Elastic scattering of 28Si on 24Mg and 26Mg

Nuclear Physics A459 (1986) 438-444 North-Holland, Amsterdam

ELASTIC

OF **Si ON 24Mg AND

SCA’ITERING

N. CINDRO

and

D. POCANIC

Rudjer BoSkovif Institute, 41001 Zagreb, Croatia, D.M.

DRAKE,

J.D.

University of California,

MOSES,

J.C.

PENG,

Los Alamos National

26Mg

N. STEIN

Laboratory,

Yugoslavia and

J.W. SUNIER

Los Alamos,

NM 87545, USA

Received 24 March 1986 (Revised 9 June 1986) Abstract: Backward-angle excitation functions and angular distributions measured in 28Si+24Mg elastic scattering show structure of intermediate width. The nature of this structure is investigated. Complementary data for 28Si + z6Mg display a smooth backward-angle excitation function. NUCLEAR (“Si,

REACTIONS

26*24Mg(2sSi, %i), E = 74.5-83 MeV; 24Mg(z8Si, 24Mg), o(e), o(E); deduced immediate structure

26Mg),E = 83 Mev; measured

Numerous examples have been reported for resonant-like behaviour and enhanced oscillatory behaviour of backward-angle scattering in collisions between lp and 2s-ld shell nuclei, e.g. 12C +28Si and 160+24Mg. More recently, similar phenomena have been observed in the scattering of sd shell nuclei 24Mg+ 24Mg and “Si + 28Si [ref. ‘)I, thus extending

the experimental

data on this subject

to heavier

systems

than measured previously. In this paper we present results for two systems of non-identical interacting sd shell nuclei, namely 28Si+24Mg and 2sSi+26Mg. Resonant behaviour has been predicted for composite systems as heavy as 52Fe and 56Ni, using phenomenological models of orbiting clusters ‘) or nuclear molecules. However, other theoretical explanations have also been advanced to explain the energy and angular effects observed in heavy-ion collisions 3-5310).The latter include direct-reaction interference phenomena, l-dependent potentials, exchange processes, shape resonances, etc. In the present work, large-angle elastic scattering is measured by detecting forward recoiling Mg ions in the reactions 24,26Mg(28Si, 24,26Mg)28Si. These reactions are chosen to provide additional data on interacting sd-shell nuclei forming composite systems in the mass range A = 50.In particular, the difference between the behaviour of an “alpha” system (24Mg+28Si) and a “non-alpha” system (26Mg+28Si) should be visible from comparison. In fact, existing models do predict a different resonant behaviour of the two systems 2710). 0375-9474/86/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

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The experiment was performed using 8+ and 9 + 28Si beams from the Los Alamos National Laboratory tandem Van de Graaff. The energy range for the incident 28Si beam was ELab= 65-86 MeV (E, ,,, = 30.5-39.7 MeV) for the scattering on 24Mg and Elab=71-85 MeV (EC,,= 34.2-40.9 MeV) for 26Mg. A heavy-ion detecting system consisting of a position-sensitive ionization chamber placed in a Q3D magnetic spectrograph “) was used to provide clear identification of the scattered Mg (and 28Si) ions. Excitation functions for the scattering of 28Si on 24Mg were measured with a thick self-supported 24Mg target (91 t.r.g/cm2) at 8,,,=6”rt2” in the energy range Etand = 70-86 and with both thick (74 pg/cm*) and thin (20 Fg/cm’) targets at Blab= 15”* 2” in the energy ranges E,,,, = 77-86 MeV for the first and Etand = 65-78.5 MeV for the second target. The steps in energy were most often 1 MeV (AEtand), with frequent ranges of finer-step measurements. The excitation function for the scattering of 28Si on 26Mg was measured only at elab=60 in the range 71-85 MeV (lab). The excitation functions are shown in fig. 1. Structure is visible

f 26

Mg(28Si,26Mg)28Si .**..*0 *o** 46’ *

200, 65

70

80

85

Fig. 1. Excitation functions at f& = 6” and 15” for the elastic scattering of “Si on 24Mg, and at 6” on 26Mg. In each case, Mg ions were detected. Full circles are data obtained with thicker targets, empty circles with a thin target (see text).

N. Cindro et al. / Elastic scattering

440

in the 24Mg + ‘*Si excitation functions: the data at 6” show regularly spaced (approx. 5 MeV) oscillations. The 28Si+26Mg excitation function measured at the same laboratory angle is smooth and the cross sections are considerably larger. Fig. 2 shows the 28Si+24Mg angular distributions measured at four energies with thick 24Mg targets (70-90 Fg/cm*). These energies were chosen as representative of the on- (&, = 74.5, 78, and 83 MeV) and off-peak (Elab = 79.5 MeV) positions in the excitation function at 6”. All four angular distributions show oscillatory behaviour, but they differ markedly from each other in the pattern of this behaviour. For instance, the angular distribution at 74.5 MeV shows regularly spaced oscillations

1

I

I

,

I

-

loo-

79.5

MeV -

a3 MeV

2O0

I 20

I 40

0 I 60

I 80

I

100

Fig. 2. Angular distributions of 28Si+24Mg at four laboratory energies of **Si. The empty and full circles for the 83 MeV angular distribution are data from two different sets of measurements.

441

around

N. Cindro et al. / Elastic scattering

an increasing

average.

shows a pattern characteristic posed on a smooth background

On the other hand, the angular

distribution

at 83 MeV

of a squared-Legendre-polynomial shape superimdecreasing towards 90” (c.m.). No such regularities

are observed for the angular distributions at 78 and 79.5 MeV. With the above in mind, we have concentrated on the analysis of the angular distributions at 74.5 and 83 MeV, using the computer codes GENOA ‘) and LOLA “). The results are displayed in figs. 3a-c. The full curves in figs. 3a and b show optical-model calculations obtained with the code GENOA using a set of parameters adjusted to fit the forward-angle scattering of 24Mg + 28Si. (Note that the data in figs. 3a and b are displayed with the 28Si ion detected; hence forward angles in figs. 1,2 and 3c correspond to backward angles in these figures). The parameters were as follows: V = 29.59 MeV,

W, = 19.37 MeV ,

rOR= 1.404 fm ,

ror = 1.400 fm ,

aR = 0.3532 fm ,

a, = 0.1704 fm.

It is gratifying that the above set of parameters reproduces the average trend of the data correctly for both angular distributions (Flab = 74.5 and 83 MeV) throughout the whole angular range. The inclusion of a term representing the exchange of an LYparticle between the 24Mg and 28Si nuclei (computer code LOLA) substantially improves the fit for the 74.5 MeV data, reproducing most of the characteristic oscillations (dashed line in fig. 3b). The value of the fractional-parentage coefficient for the 24Mg+ (Y configuration in *‘Si was a free parameter in this calculation. However, when the same procedure is applied to the 83 MeV angular distributions, the fit to the data is less than satisfactory (dashed line in fig. 3~). On the contrary, these data appear to agree much better with a P:,(cos 0) shape (solid line in fig. 3c), which reproduces the trend and, to some extent, the oscillations of the data. None of the above calculations (optical model, optical model + exchange) could reproduce the structure observed in the excitation functions. Although the above results are far from permitting a clear-cut establishment of an intermediate width structure in 24Mg + 28Si elastic scattering, the peculiar shape of the angular distributions combined with the structure in the excitation data allow some interesting comments. Of all the angular distributions studied, only the angular distribution at 83 MeV shows a resonant-like behaviour that would be characteristic of the presence of an intermediate configuration in the 52Fe composite system. Phenomenological models ‘) have, indeed, predicted a rotational-like resonance band in s2Fe, with J = 24-26 terms at an excitation energy of about 50 MeV. Although the analysis of the 83 MeV angular distribution agrees with such an interpretation, the absence of

et af./ Elasticscattering

N. Cindro

442

10*

0

10’

Elab==83 MeV

-a bo”2

1C3

1

-4

0

_

.

l

t

I

/

,

_d,30

50

70

90

%rn ,

I

110

I

130

1

150

17f

24~Q~28Si~8Si~24MQ Elab= 74.5

I 4

100

5 110

t

,

120

130

I 140 24

8--Q

iI

I

0

10

I

20

I

30

I

40

--\

I

50

I

I

150

160

MeV

I 170

MQ(28Sif4MQ)28Si

i -\

II

E ,,b=83

I

80

70

MeV

,

80

I

ecrn

Fig. 3. (a) Optical-model calculations for the 83 MeV angular distribution of 24Mg+2sSi. (b) Opticalmodel calculations (full line) and calculations with an exchange term included (dashed tine) for the 74.5 MeV distribution. (c) Same calculation with an exchange term included (dashed line) and a I = 25 squared-Legendre-polynomial fit (solid line) for the 83 MeV distribution.

N. Cindro et

polynomial-like angular between the peaks (-2.5

al. /

Ehstic scattering

443

distributions at other peak energies as well as the spacing MeV (c.m.) instead of the predicted 1 MeV for two consecu-

tive resonances with J around 25) is not easy to explain. Furthermore, the relatively good fit obtained for the angular distribution at 74.5 MeV with the computer code LOLA indicates that exchange mechanisms may play an important role in backwardangle elastic scattering of ‘*Si on 24Mg is physically indistinguishable from a process in which an a-particle is transferred from a backward-directed “Si nucleus to a forward-directed 24Mg nucleus. Although the two processes are intrinsically different, the entrance and exit channels are identical for both of them. The scaling of the relative amplitudes for the two processes is governed by the fractional parentage of 24Mg+ CYin the ground state of *‘Si; this factor was taken as a free parameter in the present calculation. The value (= 1) needed to obtain the fit in fig. 3b is, however, rather large and may just serve to simulate the contribution of an amplitude restricted in angular momentum space (“resonant” amplitude) in the backward-angle elastic scattering of 28Si + 24MG. The smoothness of the excitation function and the large values of cross sections for 28Si+26Mg are not unexpected. The departure from the so-called a-nuclei by one or two nucleons has been known to smooth out the intermediate structure in the excitation functions, and several explanations have been advanced to account for it *,‘,“). Both the smoothness and the large cross sections may indicate that at backward angles (forward for the detected 26Mg ions) the process is dominated by nucleon exchange. No calculations are available at the moment to corroborate this conjecture. To summarize, we have measured excitation functions and angular distributions for **Si + 24Mg and 28Si + 26Mg elastic scattering. The first experiment shows structure of intermediate width in the excitation functions measured at two angles. The angular distribution measured at 83 MeV (peak of the excitation function at 6”) shows features characteristic of a possible J =25+ 1 resonant intermediate state at an excitation energy of about 50 MeV in 52Fe. On the other hand, the angular distribution at 74.5 MeV (another peak in the excitation function) can be fitted by adding an a-particle exchange term to the optical-model scattering amplitude. However, the fit is obtained by using an unrealistically large fractional-parentage coefficient for the (Y+ 24Mg configuration in the 28Si ground state. Thus, at present, there is no single reaction mechanism that can account for the difference in behaviour between the *‘Si + 24Mg angular distibutions at 74.5 and 83 MeV. Rather, it is likely that there is an interference of the a-exchange amplitude and a peripheral (high-L) elastic amplitude. The interplay of these two amplitudes determines the shapes of angular distributions at different energies. A situation of this kind may have been observed earlier in the scattering of 160 from “Ne. While these data I’) did not require at interpretation in terms of resonances, they were consistent with it; at the same time the data demonstrated the importance of the elastic transfer in the far backward angles.

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