Nuclear Physics A534 (1991) 445-460North-Holland

S

E

IC A

NEA -SY E

C FISSION OF 24 r*i AN

Received 4 February 1991(Revised 31 May 1991)

l. Introduction

J.S. LILLEYSERC Daresbuy Laboratory, Daresburt; Warrington WA44AD, UK

0375-9474/91/$ 03.50 © 1991 - Elsevier Science Publishers B.V. All rights reserved

PLE

YSICS

S.J . BENNETT, M. FREER, B.R. FULTON, J.T. MURGATROYD and P.J. WOODS'

Department of Physics, University ofBirmingham, Birmingham BIS 2TT, UK

S.C. ALLCOCK2, W.D.M. RAE and A.E. SMITH

Nuclear Physics Department, University ofOxford, Keble Road, Oxford OXI 3RH, UK

R.R. BETTS

Physics Division, Argonne National Laboratory; Argonne IL

39, USA3

Abstract: In several recent measurements the symmetric fission of'Mg has been reported . In this paperthe results of a search for similar processes in 28Si and 32S are presented. In contrast to the r,aultsfor 24Mg, no evidence is seen for the fission of 2gSi to ' 60+'2C or 32S to '60+'60 followinginelastic excitation . However, these processes are observed to occur following pickup onto 24Mg .

The results are consistent with a simple model of the fission process developed by Harvey andsuggest the existence of large scale cluster structure in all three nuclei.

NUCLEAR

REACTIONS

'2C(28Si, F),

(2gSi, X),

(32S, F),

(32S, X),

E=200 MeV;12c(24Mg, F), (24Mg, X), E =180 MeV; measured fission, reaction (fragment)(fragment)-

coin; deduced reaction mechanism . 24Mg, 2gSi, 32S deduced fission characteristics.

In several recent studies the fission of 24Mg into two '2C nuclei in their groundstates has been observed following excitation of the 24Mg by inelastic scattering' -4) .The motivation for these measurements is an attempt to establish a direct linkbetween states in 224Mg and the well-known scattering resonances observed in the'2C+' 2C system $) . Earlier studies of the electrofission of 24Mg [ref. 6)] and theinverse process of radiative capture 7 ) had revealed the existence of an unusual setof states at an excitation of around 22 MeV in 24Mg which are linked to the groundstate and also have an appreciable overlap with a '2C+'2C configuration . However,

' Present address : Physics Department, University of Edinburgh, Edinburgh EH9 3JZ, UK.2 Present address : ISTEL Ltd ., Redditch, UK.3 Work supported by Department of Energy Nuclear Physics Division under contract number

W-31-109-ENG-38 .

446

S.J. Bennett et al. / Fission of 24Mg, 2"Siand 3`S

the states revealed in the electrofission and radiative capture measurements do notappear to coincide with resonances observed in '`C +'-C scattering, or to be associ-ated with fragments of the giant quadrupole resonance strength in 24Mg [ref.')] .The useof inelastic scattering (as opposed to electromagnetic excitation) provides

an alternative means of investigating these unusual states as well as removing thepossible restriction to low multipolarities. The experiment of Lawitzki et cal. ') usedinelastic scattering of 120 eV alpha particles to determine the energy of thefissioning states which were identified by coincident detection of the two "2C

fragments.

similar measurement technique using inelastic scattering of 190 MeVprotons has also been reported recently by Davis et al. 2). In the measurements of

ilczynski et aL ") and Fulton et al. `~) the kinematic advantages of inverse reactionswere exploited by scattering high-energy 24Mg projectiles from a 12C target . Thetwo '2C fragments from the fission of 24Mg were detected in coincidence and theirmomentum vectors used to establish the excitation of the fissioning system. Theresults of all four experiments show fission occurring from specific states in 24Mgin the excitation energy range 20-25 MeV. These measurements are similar to theresults of the electrofission and radiative capture experiments demonstrating thattheoccurrence of fissioning states covers a wider region ofexcitation than previouslyrealised . In addition they show evidence for fission occurring to channels involvingone or both of the ''C fragment nuclei excited to the 2+ state at 4.44 MeV. Morerecent experiments have shown that the 24Mg nucleus can also breakup to the'60+ 813e channel') and that the fissioning states have spins J> 2 [ref. 9)] and socannot be fragments of the giant quadrupole resonance.The origin of the fission process remains unknown. Clearly it must involve some

special states at high excitation in 24Mg which are linked to theground state (throughelectromagnetic transitions or inelastic scattering) and yet which have an appreciableoverlap with a configuration involving two 12C nuclei . However, a microscopicdescription of these states has still to be determined. In an effort to elucidate furtherthe nature of the fissioning states we have performed new measurements to searchfor similar fission processes in the neighbouring nuclei 28Si and 32S. The decaychannels for these nuclei, 160+12C and 160+160 respectively, are systems in whichscattering resonances are known to occur. electrofission of 28Si to 160+'2C hasbeen reported '°) and radiative capture has also been observed in the 160

+'2C

system "), although the decay is primarily to the first excited 0+ state in 28Si withthe decay to the ground state being much weaker .

In this paper we report the results of measurements made with 28Si and 32S beamsto look for breakup of 28Si to 160+'2C and 32S to 160+'60 following inelasticscattering . We have also looked for breakup of the same nuclei excited throughpickup reactions using 24Mg and 28Si beams. The results of these measurements,taken along with the earlier 24Mg results, appear to be consistent with the predictionsof a simple model proposed by Harvey '2) and show evidence for the existence oflarge cluster structure in all three nuclei .

S.J. Bennett et al. / Fission of 2"Mg, 2sSi and "S

447

2. Experimental method

The means by which information on three-body breakup channels is determinedin these experiments has been outlined in ref. 4). A bean' of the nucleus toinvestigated is directed onto a target and fragments from the breakup reactionsrecorded, in coincidence, in detectors on either side ofthe beam. From the measure-ments of energy and scattering angle of the two detected fragments (Ell 493, oil 91-1

®2 and 02) it is possible to identify the breakup channel and calculate the exchationenergy of the states from which the breakup occurred . It is convenient to transformthe data into two variables, got and E,.., . Et., is the summed kinetic energy of thethree fragments in the exit channel and is thus related to the Q-value for the reaction

got =E,+E2+E3=

.m+ Q3 "

(I)

Although the energy of the third particle (E3) is not measured directly it can becalculated from the measured energies and angles of the other two fragmments underthe assumption of conservation of momentum

Pl +P2+P3 = Pbeam -

Peaks in the Aot spectrum then reflect breakup to different final channels . For aspecific reaction channel (i.e . a particular pair of fragment nuclei) the highest peakin the spectrum will correspond to the case where all three fragment nuclei are intheir ground state (the Qggg peak) and it should occur at an energy correspondingto that required to break up the nucleus into the two fragments . Peaks at lowervalues of Aot would reflect events where either of the fragment nuclei, or theunobserved recoil, are left in excited states.The need to identify a specific breakup channel means that some form of particle

identification is required . This is achieved by the use of a conventional DE-Etelescope, where particle identification is achieved by means of a measurement ofthe differential energy loss . In order to achieve a high efficiency in detecting twofragments in coincidence, it is necessary to use large area detectors . However thisis not compatible with the need to have well defined angle information for thekinematical analysis . The solution adopted was to make use J position sensitivedetectors (PSD's) so that the angles of the fragments can be recorded and thekinematics correctly calculated on an event-by-event basis. Since both in-plane andout-of-plane angle information is needed, the DE and E detectors are arranged withtheir position sensitive axes orthogonal . In this way the full X, Y position of aparticle striking the detector is measured and this can be related to the scatteringangle .

Several experimental problems arise from the use of large area PSD's . Firstly,there is the variation of timing across the face of the PSD due to delay line effectsassociated with the resistive readout layer. This results in a degradation of the timing

449

&J. Bennett et al 1 Fission of 24Mg, `"Si and 3`S

resolution recorded in the measurement of coincidences between telescopes. Atheoretical model of the detector has been developed which describes the timevariation of the signal '3 ) and this knowledge has been used to correct the variationin the time signal arising from amplitude and position dependences. The muchimproved timing resolution allows a high fraction of random coincidences to berejected.

sition signal from a

Dalso suffers from inherent non-linearity due tovariations in the uniformity of the resistive readout layerand reflections of the signalat either end of the resistive layer. The extent of these non-linearities was measuredin each experiment by placing a calibration mask in front of each telescope andrecording a two-dimensional position spectrum for particles entering the telescopethrough the holes in the mask (usually elastically scattered 12C particles) . The maskcomprised a regular array of holes of diameter 0.5 mm and separation 1 mm. Thenon-linearides in the detector response show up as adistortion in the regularspacingof the holes. Two-dimensional fitting can then be performed to correct the non-linearity. e same technique allows the intrinsic position resolution of the detectorto becalculated by deconvoluting the profile ofthe mask. Typical position resolutionsof 0.25 mm have been achieved and such resolutions are responsible for a contribu-tion of around 80 keV to the total excitation energy resolution of 90 keV.A final problem with the use of large area DE detectors is the effect of the

non-uniformity in thickness across the detector face . This results in a variation inthe energy lost by a particle traversing the detector which depends on the positionat which it enters, and causes a smearing of the events in a DE-E particle iden-tification plot. If the thickness variation is too severe then the locus of events fordifferent particle types may overlap to such an extent as to make unambiguousidentification impossible . The elastic scattering data obtained with the calibrationmask in place can be used to develop a correction for this problem. Since the energyof the elastically scattered particles entering the detector in this measurement isessentially constant across the face of the detector, any variation in the signal fromthe DE detector results from a variation in the thickness. By using the positioninformation to sort the data through each hole separately, the thickness variationcan then be mapped across the full face of the detector. This information can beused to provide a correction to the DE and E signals and improve the DE-Eidentification . Fig. 1 shows a DE-E plot from one of the telescopes before and afterthe correction has been applied. The much improved separation of adjacent groupsallows unambiguous identification of different particle types in the analysis .The three experiments described in this paper have been carried out using the

facilities at the Daresbury 20 MV Tandem. Beams of 200 MeV 28Si and 32S and180 MeV 24Mg were used to bombard 400 ILg/cm2 targets of natural carbon . Fissionfragments were recorded in two silicon surface barrier detector telescopes positionedat 13° on either side of the beam axis . These angles were chosen to give optimumefficiency for breakup from states just above the Coulomb barrier in the exit channel .

e

S.J. Bennett et al. / Fission of '4Mg,'SSi and 32S

449

E (channels)Fig . 1 . Example of the DE-E particle identification from a telescope (a) before and (b) after the DE

and E signals have been corrected for variations in the detector thickness.

Each telescope comprised two 10 mm diameter position-sensitive detectors orien-tated so as to give information on both the in-plane and out-of-plane angle for eachfragment . The detector thicknesses in this experiment were 30 wm (DE) and 640 wm(E) ; with the front detector positioned 155 mm from the target. Table 1 lists theinformation relevant to the three experiments .

450

&J. Bennett et al. / Fission of 'Mg, '8Si and 3`'S

sh

Beam

Parameters relevant to the three experiments reported in the text

Energy(MeV)

180

Target Beam Peakthickness _xposure efficiency(tL CM- )

(PMC)

(°lo)

TABLE 1

3. Results

Scalingfactor

0.91 0.09 1.222.49 0.09 0.451.33 0.14 0.54

e

,,t spectrum obtained for the inelastic breakup channel with each beam iswn in fig. 2 for the cases of coincident C ions (24Mg beam), coincident C andions (2"Si beam) and coincident 0 ions (3'S beam). The 24Mg spectrum shows

clear evidence for the breakup of 24Mg to ',C+'-'C nuclei in their ground state(marked as Q on the figure). Peaks are also visible at lower values of dotcorresponding to events where one or both of the '`C nuclei emerge in the 2+,,

MeV excited state. Excitation of the same state in the recoiling target nucleusis also apparent. The counts above the Qgg, peak are the result of pile-up eventsand most likely occur due to the detection of an additional «-particle. This effectcan be seen as a broad vertical stripe in fig. lb for E-values of up to 30. In contrastthe spectra for 211Si and 32S show no prominent peaks which would indicate asequential process of inelastic excitation followed by fission. The arrows on the 2gSiand 32S spectra indicate the expected position ofevents corresponding to thebreakupof 2gSi to '60+'-C or 32S to 160+ '60, all in their respective ground states . It shouldbe noted that in these, as in all other Etot spectra, the resolution in the particleidentification spectrum was only sufficient to identify the Z of the detected nuclei .However in all cases the Q-value for breakup to channels involving other than ' 2Cor '60 isotopes is much more negative and cannot be confused with the Qggg peak.The spectra obtained for breakup of the projectile nucleus following inelastic

scattering can be compared with those for breakup of the same nucleus formed ina transfer reaction . Fig. 3a shows the Etot spectrum for coincident C and O ionsfrom the 24Mg beam experiment . In this spectrum the Qggg peak for breakup to the'60+' -C channel can be seen, suggesting that 211Si nuclei populated by alpha pickuponto the 24Mg projectile can breakup to 160+'2C nuclei in their ground states . Therecoiling particle in this case is "Be which is unbound and has a number of broadstates at low excitation energies. Excitation of these states will be responsible for abackground extending to lower energies in the Etot spectrum .

Fig. 3b shows the Etot spectrum for coincident O ions from the 21Si beamexperiment . This channel would correspond to alpha pickup forming an excited 12S

nucleus with a recoiling 8Be nucleus. However there are no peaks in this spectrum

rr

OV

S.J. Bennett et al. / Fission of 24Mg, 28Si and 32S

U

,~01 11 mill ,,-i150 160 170 180 190

Etot(MeV )

451

Fig. 2. Total energy spectra for the fission processes (a) 24Mg to '2C+'2C (b) 21ISi to ' 2C+'60 and (c)12S to "'0+"'0 following inelastic scattering from a '2C target. The arrow labelled Q,,e indicates the

expected position for events in which all the nuclei are in their ground state .

452

S,1! Bennett et aL / Fission of -4Mg, -"Si and 3-S

zn 30

U 20

Etot(MeV)

Fig . 3 . Total energy spectra for (a) coincident '2C and ' 60 ions from the 24Mg beam experiment (b)coincident ' 60 ions from the 2R Si beam experiment and (c) coincident "0 ions from the 24Mg beamexperiment . The arrow labelled Qee. indicates the expected position for events in which all the nuclei

are in their ground state .

vV

S.J. Bennett et al. / Fission of 'Mg, "Si and 32S

453

0.125

0.100

0.075

0.050

0.025

0.0.125

0.100

0.075

0.050

0.025

0.000

*it 0.100

Q 0.075

0.050

0.025

0.000

0.20

0.15

0.10

0.05

0.15

0.10

0.05

0.002025 30 35 40Excitation Energy (MeV)

Fig . 4. Monte Carlo calculations of the detection efficiency in each reaction as described in the text .

454

SJ Bennett et aL I Fission of `4Mg, 28Si and -12S

which would be evidence for sequential breakup of 3`S to `60+ °60 following alphapickup onto '"Si .

Finally, fig. 3c shows the

®$ spectrum for coincident 0 ions from the '4Mg beamexperiment. This channel would correspond to breakup from an excited 32S nucleus

with a recoiling 4I-Ie nucleus. In this spectrum there is evidence for the sequentialbreakup of 3'S to "O+ X60 nuclei in their ground states, and also for one or bothof the nuclei excited to around 6 MeV (either the 6.05 MeV, 02 or 6.13 MeV, 3;states) .

e results of the measurements reported above present some difficulties ininterpretation . While :!4Mg is observed to breakup to ';C+ °`'C following inelasticscattering, neither `' sSi to '60-x-'°C or 3'S to °60+'60 is observed. In contrast, bothof these last two breakup channels are observed from nuclei produced in pickupreactions. Before drawing any inferences from the breakup yield measured in thesedifferent reactions it is necessary to ensure that any differences are not a simpleconsequenceofdifferent detection efficiency in the measurements. We have estimated

is by means o a

onte Carlo simulation which enables the detection efficiencyto be calculated as a function of excitation energy for each reaction.

e Monte Carlo calculation requires a knowledge of the primary scatteringangular distribution of the excited nucleus prior to the breakup. Little data existson such measurements, so we have assumed an exponential fall off with a slopesimilar to that measured by Betts et al. '4) for excitation of high-lying inelastic states(20-25 MeV) in the 12C+ 27Al system . In practice, while the absolute value for theefficiency in a given channel depends on this choice, it has little effect on the relativeefficiency betweenchannels. Thebreakupof the emerging excited nucleus is assumedto be isotropic in its rest frame. For a given channel the kinematics are calculatedfor the reaction process and a choice of scattering angle and breakup angle madewithin the above constraints. The particles are then tracked to see whether they hitthe detectors. Other experimental cuts, such as energy thresholds in the detectors,are also included in the simulation.

Fig. 4 shows the resultant efficiency profiles for the various breakup channelscalculated as a function of the excitation energy of the fissioning nucleus. Theoverall shape is similar for all channels and shows that the measurements are mostsensitive to a region of excitation extending up from the Coulomb barrier in eachcase . Although there are some differences between the different channels the overallvariation in efficiency is relatively small. As a rough measure of the relative efficiencyfor each measurement we take the peak value in each channel and these are listedin table 1 .From the beam exposure, target thickness, dead time and estimate of detection

efficiency we can calculate a relative scaling factor for each measurement and thisis listed in table 1 . An inspection of these values shows that the scaling is roughlysimilar for all measurements . It is clear that the variations are not sufficient toexplain the observation of breakup from a nucleus in one measurement and its

SJ Bennett et al. / Fission of 'Mg, 2 Si and 3`S

455

absence in another. Some other explanation based on the structure of the nuclei orthe dynamics of the reaction process must be sought.

4. DiscussionThe fission of a nucleus into two ground-state fragments is a dynamical process.

From a microscopic viewpoint the individual nucleons must rearrange themselvesfrom single-particle orbits in the fissioning nucleus into single-particle orbits in thefragment nuclei. The details of the process then depend on the evolution of thesingle-particle orbits and on thenature ofthe dissipative forces during the separationof the system . In the two-centre shell model it is possible to study the evolution ofthe single-particle orbits as a function of the fragment separation. Chandra andMosey") have performed such a calculation for the inverse process of two '2Cnuclei fusing to form 24Mg. They find that under the assumption of a diabaticreaction process, various level crossings occur, as a consequence of which nucleonsoccupying the P3/2 orbit in one of the approaching ' 2C nuclei are driven up intothe f,/2 orbit in 24Mg. This results in the population of a highly excited 4p4hconfiguration. Such two-centre shell model calculations are of considerable com-plexity. However, Mosel '6) has pointed out that the level crossings predicted arenot dependent on the specific model but are a general consequence of the Pauliprinciple, and that these ideas are contained in a simple schematicmodel previouslyproposed by Harvey 12).

In the Harvey model the separated nuclei are described by simple harmonic-oscillator wave functions with oscillator quanta n.,,, n,, and nZ along the three axes .Each level can contain two protons and two neutrons (spin up and down). The twonuclei are assumed to approach along the z-axis which connects their centres. Sincethe relative motion is along the z-axis it is assumed that only the oscillator quantaon this axis can change to satisfy the Pauli principle - the x and y degrees offreedom remaining unchanged - and this imposes constraints on the levels filled inthe fused nucleus. These arguments can of course be applied in reverse to predictthe possible configurations in fragment nuclei resulting from fission .

Fig. 5 shows the result of applying the Harvey model to the fission of 24Mg, 2gSiand 32S nuclei, where the initial oscillator configuration for each nucleus is thatdeterluiued 1 oin the known ground-state shape ") of each nucleus (roughly prolatefor 24Mg, oblate for 28Si and roughly spherical for 32S) . In a spherical potential thelevels within a major oscillator shell are degenerate with respect to the oscillatoraxes ; however, in a deformed nucleus the oscillator quanta differ along the axesand nucleons will preferentially occupy the levels with lowest energy (the energyof the quanta will be inversely proportional to the length of the axis). The predictionof the Harvey model is that while 24Mg in its ground-state configuration can fissioninto two ground-state '2C nuclei, neither 2gSi fission to '60+' 2C or 32S fission to'60+'60 can occur with both fragment nuclei in their ground states - one or other

456

SJ Bennett et aL J Fission aT 2- Mg, `"Si and ;`S

29Si

3 : 2

(gs

c). : coy

: wZ= 2 : 1 . 1

003

003

020X 3 0200011 ~

www

301

`002 "

"0 3 0

4300

4

~ "

Y

t SO

411020001 1

41 0 1

"002 a ""

01 0

41 0 0

4

" ~001

4

~ "

Nny"z

zeso9s

12C 9s i. led.

Fig . 5 .

Predictions for the fission of various sd-shell nuclei from the Harvey model . The oscillator levelsfilled in the fissioning nucleus are those appropriate to the known ground state deformations ") .

1

(3) 2p1f

003t4 020

110

200( (2) 2s Id01 11

1 01

0021

4 4 01 0

4 1 0 0 (1) 1P4 001

1e

(3) 2p 3f

003

0201 1 O

200 (2) 2* 3d011

101

002

4 4 0 1 0

8 100~(1)1P4 001

000 (0) Is

12 1Nn

fl1 =G9,

�t

Fig. 5-continued

is required to be in a highly excited 4p4h configuration. An implicit assumption isthat the inelastic excitation prior to the fission does not appreciably perturb theparticle configuration appropriate to the ground-state wave function. The Harveymodel is thus in accord with the experimental observation that in inelastic scatteringmeasurements the fission of 24Mg to two ground-state '2C nuclei can occur. Sincethe 4.44 MeV state in '2C is the first member of a band based on the ground state,the observation of breakup with excited '2C nuclei is also in accordance with theHarvey model . However, since the yield in this case arises from a different regionof excitation in 24Mg it is difficult to draw any inference from the relative strengthsof the peaks in fig . 2 . Similar processes are not observed with 2gSi or '2S .The model can also be applied successfully to the case where the fission occurs

from a nucleus excited in a transfer reaction process. In the case of 2gSi there is anapparent difference in the fission of 2gSi following inelastic scattering (fig . 2) orfollowing alpha pickup (fig . 3a) . Since in the latter case the nucleus is formedthrough an alpha-transfer reaction there is no reason for it to be formed with aconfiguration similar to than of the ground state ; indeed we may expect states withpredominantly 4p4h configurations to be excited . Reference to fig. 6a shows that aconfiguration of 2gSi comprising 4 particles in the n = 2 shell outside the 24Mgground-state configuration can fission into ' 60 and '2C both in their ground states .The different character of the decay of 2gSi is thus a consequence of the differentconfiguration of states excited by inelastic scattering and alpha transfer .

For 32 S the situation is somewhat different . In this case the alpha pickup involves

S.J. Bennett et al. / Fission of 24Mg, 2"Si and 32S

0

457

(3) 11

003 0031

020 4 4 020

110 110

200 200(2) 281d

011 4 A1132S 101 4 . 101

002 4 002(gs SPHERICAL) v

01 0 4 % %~ % % 4 4 010w. :wy :wZ=5 :4 :3100 4 % %_4 4 1 0 0 (1) 1p001 4 %% 4 001

000 4 4 4 000 (0)1SNnrnz

ft es~ Isa Nny"z9S

458

Si

®®g 4

1zC isC" o

003

020

~

02011O

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110200

~

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4

%

0 1 1w v

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d

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002

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"%. 4

4

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32e

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e

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(2) n 1d

ono a

a a ova1 0 0

4

1 0 0

(1) 1P

000

4

'-, 4

4

000

(0) 1s

Fig. 6 . Application of the Harvey model showing that (a) a configuration formed by alpha transfer onto24Mg can fission to the ' 2C+'60 channel and (b) a configuration formed by transferring two alpha

particles on to 24Mg can fission to the ' 60+'60 channel .

a 28Si nucleus in which the (020) orbit is already filled (fig. 5) . The Pauli principleprecludes particles in this orbit from evolving into the lower shell in the separatednuclei . 1-fence it is not possible to form a configuration in 32S which can decay toground state '60+'60 nuclei no matter which level the transferred alpha particlegoes into . One or other of the two fragments must always be in a 4p4h state . This

002 `, `, 0 0 2J

01 0 4 4 0 1 0

100 4 m 100 (1) 1p001 `, a 001 r

000 4 4 000 (0) 1s

&,. Bennett et aI / Fission of `4Mg, 8̀Si and 3`S

(3) 2P 1f

003 003t020 020

110 110

200 2001 (2) 1d

S.J. Bennett et al. / Fission of 24Mg, 28Si and 32S

459

is entirely in agreement with the lack of any breakup of 32S to '60+'60 followingpickup onto a 2gSi projectile (fig. 3b). In the case of 32S formed by pickup onto the24Mg beam it is not immediately clear what reaction mechanism is responsible.However, if we consider it as the successive transfer of two alpha particles, thenwe can apply arguments similar to those above. Fig. 6b shows that a configurationinvolving two alpha particles transferred onto the 24Mg core can produce a configur-ation in 32S which can fission to '60+'60 nuclei in their ground states - just asobserved in the data (fig . 3c). This configuration can also breakup to excited statesin '60 as observed in fig. 6b. Again, since the yield arises from a different regionof excitation in 32S it is difficult to draw any inferences from the relative strengthsof the peaks.

It must be stressed that the role of the Harvey model as outlined above is onlyto indicate whether a particular fragmentation channel can or cannot occur. Henceit is only a prerequisite for observing cluster breakup and not an indication thatcluster structure exists in the nucleus. However, the results of the measurementsdescribed in the previous section have shown that, under the correct conditions,breakup has been observed from 24Mg, 28Si and 32S. This suggests that large scaleclustering does exist in all three nuclei.

It is interesting to compare this finding with the predictions of Nilsson-Strutinskycalculations for the same nuclei ".'g) . These reveal secondaryminima in the potentialenergy surfaces at large deformations . For the 24Mg nucleus the calculations showa ground state well with a large prolate deformation. This prolate shape hasanaturaloverlap with that of a nascent fissioning system, and may be the reason why the24Mg nucleus can be induced to fission in inelastic scattering . For 28Si and 32S thecalculations show ground state wells at oblate and spherical shapes, but also predictthat a prolate well should exist as a secondary minimumin both nuclei . Examinationofthe shell-model configurations appropriate to these secondary prolate wells showsthat they comprise 4p4h excitations "). It may well be that the excitation of 2gSiand 32S nuclei into this prolate well following alpha pickup mayprovide the doorwayto fission as in the 24Mg nucleus.

5. Summary

In summary, a search for fission following inelastic scattering of 28Si and 32Sbeams has failed to show evidence for processes similar to the symmetric fissionobserved from 24Mg. Specifically, the fission of 2gSi into '2C and '60 nuclei in theirground states or of 32S into two '60 nuclei in their ground states is not observed .In contrast, however, the breakup of 2gSi to '60

+' 2C and of 32S to '60+'60 hasbeen observed following pickup reactions onto 24Mg. These results, and thosepreviously recorded for 24Mg fission, are seen to be consistent with the schematicoscillator model of Harvey, indicating that the process of fission involving theselarge clusters is strongly dependent on the deformation of the fissioning nucleus.

460 S.J. Bennett et al. / Fission of 24Mg, 28Si and 32S

The results also suggest that large scale cluster structure occurs in all three nuclei(2aMg, 28Si and 32S) which may be related to the occurrence of prolate minima ithe potential energy surface predicted by Nilsson-Strutinsky calculations .

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3) 1 Wilczynski, K. Siwek-Wilczynska, Y. Chars, E . Chavez, S.B . Gazes and R.G. Stokstad, Phys . Lem181 (1986) 229

4) B.R . Fulton, S.J . Bennett, C.A. Ogilvie, J.S. Lilley, D.W. Banes, W.D.M. Rae, S.C . Allcock, R.R.Betts and A.E . Smith, Phys . Lett. 13181 (1986) 233

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