2.N I Nuclear Physics A250 (1975); 351 --363 (~) North-HoUandPublishino Co., Amsterdam 1

Not to be reproduced by photoprint or microfilm without written permission from the publi,~h~"

COMPLETE FUSION AND QUASI-FISSION REACTIONS

INDUCED BY a4Kr IONS ON HEAVY TARGETS

J. P~TER, C. NGO and B. TAMAIN

Chiraie Nucldaire, lnstltut de Physique Nucl#alre, BPI, Orsay, France

Received 15 May 1975

Alastraet: Cross sections for fission (complete fusion) and quasi-fission are measured at a given angle for the systems Kr-~Ho, K r + W , Kr+Bi , Kr-kU in the energy range 450--525 MeV. The cross sections for complete fusion are unexpectedly low and the cross sections for quasi-fission are high. The cross section for close collisions (sum of the complete fusion and quasi-fission cross sections) is compared to the value calculated with the critical distance concept. The possibility that complete fusion does not occur for the lowest impact parameters is discussed.

E

NUCLEAR REACTIONS, I*SHo(S4Kr, F), E = 450, 492 MeV; l s6w(S 'Kr , F), E = 492 MeV; 23su(*°Ar, F), E = 300 MeV; a°gBi(S4Kr, F), E = 500, 525 MeV; 23sU(a4Kr, F), E = 500 MeV; measured correlated kinetic energies; deduced acar

and aqr.

1. Introdnctton

In a preceding paper 1), we have studied the cross sections for complete fusion ~rcT between 4°Ar projectiles and medium or heavy targets. We have shown that, for energies up to twice the interaction barrier, OCT is always more than 60 % of the reaction cross section ~Tnt, as is also the case for lighter projectiles. The aim of the present work is to investigate the probability of complete fusion with heavier projectiles, such as 84Kr. An obvious reason is to determine the possibility of pro- ducing super-heavy compound nuclei by fusion of Kr with a heavy nucleus. Partial results have been published, which show that complete fusion is not the main reac- tion channel open at energies up to 1.2 times the interaction barrier 2, 3), and a new type of reaction was observed which was named "incomplete fusion" 3) then "quasi-fission" 4).

The measurements have been done with S4Kr projectiles and with several targets: 238U at 450 and 500 MeV bombarding energy, 2°9Bi at 500 and 525 MeV, '86W at 492 MeV, and ~6SHo at 450 and 492 MeV.

If formed, the compound nuclei have a low fission barrier and the heaviest probably have no fission barrier at all. In any case, the probability of fission is very high due to the excitation energy of several tens of MeV and due the orbital angular momen- tum brought in by the projectile. All the nuclei which result from the complete fusion of the projectile and target nuclei undergo fission, whether or not these nuclei

351

352 J. PI~TER et al.

have lived a time long enough to reach the thermal equilibrium which characterizes the compound nucleus. The measurement of the cross section o r of fission fragments issued from a complete fusion nucleus is thus equivalent to the measurement of ¢rCF.

2. Expe~raental technique

We used the correlated fragments technique, already used for measuring a t in the case of reactions induced by 4°Ar ions. This technique is detailed in ref. ~): the energies of two coincident heavy products are measured with surface-barrier detectors X and Y; X is held at a fixed angle and Y is moved in order to cover the whole angular correlation between the two products. An off-line analysis allows us to determine which reaction each event is due to: elastic scattering, quasi-elastic transfer, quasi-fission or binary fission. In addition, the difference in time of flight between the two products is also measured and helps us to reject random events and to determine if the reaction is a two-body one (two main heavy final products).

The main differences between the Kr induced reactions and the Ar measurements are due to the higher masses and energies of the S'Kr projectiles: (i) the c.m. velocity of the system is higher and the average correlation angle between the two products is smaller, and (ii) the kinetic energies of the products range from 500 MeV for S4Kr ions down to 40 MeV for products of mass around 200. The relationship be- tween the pulse height delivered by the detector and the mass and energy of the product is not well known for such a wide range of masses and energies. Some cali- bration work has been done ,9) and we have checked that the masses and energies of elastically scattered projectile and target nuclei are correctly reproduced. The

Kr. U 50OMeV >, ex-- 55"

~ Uf(x)- Kr(y) Oy =40- 85 = ¢-.

500

J Kr{xl-U(y) I

.f i

, o o

I !

I00 500 ChQnne l x

Fis. I. Pulse-height (eneriD') o f detector Y versus pulse-height o f detector X contour diagram. M e V Kr ions on a ===U target. X was held fixed at 0x = 55", Y was moved over the range

#v = 40-85 °.

**Kr 353

remaining errors due to this technique do not allow a precise study of the distri- butions of the fragments, but they have little effect on the gross features of the distributions and the cross sections which are studied in this paper.

Fig. I shows a two-dimensional diagram of the events detected, the axes being the pulse heights delivered by each detector. This figure has been drawn for a fixed value of 0x, 0v being varied over the range indicated.

In the case shown in fig. I, several events are due to fission following transfer reaction. This type of event has been observed with Kr ions and Z°gBi and 238U targets, as was also the ease with Ar projectiles. As explained in ref. ~) such ternary events can be eliminated when the results are transformed into the c.m. system.

For most of the systems studied, the fission differential cross section has been measured only at one angle 0x, close to 90 ° c.m. To calculate af, we assumed that the angular distribution of the fission fragments is close to the I/sin0 shape which has been predicted by Halpern and Strutinsky 5), and experimentally measured in the case of lighter heavy-ion projectiles ranging from tZC to 4°Ar [refs. 22-26)].

3. Resu l t s

Figs. 2, 3a and 4 are two-dimensional contour diagrams of the binary events de- tected for several systems, after transformation to the c.m. system. The total c.m. kinetic energy is plotted versus the mass of the fragment detected by the fixed X- detector. The high peaks are due to elastically scattered Kr or target nuclei. Their width is due partly to resolution effects (angular width of the detector, energy reso- lution) and partly to the presence of quasi-elastic transfer products which have masses and kinetic energies in the vicinity of those of the initial system.

The fission fragments have a mass distribution peaked at half of the mass of the complete fusion nucleus. Their kinetic energy is expected to be lower than the c.m.

40o 381

u ".7

-~ 300

200

i i

B4Kr ~.2}eU Elab. 500MeV Ecjw - 381 MeV ex • 55"

- ~ I ey . 4 0 - 8 5 " / / ~

84 150 238 Moss X (a.m.u.)

FiI. 2. Two fragment total kinetic enerly in the c.m. venus mass o f one fragnwnt contour diaIram with the same experimental conditions as in i l l . I. The "ternary" events o f ill- I are not included in this flIure since they do not satisfy the requirements for a two-body reaction. The trianIIe is the

aroa where fission fragments issued from complete fusion nuclei are expected.

>.

350 339

[ I : ' * . IOOMeV El~ = 492 MeV 84Kr *186W -- 2"fOlio ~ , = 173 Ecru = 359MeV

e= . 40 °

300

250

200

=E

=., 150 g u

257 ~ zso 0 p .

200

150

354 J. PETER e t al.

, t , t , t , 50 84 tOO 135 150 186

40"~ Z38U ZrlIIIO t E*= 125 MeV E~= 300MeV - - g.,...166 Eom- 257 MeV

- ~ e x . 65"

!

]

total bombarding energy (elastic scattering energy) for the cases studied here. Such events are not present in fig. 2 ( K r + U ) , only a few are present in fig. 3a (Kr + W) and some more are present in fig. 4 (Kr + Ho). For the case of Bi bombarded by 500 and 525 MeV Kr ions, the figure is quite similar to fig. 2 and can be found in ref. 3).

Two other peaks appear at masses close to the mass of Kr or to the mass of the target nucleus. Their kinetic energy is close to the expected fission kinetic energy. They are due to "quasi-fission" or" incomplete fusion" events.

a t f l t 40 50 lbO 139 150 200 2:38

Frogment moSS (omu)

Fig. 3. Comparison between the interactions of Ar on "3sU (bottom) and Kr on t s~w (top), giving fusion nuclei of equal charge (110) and similar masses (278 and 270). Excitation energies and orbital angular momentum distributions are similar. Elastic scattering and/or transfer reaction products are either detected or not, depending on the value of the detection angle as compared to the values of the grazing angles for the projectile and target nuclei. In the case A t + U , the triangle-shaped distribution which is characteristic of fission fragments following complete fusion is observed. A few similar events seem to be present in the case of Kx+W, but much more numerous are the incomplete fusion products (mass around 84 or 186, and kinetic energy close to that of fission). Very few elastically scattered Ar nuclei or light quasi-elastic transfer products are

detected, since 0x is above the grazing angle for the projectile ( ~ 53°).

S'Kr 355

e4,... 16S.^ 249..~ (E*.91MeV Eicb-492MeV | . . . . . . ,03 L . I I _ . ,7o Ec~, - 3Z~ ~ v

:1

, 1 1 , 50 84 I00 124 150 165 200

Fraqrnent mass (a .m.u)

Fig. 4. Same as fig. 2 for 492 MeV Kr on a 16SHe target. No elastically scattered He nuclei (or quasi-elastic transfer products of mass around 165) are detected, since the detection angle 0x is

well below the grazing angle for the scattered target nucleus ( ~ 60°).

The corresponding fusion cross sections are given in table 1. The low accuracy is due to the dimcult separation between fission events issued from complete fusion and quasi-fission events issued from incomplete fusion. The integrated quasi-fission cross section is given when the angular distribution has been measured 4). In the other cases, the differential quasi-fission cross section has been measured only at one angle.

The very low differential quasi-fission cross section observed for K r + U (fig. 2) as compared to the values measured for the other targets can be explained in two ways. First, in this case, the measurements have been done at an angle which is 50 ° lower than the grazing angle for the projectile, while the observed quasi-fission angular distribution 4. 6. 7. to) indicates that the differential cross section may have vanished at such an angle. Second, the heavy quasi-fission products in the vicinity of U have a high probability of undergoing fission even if their excitation energy is only a few MeV. The ternary events observed in fig. I can be due to this two-step process, as has been confirmed recently by an analysis of the products of reactions induced by 600 MeV Kr ions incident on a thick U target it).

The influence of the entrance channel appears clearly in fig. 3. Fig. 3b referr to the system *°Ar+2~su which leads to nearly the same fusion nucleus as the system S ' K r + lS6w (fig. 3a). The bombarding energies have been chosen so that the exci- tation energies and the distributions of orbital angular momenta are nearly the same.

TA

BI.E

I

Exp

erim

enta

l co

mpl

ete

fusi

on a

nd

qua

si-f

issi

on c

ross

sec

tion

s

Pro

ject

ile

Tar

get

Fu

sio

n

nucl

eus

S4K

r *S

SHo

,4tL

w

S4K

. r ls

~ W

a~

Oll

0

"OA

r =

ssu

=~

S110

S

'Kr

~°*B

i =9

~119

S*K

r 23

s U

3"=1

2 8

(MeV

) (M

eV)

calc

ca

lc

(mb)

(M

eV)

(rob

)

450

298

263

630

20

0~

100

49

2 32

6 10

50

23

0±

10

0

492

339

284

900

15

0~

70

30

0 25

7 17

2 20

15

1030

:k12

0 50

0 35

7 31

2 73

0 <

40

52

5 37

3 92

0 <

25

50

0 37

0 33

5 59

0 <

10

(da/

d.O

)°r

(mb/sr)

0x

(deg)

20 +

10

15-/

- 7

70

+ 1

5 20

to

280

?

50 °

35 °

40 °

65 °

54 °

26°-

120

° 55

°

O'q

f (rob)

500

m

t~

Vs

is t

he i

nter

acti

on t

hres

hold

.

t*Kr 357

The binary fission cross section (and thus the fusion cross sections) are quite differ- ent for the two systems (table 1).

The ternary fission contribution cannot explain this difference. Indeed the orbital angular momentum populations are nearly the same for the two systems and the ternary fission contribution to the total fission cross section has been found to be low for both. the argon case a) and the heavier-ion cases 9). [It should be noted that the binary events in ref. 9) may be quasi-fission events, but the conclusion rel- ative to the low value of ¢CF is not modified.]

4. Discussion

We will discuss first results on quasi-fission, and second, results on complete fusion and quasi-fission together. The data we use are from the present paper and from refs. 6.7.,o. 11).

4.1. QUASI-FISSION

Let us first summarize the observed characteristics of quasi-fission. (i) The quasi-fission crosssections for Cu and Kr beams are high ( ~ ½ of the total

reaction cross section). (ii) The angular distribution of quasi-fission is narrow and peaked at an angle

lower than the grazing angle by around I0 °. (iii) The total kinetic energy for quasi-fission is close to that for fission with the

same mass ratio. The consequences of these properties are: (i) Several tens of/-waves contribute to quasi-fission. (ii) Trajectories of different /-waves have been focused to a rather well defined

direction. An interpretation is that the Coulomb trajectories for highest /-waves h.ave not been perturbed while those for lower/-waves have been forward scattered.

(iii) The initial kinetic energy is almost completely damped during the collision of the two initial nuclei: a composite very deformed system is obtained; the strong Coulomb repulsion between the two parts of this system tends to separate them; a neck appears between them and finally scission occurs for a shape quite similar to the scission point shape in fission.

In quasi-elastic reactions the products are observed around the grazing angle and the damping of the relative motion is small. In fig. 5a it is shown that at the grazing angle a nearly continuous energy spectrum exists between the energy corre- sponding to elastic scattering and the energy of quasi-fission products. Quasi-fission reactions can thus be considered as the deepest inelastic collisions. The kinetic energy loss between the entrance and the exit channel cannot be greater, because the final kinetic energy cannot be lower than the repulsion energy between the two deformed charged separating fragments.

358 J. PI~TER e t al .

~so • a) Kr + Bi 525 HeY I I

5 9 - 69" Lob.

100 i

F x 1/lO

so o i

100

SO

L II E =1

Z

b) --Ix 111o

ct - Oi

4 9 - 59" Lob.

quosi - fission (Light f rogmtn t )

~ m

x I110

el. K r

"I

!

i

i

r I t

200 400 600 go0 Kine t i c e n e r g y (channeLs)

Fig. 5. Energy distributions of the light quasi-~ssion products observed at an an~e close to the grazing an~e for the I~" projectile (1) stud lower than this Ip'azing angle (b), The width oftbe elastic peaks is due to the I0 ° angular aperture of the detector, Th~ width can also contribute to the

filling in of the separation between quasi=elastic and quasi-llssion products,

S ' K r 359

4.2. C O M P L E T E F U S I O N A N D QUASI-FISSION

The complete fusion cross sections acv indicated in table 1 for the Kr induced reactions should be regarded as maximum values. It is indeed possible that the mass exchange during the quasi-fission process is sufficiently important to produce two final fragments of similar mass. This has been observed in the two experiments for which the mass distributions were measured at several angles 6, ~). The result for Kr + H o is possibly less affected by this effect: a broad maximum appears around the mass value equal to half the total mass. The mass of the system (fig. 4), and the attribution of these events to the "complete fusion-fission" process is more probable.

The systematics of OCF as a function of the kinetic energy, masses and charges of the projectile and target nuclei do not allow us to predict the low values of Ocv since for projectiles up to 4°Ar, OCF is always more than half the reaction cross section oa. The first simultaneous observation of a high quasi-fission cross section and an unexpectedly low complete fusion cross section for the system K r + B i led to the remark that quasi-fission occurs "instead o f " complete fusion 3,,): the sum of OcF and Oqt. is more than half o~

A more quantitative comparison can be done using the concept of critical distance introduced by Galin et aL 12). The energy density formalism in the framework of the sudden approximation was used to calculate the interaction potential of the system of the colliding ions. They have noticed (for projectiles up to argon ions) that within a large region of the bombarding energy, a critical distance Re,it must be reached for fusion to occur. Moreover, this distance remains constant with the bombarding energy for a given system and the critical parameter defined by

Rc, , (I) refit ~'1" .a_ zf t '

where A t, ~ are respectively the mass of each partner, is nearly constant for all the systems.

This concept can be used to calculate the critical angular momentum of a given system at a given bombarding energy. Then, the fusion cross section can easily be calculated by the following formula 2o):

2 = R<, , , ( i - V(R<,,,)IE), (2)

where V(R,:,) is the corresponding value of the calculated potential at the critical distance and E is the c.m. bombarding energy of the system. This formula is only valid when the inequality

e V(R,,,,) + t<'"(#<'"+ l)h2 #°'"(l°r" + l ) = > v , + (3) 2/~ 2 Refit 2/J Rs 2

is satisfied (I,r~t is the orbital angular momentum,/z the reduced mass of the system, VB is the interaction threshold and Rs its location). This inequality is deduced from

360 J. PI~TER et al.

the work of Glas and Mosel [sect. 3 of ref. 2 o)]. For most of the system studied here, this condition is valid for any value of the bombarding energy, since V(R©rit ) is greater than V12 when the product ZtZ2 is greater than about 1700 [ref. 1~)]. For the system Ar+ Bi (ZtZ2 = 1494), the condition is fulfilled at the high bombarding energy of table 2.

We have calculated the interaction potential in the way described in ref. t3). The parameter refit was taken as 1.05 fm, which reproduces the experimental critical angular momentum values of the reactions induced by ions up to Ar, and is in agree- ment with the value directly deduced from an analysis of the experimental data. The calculated cross sections are given in table 2. They are much higher than the experimental complete fusion cross sections, but they are of the same order as the cross sections for complete fusion and quasi-fission together.

TAnLE 2

Comparison of experimental complete fusion and quasi-fission cross sections (in nab) with calculated close collision cross sections for reactions induc_-d_ by Cu and Kr ions

Projectile Target F~,b Exp Calc

(MeV) Oct, aer ac t +,t ref. o,j~. ,.it

63Cu a 86 w 395 200 250 450 5:120 i o) 670

ag~Au 365 0-30 280-250 280-t- 50 ~) 320

*4Kr 2°*Bi 525 0 450 4 5 0 5 : 8 0 4) 480

605 0 1500 15005:? e) 900

a3su 450-600 55 470 525*5:80 Jr) 480*

* Values averaged over the indicated energy range.

We are thus led to consider the possibility that quasi-fission and complete fusion belong to the same class of reactions, characterized by a complete damping of the initial relative motion during the first step of the reaction.

For complete damping to take place, a "close" collision is required, and we can use this name for the whole class of reactions.

When the initial kinetic energy is damped into other degrees of freedom, what determines that some /-waves contribute to complete fusion and others to quasi- fission?

Let us look in a qualitative way at the schematic potential energy curves (including nuclear, Coulomb and centrifugal parts) as a function of the distance between the two ions (figs. 6 and 7). During the interaction, several parameters are changed due to friction forces: the relative kinetic energy E and relative orbital momentum 1, and the masses, charges and shapes of the nuclei. One can assume that the system will evolve to complete fusion only if the potential energy curve for the final/-value exhibits a pocket and if the system is trapped within this pocket.

*4Kr 361

". El

.

\ / ~ \ ,.. f , . io . \ \ . -,

- ' ~ \ '.

IL Disto~Q

Fig. 6. Strong radial friction, low tangential friction. Variation of the kinetic energy for three values of the impact parameter b and potential energy curves for the corresponding final angular momentum If, (which is not very different from il). Dots - large b: qtmsi-elastic scattering.

Dashes - intermediate b: quasi-fission. Continuous line - low b-value: complete fusion.

E 2 , ~ j ~ . ~ . ................... ..m.. quosi .et

" ' " " . . . . . .

'...

Distance

Fig. 7. St rong tangent ia l f r ic t ion, modera te rad ia l f r ic t ion. Same nota t ions f o r the curves as in fig. 6. Here It < lj and complete fus ion occurs fo r in termedia te b-values.

We can now assume two extreme situations depending on the relative values of radial and tangential friction forces. If tangential friction is low, the change in relative orbital momentum is negligible and, during the interaction, the potential energy curve is unchanged. It is then easy to see that fusion occurs for low impact param- eter values, quasi-fission for higher ones, and that the quasi-elastic or transfer reaction will take place for the highest values. Gross et al. 14) have been able to explain many data on fusion and quasi-fission by using such a hypothesis.

Let us look now at the case of high tangential friction. Bondorf et al. is) have shown that the inclusion of a sufficiently high tangential friction can make complete fusion occur for low and high impact parameter values, whereas intermediate impact parameters correspond to scattering (quasi-fission). Tsang has concluded that com- plete fusion occurs only for high. impact parameters, but this result seems to be strongly dependent on the simplifications made in the calculations 16).

The possible effect of a strong tangential friction combined with an intermediate radial friction is shown in fig. 7. For the lowest impact parameters, the energy loss is not large enough for the system to be captured in the pocket corresponding to

362 J. PI~TER et al.

the final/-wave. For high impact parameters, the final angular momentum value If is much lower than the initial one li but the potential energy curve for If has no pocket and complete fusion cannot occur. For some range of intermediate impact parameter values, both the energy loss in the entrance channel and the orbital angular momentum loss are sufficient to obtain potential energy curves with pockets and low kinetic energies which allow the system to be captured and complete fusion to take place. The location of the range of impact parameter values corresponding to complete fusion depends on the balance between radial and tangential friction, and on the Coulomb and nuclear potentials. In the extreme case, quasi-fission occurs for the lowest impact parameter values, whereas complete fusion occurs for higher values. Similar views are given in ref. 21).

How can the experimental results help to decide between these two cases? The difference in fusion cross sections between C u + W at 395 MeV and C u + A u

at 365 MeV (table 2) could be taken to be in favor of the second case above (high tangential friction). For C u + W at 395 MeV, many more /-waves are involved in the C F + q f process, and the complete fusion cross section is much higher than for Cu +Au at 365 MeV. This would be expected if complete fusion occurs only for sufficiently high/-waves.

The relative proportion of complete fusion and quasi-fission depends very much on the entrance channel for a given system (fig. 3). The difference can be due to the variation of the Coulomb repulsion forces with the product Z I Z 2 of the charges of the projectile and target nucleus. When Z 1 Z2 decreases, the slope of the potential energy curves (figs. 6 and 7) is smaller, more of these curves have a pocket and com- plete fusion is more probable. This is true in both cases discussed above.

Another experiment studying the effect of the entrance channel by varying the product Z i Z 2 has been done by Gauvin et al. ~7): the complete fusion cross section for 84Kr+ 74Ge is lower than for A t + I ISSn. Moreover the shift of the compound nucleus excitation functions may be interpreted by assuming that for the Kr induced reaction no complete fusion occurs for the initial/-waves between 0 and 45 ['ref. 18)].

Thus, a consistent explanation of the complete fusion and quasi-fission cross sec- tions induced by very heavy ions on medium to heavy targets would then be that for the low impact parameters, no complete fusion occurs but only quasi-fission reactions take place.

To check this hypothesis, it is necessary to check if indeed quasi-fission occurs for the system K r + G e or a neighbouring system. The measurement of complete fusion and quasi-fission excitation functions for other system can also provide useful information.

References

i ) B. Tamain, C. Ng6, J. P~ter and F. Hanappe, to be published 2) B. Tamain, M. Lefort, C. Ng6 and J. P~ter, J. de Phys. 33, colloque C$, vol. 2 (1972) 50 3) M. Lefort, C. Ng6, J. P~ter and B. Tamain, Institut de Physique Nucl6aire Orsay, report

IPN-RC-73-07 0973)

| '*Kr 363

4) F. Hanappe, M. Lefort, C. Ng6, J. P6ter and B. Tam&in, Phys. Rev. Lett. 32 (1974) 397 5) I. Halpern and V. M. Strutinsky, Proc. 8th Int. Conf. on peaceful uses of atomic energy 15P

(1958) 1513, 408 6) K. L. Wolf, J. P. Unik, J. R. Huizenga, J. Birkelund, H. Freiesleben and V. E. Viola, Phys. Rev.

Left. 33 (1974) 1105 7) J. P6ter, C. Ng6 and B. Tam&in, J. de Phys. Left. 36 (1975) L23 8) R. Brandt, An$. Chemic 10 (1971) 890, and references therein 9) H. J. Becker, P. Vater, R. Brandt, A. H. Boos and M. Diehl, Phys. Lett. $0B (1974) 445

10) F. Hanappe, C. Ng6, J. P6ter and B. Tam&in, Proc. Int. Conf. on reactions between complex nuclei, Nashville, ed. R. L. l~.obinson et al. (North-Holland, Amsterdam, 1974) p. 116

11) J. V. Kratz, A. E. Norris and G. T. Seaborg, Phys. Rev. Left. 33 (1974) 502 12) J. Galin, D. Guerreau, M. Lefort and X. Tarrago, Phys. Rev. 69 (1974) 1018 13) C. Ng6, B. Tam&in, J. Galin, M. Beinex and R. J. Lombard, Nucl. Phys. A240 (1975) 353 14) D. H. E. Gross, H. Kalinowski and D. N. De, preprint (1974) 15) J. P. Bondorf, M. 1. Soboe and D. Sperber, Phys. Reports 15C (1974) 16) C. F. Tsang, Lawrence Berkeley Laboratory report LBL-2928 (1974) 17) H. Gauvin, Y. Le Beyec, M. Lefort and R. L. Hahn, Phys. Rev. CI0 (1974) 722 18) M. Lefort, Y. Le Beyec and J. P6ter, ref. ao), p. 81 19) B. Borderie, Th~se de 3e cycle, Orsay (1972), unpublished 20) D. Glas and U. Mosel, Nucl. Phys. A237 (1975) 429 21) M. Lefort, Phys. Rev., to be published 22) G. E. Gordon, A. E. Larsh, T. Sikkeland and G. T. Seabor8, Phys. Rev. 120 (1960) 1341 23) H. Britt and A. Quinton, Phys. Rev. 120 (1960) 1768 24) A. M. Zebelman, L. Kowaiski, J. Miller, K. Beg, J. Eyal, G. Jaffe, A. Kandil and D. Logan,

Phys. Rev. CI0 (1974) 200 25) H. H. Gutbrod, F. Plasil, H. C. Britt, B. M. Erkkila, R. H. Stokes and M. Blann, Proc. 3rd

Symp. on physics and chemistry of fission, Rochester, 1973, vol. 2, p. 309 26) B. Tamain, C. Ng6, J. P6ter, R. Lucas, J. Poitou and H. Nifenecker, Institut de Physique

Nucl~tire Orsay report, IPNO-RC-75-04