Nuclear Physics A279 (1977) 110-124;©North-Holland Publishing Co ., AmsterdamNot to be reproduced by photoprint or microfilm without written paminion flom the publisher

QUASIFISSION AND OTHER STRONGLY DAMPED COLLISIONSBETWEEN "CuIONS AND 1°7AuNUCLEIJ. PÉTER, C. NGO, F. PLASILT andB. TAMAIN

Institut de Physique Nucléaire, BP 1, 91406 Orsay, FUanceand

M. BERLANGER andF. RANAPPEUniversité Libre de Bruxelles, Physique Nucléaire Expérimentale, CP 229, 1050 Bruxelhs, Belgique

Received 12 July 1976(Revised 27 September 1976)

Abwnet: The interaction of a'CU ions with 19'Au nuclei have been studied experimentally at in-cident energies of 365 and 443MeV (1 .1 and 1.4 times the Coulomb barrier). Mass and kineticenergy distributions of reaction products have been measured at several angles. Near thegrazing angle, a continuous transition was found from elastic events to partially damped (PD)events, and to fully damped events (quasi-fission, QF). Away from the grazing angle a cleanseparation between elastic and QF events was observed. Events that may be due to fissionfollowing fusion (CF) were also obtained . Results are discussed in terms of decompositionintoPD, QF, and CF components. The QF kinetic energy is independentof the incident energy(implying full damping of the initial relative motion). It is lower than the Coulomb barrier andclose to the kinetic energies from the fission of similar systems . The angular distribution ispeakedsomewhat forward of the grazing angle for lowmass transfers. For large mass transfersthe yield increases slowly with decreasing angle. At 443 MeV a large contribution fromnegative angles is present. sopaccounts for more than 65 % ofthe reaction cross section cra at443 MeV and for more than 50 % at 365 MeV. The upper limit on CF is about 10 * of Qe,and aro is of the order of 25 % of oa.

E NUCLEAR REACTIONS 197Au(e'Cu, F), (e'Cu, X), E- 365,443 MeV; measuredmasses, kinetic energies, angular distributions ; deduced cross section s.

1. Introduction

The original purpose of this work was to investigate competition between completefusion (CF) and quasi-fission (QF) for reactions induced in heavy targets by projec-tiles between Ar and Kr. It is ]mown that in bombardments of heavy nuclei forprojectiles up to 4°Ar the complete fusion reaction dominates 1) while for Kr-induced reactions almost no complete fusion is observed andthe reaction is dominatedby quasi-fission ' -'4) . A preliminary experiment performed with the first Cu projec-tiles available from the Orsay heavy ion facility ALICE indicated that quasi-fissionaccounts for a large fraction of the total reaction cross section in 395 MeV 63Cnbombardments of 186W Cref5)].

t Present address: Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA.

197Au+saCu 111

Further motivation was provided by the desire to study in greater detail thecharacteristics of quasi-fission (for example, the energy dependance of the process)and to compare them to those of other strongly damped processes. Let us recall thedefinition of quasi-fission reactions which may be considered a subset of reactionsreferred to as deeply inelastic and strongly damped collisions . Quasi-fission are thosereactions in whichthe initial relative motion ofthe two nuclei has been fully dampedt.(This definition is justified by the observation that for reaction products away fromthe grazing angle the average kinetic energy is independent of bombarding energy.)The interacting nuclei mayexchange some number of nucleons, but they do not fuse .They separate under the influence of their mutual Coulomb fields and are observedwith fission-like kinetic energies . Thus quasi-fission may be regarded as the most in-elastic of two-body collisions, and as belonging to the incomplete fusion category 6).We have studied the interaction of "'Ca ions with t9 .Au nuclei at 365 and 443

MeV (276 and 336 MeV c.m.). The target was chosen partly because it produces thecomposite system 26 °108 which can be compared with the neighboring systems '8110and 272108 which were formed at similar excitation energies and angular momentabut with Ar ions.

In the present work we have determined the mass of one of the reaction productsdirectly by atime-of-flight technique. Such results are much more reliable than thoseobtained by the measurement of kinetic energies of fragment pairs in which massesare calculated based on principles of momentum conservation 4. 7). Certain aspectsof this work have been published earlier. Some of the data obtained at 365 MeVhave been discussed in ref. 2s), a comparison ofthe angular distributions obtained at365 and443 MeV was made in ref. 22), andthe mass distributions were presented,together with an interpretation, in ref. 12 ) . In this paper, we present a detailed com-parison of the energy and angular distributions at the two energies (as a function offragment mass) and results on "ternary" or sequential fission are also given.

2.Festal methodOur apparatus was capable of measuring both single events and coincident pairs

of events. Foreach single fragment we have measured the kinetic energy and the timeofflight over aknown distance (80 or 100 cm). The start signal wasprovided by a thinscintillator foil (NEI11, 145 hg - cm-2) coupled to a Radiotechnique XP 20220 fastphotomultiplier . The timing pulse was generated by means of a constant fractiondiscriminator built into the photomultiplier base. Energy and stop signals were ob-tained from a 600 mm' surface-barrier detector depleted to a depth of 80 gm. TheSherman-type preamplifier andthe constant fraction discriminator used in generatingt The name quasi-fission was first applied to events that had fission-like energies and sideward-

peaked angular distributions. The definition given here is consistent with the above propertied, butemphasized energy damping. Other authors often do not distinguish between quasi-fission and otherstrongly damped events, or define quasi-fission with emphasis on sideward-peaked angular distri-bution and/or narrow mass distributions.

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the signals have been designed for the large capacitance of the detector °) . Theangular acceptance of the stop detector was either 1.1° or 1.4° .In cases where coincident fragments were detected, a surface-barrier detector was

used such that it covered 11° in the direction perpendicular to the reaction plane, thuscovering most of the out-of-plane angular correlation . Runs were made with differ-ent positions of the coincidence detector in order to cover the in-plane angular corre-lation 9).The bias voltage of all surface-barrier detectors was adjusted such that the field at

the surface did not exceed 14 kV - cm-1 . At higher fields multiplication effectsappeared as evidenced by the presence of satellite elastic scattering peaks severalMeV above the normal peak. Details of the experimental method are given inrefs. 9- 10) .

The system was calibrated by means of elastically scattered target and projectilenuclei and by means of fragments from a spontaneously fissioning 1''Cf source .Corrections were made for energy losses in the target, the scintillator foil (time-of-flight system) and in the nickel shielding foils (coincidence detectors) . The time reso-lution of elastically scattered Cu ions was about 300 ps . The overall mass resolutionwas about 2 amu for masses near 63 amu and better than 4amu for masses near 130amu. For heavier fragments, the mass resolution is governed by the energy resolutionand is particularly poor (> 10 amu) when the energy is low (S 30 MeV) . Further-more, for these heavy fragments the light output from the scintillator foil is low (inspite of the large energy loss) and the efficiency is less than 100 % [ref. ii)].

3.1 . GENERAL

3. Results and discussion

Two typical contour diagrams are shown in fig . 1 for the 365 MeV case . At 56°,which is a smaller angle than the projectile grazing angle, thelight quasi-fission prod-ucts are well separated from the elastic (and quasi-elastic) Cu peak . At the angleclose to the grazing angle (86°), however, there is a continuous distribution of prod-ucts from the elastic peak to the quasi-fission region. These partially damped (PD)events appear to be a general feature of deeply inelastic scattering. The heavy quasi-fission products are not well separated from elastically scattered Au nuclei due to thelimitations in mass and energy resolution discussed in sect. 2.One of the most complete ways of presenting the data is illustrated in fig . 2 for the

higher (443 MeV) bombarding energy. For a range of final masses the differentialcross section integrated over the azimuthal angle, do/dB, is plotted as a function ofthe c.m . angle and ofthe kineticenergies is). In this figure, and in other results shownin this work, the kinetic energies and masses of the fragments have been correctedfor neutron emission . The total available excitation energy has been taken to beequal to the difference between the kinetic energies in the entrance and exit channels,plus the energy difference due to the different ground-state masses involved . It was

200

150

100

50

250

-200

x150

500

0

3.2. ELASTIC SCATTERING

3.3 . PARTIALLY DAMPED EVENTS

"'Au+a3Cu

113

Fig. 1 . Distribution of the reaction products observed at 56° (forward of the grazing angle) and 86°(close to the grazing angle). The ordinate is the lab kinetic energy and the abcissa the mass of theproduct, deduced from its time-of-flight and energy . At 86°, no heavy quasi-fission fragments arepresent since, because of their low velocity, they cannot recoil to angles larger than about 70° in

the lab. The contour labels denote the relative yield.

assumed that this excitation energy is shared between the two fragments in propor-tion to their respective masses, and that mainly neutrons and gamma rays are emitted.

Angular distributions of elastic scattering were measured at 365 MeV in order toobtain an estimate of the quarter-point angle, e*, where the elastic scattering is 25of the Rutherford value. The related quantities Im,=, the angular momentum at 0+andcR, the total reaction cross section, were also obtained. The values were found to beBk = 110° t5° c.m., l. = 100± 10 6 and cß = 500± 100 mb. The value of 0+ wasnot obtained experimentally at 443 MeV, but from the above results (and assuminga constant value of the effective radius parameter). The values at 443 MeV were cal-culated to be 0+ - 70°f5° c.m., l. = 190f10 fl and aa = 1500t200 mb.

Fragments with kinetic energies between those of elastically scattered particles andthe completely damped quasi-fission products form a continuous transition betweenelastic scattering and quasi-fission at angles near the grazing angle. They are localized

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5:200m

150Tm 100

.2mE 250YE 200V

150

100

250

200

150

100

1

1

1

1

d 20'

mb

UCU+ 197Au 443MeV

aUW .am .u M.84-92(M .75-130)

M=48-56

0 30 60 90 120 150 180

300

200

1001,231

300 "S2

200 .2:E

300

200

100

ecruFig. 2 Contour diagram of the "light reaction products as a function of their cm. angle andkinetic energy (left scale) for several groups of masses. Elastically scattered 66Cu ions have beenexcluded. The scale on the right gives the total kinetic anergy corrected for particle emission by a&-suming that the excitation energy is shared bythe two products in proportion to their respective meal.The shape of the figure for products in the mass range 75-130 is the same as that for M- 8492.The dashed line indicates the decomposition into partially damped events and quasi-fission events .

both in angle and in the extent of mass transfer involved. (See the dashed lines offig. 6.) The question of whether these events should be separatedfrom thequasi-fissionevents and treated separately is debatable. We chose to do so primarily to underlinethe completely damped nature of the quasi-fission reaction, and dueto the fact thatquasi-fission accounts for a very large fraction of the total reaction cross section. Inorder to make the decomposition between PD and QF events, we proceeded asfollows. At a given bombarding energy, for a given final mass, we observe that theenergy distribution is almost Gaussian with a constant c.m. width at the angles awayfrom the grazing angle. Thus, at the angles close to the grazing angle, we have ex-tracted the QF component by applying the same width at the low energy maximumor shoulder . In this decomposition at 365 MeV, approximately all PD events arethose having a total kinetic energy greater than 240 MeV. At 443 MeV, this limit is280 MeV, due to the increase of the width of the QF kinetic energy distribution (fig.2).

3.4. QUASI-FISSION

19 11Au+63Ca

113

The masses of partially damped events are always close to those of the target andprojectile, but the greater the energy loss, the broader the mass distribution (see forexample fig. 5) . The mass distributions of PD events, however, are considerablynarrower than those of QF events (see figs . 5 and 8).The decomposition between QF and PD described above leads to large errors in

the estimated PD cross sections : 160±50 mb at 365 MeV and 300±100 mb at 443MeV.

Acm(Ught fragment)Fig. 3. Average quasi-fission c.m . total kinetic energy for fragments of mass sw 63 amu (projectilemass) versus the c.m. angle at the two different bombarding energies, E,�. The two stars refer todoubly-energymeasurements corrected for neutron emission on the assumption that the total avail-able excitation energy was divided between the two fragments in proportion to their masses. Allother points were deduced from the measured kinetic energy of the light fragment only. The trian-gles giveenergies thatwere corrected for neutron emissioninthe same way as the stars, theopen circleswere obtained by assuming that neutron emission takes place from the heavy fragment only, and theclosed circles were obtained on the assumption that neutron emission takes place before scission .

The dashed lines indicate regions ofpartially damped events.

3.4.1 . Bltary process. From coincidences experiments we have determined that atleast 90 % of the quasi-fission (and partially damped) events are binary . This followsfrom the number of coincident events observed, andfrom the fact that the sum of thec.m. angles of coincident pairs add up to 180°. Of the remaining events for whichpartners were not observed, a large fraction can be accounted for by the finite sizeof thecoincidencedetector in the out-of-plane direction. Particle evaporation from thefragments causes a substantial out-of-plane spread of events that may initially havebeen strictly binary, and hence, co-planar with the beam. Thus true ternary quasi-fission events, if they exist at all, amount to only a few percent ofthe total number ofQF events . (Ternary events of the sequential-fission type will be discussed later.) We

100

130C.M .

Fragmentkinetic 150energy(uncorrected)

200

150

150

63 Cu +197Au

443 MeV

4

Fig. 4. Average c.m. kinetic energies for several mass ranges at 443 MeV. The single fragment c.m.kinetic energy scale (uncorrected for neutron emission) is given on the left. The total kinetic energyvalues (corrected for neutron emission)are given on the right for the horizontal solid lines which de-note average quasi-8ssion values (label q-f). Corresponding fission values are also given (label F,see teat for references). The dashed lines indicate regions where partially-damped events contribute.

30 60 90 120 150 1809 cm.

220215

207 200 c.m .rotdkketic

200 energy

204

180

195 correctedforneutron

emission

190

Fig. 5. Contour diagrams of the yield of light reaction products as a function of the c.m. totalkinetic energy and the fragment mass for ssCu+197Au at 363 MoV. The 86° results are at an aagieclose to the grazing angle, while the 56° data are forward ofthe grazing eagle. Contour labels denote

the relative values.

M =121- 129

t M = 84- 92

Mt t

= 75 -63

1I M

+ II II I

t t

=66-74

I II- M =48 -56

197Au+63Cu

117

have assumed that all observed quasi-fission events are binary and show our resultsonly in terms ofthe "light" fragments, i.e. the fragments lighter than half of the totalmass of the composite system `108.3.4.2. Kinetic energies. Fig. 3 shows average quasi-fission kinetic energies as a

function ofthe c.m. angle for fragments which have masses close to those of thetargetand projectile. Results for both bombarding energies are shown. Different symbolsrepresent different assumptions that were made regarding particle emission from thefragments (see caption to fig. 3) . For any given assumption, within experimentaluncertainties, the average kinetic energy is constant as a function both of angle andof bombarding energy. The average value is 200t5 MeVt. The amount of energyconverted from relative motion into other degrees of freedom is very large: 75 MaVat 365 MeV bombarding energy and 135 MeV at 443 MeV.

In fig. 4, the average kinetic energy is given as afunction ofthe c.m . angle for differ-ent product mass groups for the 443 MeV case . Near the grazing angle, where QFproducts are arbitrarily separated from PD products, the average kinetic energy ishigher than that obtained at other angles for quasi-fission alone. There may also beangular momentum effects near the grazing angle that increase the energy, as will bediscussed below. The average QF kinetic energy is highest (215 MeV) for nearlysymmetric mass-splits (fragment masses from 121 to 129 emu) and decreases slowlyfor more asymmetric mass ratios . This behavior can also be seen for the 365 MeVcase in the contour diagram of fig . 5.The average kinetic energy values are close to those observed for similar mass splits

from the fission of compound nuclei 20710S and 278 110. These systems have boonobtained from Ar bombardments of 232Th and 2ssU [ref. 14 )] . The excitation ener-gies and angular momenta involved in the Ar cases are similar to those involved inthis study. The comparison, however, cannot be made for the peak of the QF yield,since no fragments are observed at such asymmetric mass divisions in Ar-inducedfission. The fission-like kinetic energies observed here imply that quasi-fission eventsresult from a descent down the fission valley ofthe potential energy surface 1 s).The fact that the observedkinetic energies are considerably lowerthanthe Coulomb

barrier suggests that the nascent fragments are considerably deformed. This is alsoconsistent with a fission-like process. Similar results were obtained in the case ofquasi-fission for the "Kr+2 e 9Bi system 6).We have made the following estimates ofthe portion of the kinetic energy which is

due to the rotational energy of the system. The orbital angular momentum of thesystems can be estimated by assuming that the two nuclei clutch together andform arigid body at a distance equal to the sum of their radii 16, 17). ForCu +Authe totalt In contrast to the 200 NEWgiven here the value of 20615 MeVgiven in ref. ") was obtained

when all the final fragnents are taken into account. The average nus ofthe light fragment is greaterthan 63, and since the total kinetic enarly increases as the mass asymmetry decreases, the overallaverage kinetic energy is greater than that ofthe fragment pair 63-197. Total kinetic energy resultsgiven in ref. ") forthe 365 MeVcase am in error, since the data of fig. 4 in ref. ") areplotted too lowby 15 MeV.

11 8

J. PÉTER et aL

rotational energy is 60 % of the value before contact. This decomposes into 20.9associated with the heavy quasi-fission fragment, 3.1 % associated with the lightfragment and 36 % with the orbital angular momentum . At 365 and 443 MeV theaverage initial angular momenta contributing to quasi-fission are 53iî and 12411,corresponding to average orbital rotational energies of 3 and 14 MeV. Since thesystem at scission is likely to be more elongated than the clutching sphere configu-ration, the rotational energy contribution to the observed kinetic energy is lower thanthe above values, andthe difference between the contributions at the twobombardingenergies should be less than 10 MeV. The fact that the average kinetic energies at thetwo bombarding energies were found to be within 10 MeVof each other supports theabove conclusion.The obvious reason whythe kinetic energies near the grazing angle are higher than

those away from it is that the incident energy has not been completely damped (seefigs . 3 and 4) . Angular momentum effects, however, could also play a role. If weassume that the events near the grazing angle are due to the highest possible partialwaves which contribute to quasi-fission, then the orbital rotational energy contri-bution maybe substantial. At 443 MeVand 1 ~ 175b the rotational energy is expectedto be 27 MeV. At 365 MeV, the highest partial wave that can be reached is 75 handthe corresponding rotational energy is 5 MeV. Thus no effect is expected at thislower energy . The experimental results are consistent with the above speculations .The above remarks concern the average kinetic energies . The width of the kinetic

energy distributions can be measured, for different masses, at angle away from thegrazing angle. At a given incident energy, it is almost constant, but varies from ;ts 25MeV at . 365 MeV incident energy up to ss 50 MeV at 443 MeV. This increase isroughly proportional to the calculated increase in temperature of the compositesystem 11). This broadening is similar to the broadening of the fission . fragmentkinetic energy distributions with the temperature of the fissioning nucleus 9).3.4.3 Angular distributions. The overall angular distributions of the,light QF frag-

ments integrated over the azimuthal angle, dv/d9, are shown in the top part of fig . 6(solid line). They peak at an angle slightly inside the grazing angle as was observedfor the Kr+Bi system at several energies a' 7. 18 ) . At 365 MeV this peak is rathersharp. (FWHM sts 30°) and da/dB decreases strongly at very forward angles . Incontrast, the peak at 443 MeV is broader and decreases slowly at forward angles.Close to 0°, it still has 50 %of its peak value. This implies a contribution from nega-tive angles and distributions observed at a given angle result from acombination ofevents from two different (one positive andone negative) angles . Such decompositionsinto positive and negative angles are shown in fig. 7. The 365 MeV data can be ex-plained without the postulation of negative angles since in this case da/d9 appearsto be near zero at 0° . As we go from 365 MeV to 443 MeV, the finite values of da/dsat 0° can be anticipated. from the observation that the angular distribution peak hasbroadened and moved forward in .angle.Also shown in fig. 6 are angular distributions for specific regions of the fragment .

M " 111-130

mb/red

443 MeV365 MeV

ded6

Cu + Au

443 MeV

1000

500

2010

Fig. 6. The cm. angular distributions of quasi-fission events (solid carves); fusion-fission eventsif any are included . Also shown is one angular distribution for partially damped events (togetherwith quasi-fission events, see dashed lines).The bottom curves are for several light-mass windows,

the upper curves are for the overall mass distribution. Note the different ordinate scales .

0 30 60 90 120 150 180

110

90

75

.f.

----- -------- ----. ..

.~.... . . . . . . ....... . . . . . . . . .... . .. . . . . .. ....~ .

~~130

" .<M>a~30

-180

-90 "

-30

0

3

90

""180'8 cm.

Fig. 7. Possible interpretations of the angular distribution at 443 MeV (see text).

9yr

M = 121-129

M 84- 92

Ms75-83

t M=66-74

1 M " 57-65i

M .49-56

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05*200ôiL

ds100

0

50 '

100

150

200moss (O.M .U.)

Fig. 8. Contour diagram of reaction products observed at 44° (close to the grazing angle) at an in-cident energy of 443 MeV. The contour numbers provide a relative scale. The "ternary" events

are not present at 365 MeV(see fig. 1) .

JLM

40 60 e0 100 120 0

100

2DOM.vMon

tab.kkwtia aasrWr(Ma11)

ddildEmbor,MW-'

Fig. 9. Mass distributions (left) and lab kinetic energy distributions (right) of the "ternary" events(see fig. 8) detected at three angles .

mass distribution . It can be seen that the peaks in the angular distributions are due tofragments that have their masses within t12 amu ofthe projectile mass. At 365 MeVthe pealsis very sharp for masses near that of the projectile andbroadens considerablyas mass transfer increases. As mass equilibration is approached the peak disappears

10a(Lob)

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o

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altogether, and the angular distributions become flat or slightly forward-peaked. Itis tempting to conclude from all of the experimental results that rotation of thesystem, mass transfer and energy damping all proceed simultaneously . Productsemitted forward ofthe grazing angle have been in contact with each other longer thanthose at the grazing angle, leading to greater mass transfer and to more completedamping.

Fig. 10. Angular distribution of the "ternary" events (see fig. 8) in the lab system. The ordinate isthe differential cross sectionfor the detected fragments (i .e . it should be divided by 2 or 3 if one as-

sumes a process producing two or three fragments of similar mass and energy).

3.5. SEQUENCIAL FISSION

At 443 MeV aregion of events was found with masses near 100 amu and with lowkinetic energies (see fig. 8). These events have been observed at all angles in tworunsinvolving different targets. They are not likely to be due to some target impurity. Theshape of the mass distribution of these events is the same at all angles . It is roughlyGaussian with an average value of about 97 amu anda width of 30 amu FWHM (seefig. 9). The lab kinetic energy distribution is also broad, and its average value variesfrom about 100 MeV at very forward angles to about 50 MeVat 90°. The lab angulardistribution dgldQ is strongly forward-peaked (see fig. 10). The integrated crosssection for these fragments is 150f30 mb. At 365 MeV no such events were seen,i.e. the cross section is less than a few mb.The characteristic feature of these events is the absence of coincident fragments in

the reaction plane. Thus they are likely to be due to a process which results in morethan two final fragments. The two possibilities are: (i) ternary fission of complete-fusion nuclei, and (ii) fission of the excited heavy quasi-fission products.The first hypothesis leads to a cross section of 50 mb, i.e. the ratio of ternary to

binary fission would be > 0.3, which is much larger than the few percent (due toternary fission or sequencial fission) observed for similar fissioning nuclei ").

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The average mass of 97 is in agreement with the second hypothesis . The crosssection is 75 mb, i.e . Ps 7 % ofthe quasi-Au could undergo fission. Calculation ofthecompetition between fission and particle emission in the de-excitation ofthe quasi-Aufragments requires a knowledge of their distributions in charge, mass, excitationenergies and angular momenta which are not known. Reasonable assumptions leadto an excitation energy of about 100 MeV and angular momenta which reach 60h.For nuclei below Au, this corresponds to a probability for fission of the order of10 % [ref. 1°)]. At 365 MeV, the excitation energy is only about 65 MeV, the angularmomentum can reach only 256 and the probability of fission is expected to decreasestrongly, in agreement with experimental observation .We have calculated the angular and kinetic energy distributions which are expected

on the above hypothesis . The results are in agreement with experimental data, al-though the calculated angular distribution is less forward-peaked than the experi-mental one.This process of fission following quasi-fission (or partial damping) becomes the

most probable process when the target is U or Th [refs. s : 14)] andwas also observedwith a Di target 14).

3.6. COMPLETE FUSION

It is possible that fragments in the mass range 110-130 amumay not be due to thetail of the quasi-fission distribution, but due to fission following fusion. Such fissionis expected to produce a broad Gaussian mass-distribution peak which has a widthof several tens of amu andwhich is centered at symmetric mass divisions 1. so).

Conceptually, fission following fusion and the extreme tail of quasi-fission are quitedifferent. Both processes have a first common step -the full damping of the initialrelative motion . There are differences, however, in the second stage of the process. Inthe fusion-fission case the two nuclei fuse, undergo several rotations as a single (com-pound) nucleus which subsequently undergoes fission. On the other hand, in quasi-fission, two nuclei remain stuck together for a complete rotation or more, duringwhich mass transfer is taking place. Thus in the fusion case, the initial axis of ap-proach is destroyed and, later, the fission direction is chosen independently. In thequasi-fission case, however,the system remain extended along the initial axis and laterundergoes scission along this same axis . Unfortunately, since this can occur afterseveral rotations of the system, expected experimental distributions in the two casesare identical. Thus it is not possible from our results to differentiate between thesetwo possibilities.From our data, we obtain an upper limit on fusion-fission of 150 mb at 443 MeV

and 30 mb at 365 MeV. These values can be compared with 90±25 mb found forFe +U at energies less than 528 MeV [ref. 21)] . Two possible interpretations of theangular distribution at 443 MeV are shown in fig. 7. In the upper part of the figure aconstant fusion-fission component is included . In the bottom part of the figure thequasi-fission tail is assumed to extend through the region of negative angles back to

167Au+63Cu

123

positive angles. The larger the rotation, the more nearly complete is the mass equili-bration. The average light-fragment masses consistent with the data are indicated infig . 7.

3.7. CROSS SEMONS AND ANGULAR MOMENTUM RANCIES

The sum of the cross sections for complete fusion acF , quasi-fission (aQF) andpartially damped (including quasi-elastic) events (QPD) is, within experimentaluncertainties, equal to cA (see table 1) . The value of ccF lies between zero and themaximum value indicated, and consequently acF varies between the maximum andminimum values given. In any case, quasi-fission is the most important reaction typesince QQF accounts for more than 65 % of ca at 443 MeV and for more than 50 % at365 MeV. The cross section QFD is of the order of 25 %, and aCF is less than 10 % at443 MeV and less than 6% at 365 MeV. These values are quite similar to those ob-tained with heavier ions, such as "Kr [refs. 2-4)].

TAWX 1

Cross sections (mb) and possible ranges ofpartial waves for the different reactions

See subsea. 3.9 for the separation between PD and QF. For each value in the first line it is as-sumed that there are no complete-fusion events, while a complete fusion contribution is assumedin the second line (sea text).

We can calculate range of initial partial waves which contribute to each reactionusing the simple sharp-cutoff approximation . This was done in table 1. The partiallydamped reactions are due to grazing collisions where only the tails of the nuclearmatter ofthe two nuclei interact and thus the friction forces do not act sufficiently toabsorb the whole relative kinetic energy. At both bombarding energies, their rangelies 20 units below lm,=. The fully damped collisions are due to a deeper interpene-tration the two nuclei and correspond to 1-waves up to 75 at 365 MeV and 175 at 443MeV. The experimental results (variation of the mass distributions and of the kineticenergies with angle, the continuity between partially and fully damped events) canbe explained at 365 MeV by assuming that the higher 1-values correspond to anglesclose to the grazing angle, and that lower 1-values correspond to forward angles . At443 MeV forward angles correspond to intermediate 1-values and backward anglesto the lower 1-values .

If complete fusion does not occur, the lower 1-waves, which involve longer inter-action times, correspond to very backward angles. (This is consistent with the

F4.s 9.e. Qe(mb)

ocr QQr vru QCF+GIQr+aru " 1cr for

365 276 500±100 0 280± 50 160± 50 440± 80 98 0 0-75 76- 9530 250± 50 160± 50 440± 80 98 0-25 26-75 76- 95

443 336 1500±200 0 1250±100 300±100 1500±150 193 0 0-175 176-195150 1100±100 300±100 193 0-61 62-175 176-195

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observation that the extent of mass transfer at these angles is high as seen in fig . 4.)There are two ways in which lower 1-waves may be associated with far backwardangles :

(i) If the composite system lives a very long time, the observed backward anglesmay, in fact, be very large negative angles.

(ü) Ifthe composite system lives asomewhat shortertime, the slow rotation oftheselow 1-waves leads to backward angles.

Ifcomplete fusion occurs, it is likely to be due to the lowest 1-values involved in thereaction (see the second line at each energy in table 1).

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