, e.g. near 110 o.

Cluster Effects in the Angular Distribution of Alphas Scattered from 34S 273

Experimental and Calculated Angular Distributions

S a x o n - W o o d s S q u a r e d S a x o n - W o o d s

n o r e s . r e s . no r e s . r e s . so'

~~,sL II=18JI0 MeV tot e

~ ~ 1 o a bz14.o4 Meu

so"

~,~ 10 4

0J,i 10 L

~Ÿ lO "l

0 10

t=* lffilR.~ ~'.u t t~ 10'

I0 4

S c a t t e r i n g Angle (LAB)

Fig .1 . Angular distributions of alpha particles scattered elastically from 34 S. The experimental points are fitted by curves based on Saxon- Woods and squared Saxon-Woocls formfactors, with of without reson- ances added to the shape elastic scattering term description. The exper- imental cross-sections displayed on Fig.1 ate corrected for compound elastic scattering according to the analysis of [1].

274 M. Brenner et al.

14.06 Me V. There is a prominent peak in the excitation function at this energy. This is manifested in the ]argest cross-section in the backward direction. Of the cases studied this is the most influenced by the resonance contribution. The (S- W)2+ resonance curve reproduces the maxima well in the backward direction, and yields an unambigous spin assignment (cf 1~.80 MeV b). The spin value is 8. The best (S-W)+ resonance fit is obtained with this spin but there is a little shift in the position of the backward maxima. The (S-W) and (S-W) ~ curves without resonance are considerably worse (cf 1~.80 MeV a). However, the (S-W) ~ has the two maxima next below the 180 ~ maximum at about the right position but its cross- section is there too high. (S-W)2+resonance gives the best fit (cf l~.8fl MeV d), whereas (S-W)+resonance gives a b a d fit in the forward direction, 45o-80 ~ The (S-W)+resonance reproduces the backward maxima well but displays a considerable difference in the cross-section at them. •) At this energy none of the curves give a point by point agreement with the data over all angles, h) We note some bad fitting, especially at intermediate angles, 65~ ~

14.56 MeV. At this energy, curves with resonances added give good fits in the backward direction with ah unambigous spin assignment (cf I~.80 MeV b). The J-value is 7. The (S-W)2+resonance curve gives the best fit (cf I~.80 MeV d), but there is bad fitting at 60o-75 ~ and 140 o. The (S-W)+resonance calculation fits the backward region well but is much too high in the intermediate region (cf 14.05 Me V h). The curves without resonances added are considerably worse cf (1~.8fl Me V a) although the (S-W) 2 has maxima at about the right position but with too low cross-section (cf 14.06 Me Y g).

I6.34 Me V. At this energy the backward cross-section is weaker than at the other energies. The fits without resonances added ate quite good. Resonances with spins 7 have maxima at the same position as the the angular distribution at this energy. Adding resonances with this spin improves the fits. This etfect is relatively small. The assignment of the spins to this energy cannot be considered as reliable as the other mentioned.

18.13 MeV. The (S-W)2+resonance curve gives the best fit in the backward direction (cf I~.80 MeV d). To get this fit two resonances with different spins 9 and 10 were added without mutual interference. There ate thus indications that none of these spins a]one is dominating in this region. Ir is rather characterized by two spins. Except for the (S-W) 2 curve without resonance the curves reproduce the maxima fair]y wel].

~0.00 MeV. The backward pattern is well reproduced by the calculated curves except for the (S-W) curve. The (S-W) 2 and (S-W)2+resonance give about the same results. This feature is comparable to the similar observation at 16.34 MeV. The reason may be the low cross-section in the backward region, which means that the effect of the resonances is small. Bad fitting is however seen in the intermediate region of from 100 ~ to 130 ~ (cf 14.06 MeV h).

Cluster Effects in the Angular Distribution of Alphas Scattered from 34S 275

5. Discussion of the Results

The analysis of the angular distributions has shown that: - The fits of the experimental data ate improved at all energies, especially in the backward direction (cf a), when resonances ate considered in the calculations. - The sole (S-W) and (S-W) ~ calculations do not reproduce the backward region in most cases (cf 12.80, 14.06, 14.56 MeV a). An exception is the 16.34 MeV distribution which is characterized by a small cross-section and small influence by resonances.

=%i =~S

20.

:E

L U

j ~ 1 0 .

.20

mmm~

.mm~

~ 1 5 . . . . . .

: = : : : : : :

~ t m m , i

10 .......... �9 ........

. . . . . . . ! ! ! ! ! ! ! ~ ! !

. . . . . . . Immt~

" :Z : . ' : : . . . . . . . �9 . . . . . . . .

5 . . . . ; ; ; ; ; ; ; ;

o + z- f 3- ( ~ 6* "F f f 9- zo"

.25

_Ÿ

r

tLt

o

_'i5 t~

.10

SpŸ - padty

Fig.2. The energy of resonances in elastic scattering from 345 (solid lines) and 2sSi (dotted) versus their spin-parity. Resonances at Et=b=12.60, 12.84, 13.27, 14.04, 14.20 are from [3] and unpublished.

- The spin of the dominating resonances at the energies of the measurement can be determined, in many cases unambiguously (12.80, 14.06, 14.56 MeV b). The dominance of one (or two) spin value(s) at arbitrary energies is a new finding in the study of angular distributions. It shows that the reanalysis of angular distribu~

276 M. Brenner et al.

tions observed in elastic alpha scattering within a large range of energies and target masses would be valuable. The dominance of one of two spins at selected energies where resonace peaks occur in alpha scattering [2], is closely related to this finding. - The deduced spins can be the subject for comparative studies involving the scat- tering from different targets. In Fig.2 the energies ate plotted as levels versus J as obtained from this study and in the study of [3] (solid lines). In the same diagram ate plotted the levels observed in elastic alpha scattering from 2aSi (dotted). The agreement of the positions of the levels is most interesting. For the zero of the ex- citation energy we have chosen the ground state of the final nuclei in alpha capture, aSAr and a~S, respectively. - The occurrence of single spin values that dominate several resonances st some energy, supports the assumption that the spin belongs to cluster states, which are formed when alpha particles of that energy hit the target nucleus. - The calculated curves did not fit the experiments point by point (cf I~.06, 1J.56 MeV g) except for one case (cf 12.80 MeV d). The reason may be that the (S-W) and (S-W) ~ potentials do not describe properly the alpha nucleus interaction in the studied energy and target mass region. Analyses of the angular distributions at higher energies have been successful in using the (S-W) 2 potential [11], which in the present study gave the best fits when the resonance term was introduced (cf 1~.80, 1~.06 MeV a, L~.56 MeV, 18.13 MeV d).

Shallow potentials should be tried as well to improve the fits. A potential de- rived from energy density formalism e.g. accounts adequately for such features of the scattering as magnitudes, locations of maxima and mŸ and back-angle enhancement in angular distributions [12].

A c k n o w l e d g m e n t

This work was supported in part by the OTKA Foundation Hungary (contract number T17298).

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Cluster Effects in the Angular Distribution of Alphas Scattered from 34S 277

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