Further experimental evidence for fast fission

Nuclear Physics A422 (1984) 447460 @ North-Holland Publishing Company

FURTHER

EXPERIMENTAL

EVIDENCE FOR FAST FISSION

Z. ZHENG ‘, B. BORDERIE, D. GARDES, H. GAUVIN, F. HANAPPE ‘, J. PETER 3, M. F. RIVET, B. TAMAIN4 and A. ZARIC institut de Physique Nucikaire, BP 1, 91406 Orsay, France ’ Institute of Modern Phvsics, Lanzhou, China ’ Lahoraioire de Physique Nuci~aire, UL Bruxeiles, Belgium a GANIL, Caen, France 4 Laboratoire de Physique Corpusculaire, Caen, France

Received 27 June 1983 (Revised 8 December 1983) products have been studied for three reactions: Ar+ Au, Ar+Bi and Ar + U (5.25-7.5 MeV/u). By measuring symmetric fragmentation components (fission-like events), cross sections for fusion were deduced and compared with the predictions of static and dynamic models. With increasing projectile energy, the width of the mass distributions strongly increases for the two lighter systems. By contrast, for Ar+U it remains essentially constant at a very large value. These results clearly demonstrate that the large increase of the width of the mass distribution cannot be attributed simply to large values of the angular momentum. However, they can be explained by the occurence of a different dissipative process. fast fission. which can be expected if there is no barrier to fission. For the reaction Ar + Au, the total kinetic-energy distributions were also studied in detail. In this case fast fission occurs only at high incident energy. The average total kinetic energy (TKE) was found to be constant with increasing energy whereas the widths of the TKE distribution increase.

Abstract: Fusion-fission

1. introduction In recent years heavy-ion reactions have been studied intensively and the basic reaction m~hanisms are now known in some detail i3’ f. The main contributions to the nuclear reaction cross section are compound-nucleus formation and deeply inelastic reactions. Both lead to subsequent particle decay, y-emission or fission. When a heavy compound nucleus is formed (A > 200), it deexcites mainly by fission which leads to a symmetric mass distribution. As the evaporation residue cross sections are negligible, the cross section for fission can be identified with that for fusion and, within the sharp cut-off approximation, it is possible to deduce a critical angular momentum for fusion, I,,. However, in many cases (particularly at high incident energies) a contradiction has appeared : one finds 1,, values that are larger than the limit expected for nuclear stability due to Coulomb and centrifugal forces (18,=e) 3-6). It has been proposed that these nuclear reactions prodeed via a different dissipative mechanism called fast fission 3s7-9). This process is involved for all angular momenta greater than lg = o but less than Z,,; therefore 447

448

Z. Zheng et al. / F~t~s~~~n

the cross section for this process is included in the fusion cross section. The time scale for this mechanism should be intermediate between that corresponding to deeply inelastic collisions and fission after compound-nucleus formation. Therefore, the mass distributions for symmetric fragmentation following such a mechanism would be expected to be broader than those for fission after compound-nucleus formation because mass equilibration has not yet been established. Such broadening has been observed experimentally ‘* ‘). During the same time that these experiments were reported, several theoretical studies of heavy-ion fusion and reseparation predicted the existence of such an intermediate mechanism lo* ‘I f. More recently an approximate generalization to noncentral collisions 12) (i.e. taking into account angular momentum effects) has been added to the dynamical model of fusion proposed in ref. lo). It has been shown i3) that the same threshold regions for fast lission as found experimentally in ref.8) were obtained for the reactions Mg+Ta and Ar+Ho. Nevertheless, distinct experimental signatures for fast versus regular fission are limited. Moreover, some theoretical discrepancies about the influence of angular momentum on the broadening of the symmetric fragmentation mass distribution still persist 14*’ 5). Clearly more systematic experimental investigations are needed. For this purpose three systems have been studied : Ar + Au, Ar + Bi and Ar + U, in the energy range X2-7.5 MeV/u. Fusion cross sections and mass and total kinetic-energy distributions have been measured. For the system Ar+U, where the calculated fission barrier of the compound nucleus is very small [- 0.2 MeV with shell effects 16)], we could expect to observe fast fission over all entire bombarding~nergy range explored 17).

2. Experimental arrangement and data analysis Beams of 209, 215, 250 and 300 MeV 40Ar ions were provided by the Orsay ALICE facility. The targets were bismuth and uranium, 500 pg/cm2 thick on aluminium backings and self-supported gold of 200 pg/crn’ thickness. The gold target was thin enough to allow the study of the incident energy dependence of the total kinetic-energy distributions for symmetric fragmentation (i.e. energy straggling effects were negli~ble). For such heavy systems it is necessary to require a coincidence between two fission fragments in order to eliminate three-body events that arise from the sequential fission of a target-like fragment following a deeply inelastic collision. A typical detector arrangement is shown in fig. 1. Fission fragments were detected in four 600 mm’ x 60 pm surface-barrier detectors. The mass of each fragment detected in the TOF arm was obtained from the measurement of its energy and its time of flight over a one meter flight-path. The full in-plane correlation for the complementary fragment was covered by three detectors located on the other side of the beam. The out-of-plane aperture () 7O) was sufficient to detect all the binary events l*). Reduction of the data for the correlated fission fragments

Z. Zheng et al. / Fast fission

449

40Ar beam

surface barrier detector

Fig. 1. Typical

detector

arrangement.

was made using the interactive NDIM ARIEL system at Orsay. First the mass and kinetic energy of one fragment were determined ; then the fusion-fission events were identified by requiring a satisfactory solution for two-body kinematics for the angle (within *So), time of flight, and kinetic energy of the coincident fragments. Sequential fission events were thus rejected. Fig. 2 shows, in the case of Ar+U, typical mass distributions at different steps of the analysis. A severe selection among the fission events clearly appears. The inclusive spectrum exhibits two peaks of E 100 and 140 u that arise from the fission of uranium-like nuclei with low excitation energies.

3. Results and discussion In this section we shall present our results for the symmetric fragmentation component, The measured cross sections will be compared with those predicted by a static model lg. 20) and by Swiatecki’s dynamical model i2). Then the evolution of the widths of the mass and total kinetic-energy distributions will be discussed. 3.1. FUSION

CROSS

SECTIONS

By assuming l/sin 19angular distribution refs. ‘, “‘)I, th e s y mmetric fragmentation

Cjustilied by the experimental results of cross sections were determined at each

450

Z. Zheng et al. / Fast fission

4oAr

xx I-

\-.*

+238U

E = 250 MeV

z!

giloc)5

Td b 00

- ... . . : ..:. . ~. .. ‘. . .

E

2

L

:

50 .I .

’

. f:

(b)

,. .. . . : . . :. ;.

25

0

50

25

0‘

0

150

A(u)

200

Fig. 2. Mass distributions at different steps of the analysis: (a) singles; (b) with coincidence requirement; (c) after kinematical selection of binary reactions, elastic and inelastic scattering excluded. The detection angle was 27O.

bombarding energy. They are listed in table 1. For the heavy systems studied here the evaporation residue cross sections are negligible. As a consequence, the symmetric fragmentation cross section can be identified with the fusion cross section bf. From these results we have deduced the critical angular momentum for fusion (I,,) as a function of the bombarding energy. We used the relation tag- xl’lzr (sharp cut-off approximation). One can first notice that at high energies the measured values of I,, are larger than Is,=0 (see tables 1 and 2). This is in agreement with the results of ref. 3), and confirms that “fusion” as defined here is not identical to compoundnucleus formation but includes other dissipative processes. These values can be compared with those predicted by a static model for fusion. In this framework the fusion process, at low bombarding energy, is governed by the fusion barrier, whereas at higher energy, or for heavy systems, a critical distance

4.51

Z. Zheng et al. / Fast~ss~~~ TABLE 1

Fusion cross sections and deduced I,, compared with calculated values (static model, see text)

System

Ar+Au

Ar+Bi Art-U

(2%

(MeV) E’m’

Detection angle calculated 1”)

L(h)

E

(2)

measured

215 250

179 208

425+ 50 840&-120

&I*4 94+7

60 89

300 215 250 209 250

249 180 210 179 214

1160-1.140 260* 50 720+ 70 30* 10 470 * 40

121+7 49*5 88+4 17&3 72+3

119 52 86

300

257

104+5

113

810,

80

75

FWHM (u) measured

corrected

51+2 71f3 70*3 83+4 53+2 67,3 71&9 72&4 70f4 so+4 80&4 72+8 78,4

53&2 74&3 73+3 87+4 55&2 70+3 74*9 77+4 75*4 85&4 X5+4 77+8 s3+4

60 45 60 40 40 45 27 27 87 27 45 60 87

For the Ar+U system at the lowest energy it is not possible to use such a simple model which is based on a sharp cut-off approximation. FWHM is the full width at half maximum of the symmetric mass distribution after and before evaporation (corrected).

R,, has to be reached 22). Then the critical angular momentum is given by V,,), where V,, is the value of the total interaction potential 4, = &&%@,.m.calculated at the critical distance R,,. For the nuclear part of the interaction potential we have used the energy-density formalism within the sudden approximation 23).Good agreement is obtained between the calculated and measured values of I,, when the critical radius parameter rcr (R,, = r,,(Af +A$)) is taken to be equal to 1.05 fm. Within this model fusion reaction is governed by a critical distance of approach between the two incident nuclei and by the existence or disappearance of a minimum (or “pocket”) in the one-dimensional potential energy. A new dynamical reaction model due to Swiatecki “) has been recently published.

TABLE

2

Limit of stability of the compound system in the rotating liquid-drop mode1 (is, = a) [for comparison, fission barriers used in this model and in the droplet model (in parenthesis without shell effects) are also indicated]

System

ArfAu ArfBi Ar+U

Ia, = 0 (h) [ref. ‘)I 62 55 30

Fission barrier (MeV) ref. 4,

ref. r6)

2.25 1.28 0.24

3.40 (2.22) 3.65 (1.07) 0.19 (0)

452

Z. Zheng et al. / Fast fission

In this model, the incident nuclei do not have to reach a critical distance in order to fuse, but they must go beyond a conditional saddle point. The location of this saddle point depends strongly on the neck degree of freedom and on the entrance-channel mass asymmetry. When the contact configuration is less compact than the conditional saddle-point configuration an “extra push” is required in order to achieve the fusion of the nuclei: this extra push is an additional radial injection energy necessary to push the contact contiguration to a shape which is more compact than that corresponding to the conditional saddle point. This model results in the same kind of shape for the fusion excitation functions as that predicted by the critical-distance model, which differs from the simple geometrical formula Of

=

nR2(1- Vf/E,.,.).

(1)

These predictions may be compared with ex~rimental results. The conditional saddle point is defined for the frozen target-projectile mass asymmetry of the entrance channel, and its location for head-on collisions can be determined using the parameter of Bass 24),

(2) where A,, A,, Z,, Zz represent, respectively, the target and projectile mass and charge. This parameter may be understood as representing the ratio of the repulsive Coulomb force to the attractive surface force. It reduces to Z2,1A, the usual fissility parameter, for symmetric systems. To take into account the shifting of the

40Ar + ’ g7Au

0 thm * ref.

.

250

ref

work

28 29

300

Ec.m.(MeVl

350

Z. Zheng 2000

z 5

453

et al. / Fast&ion

/

1500

13’

I 000

500

0 100

150

250

200 E c.m.

2

300

350

300

350

(IvIe”)

1500

b’

I 000

0 250

E ,-,,(MeV) Fig. 3. Fusion excitation functions for 40Ar-induced reactions on r9’Au, ‘09Bi and zsSU. The solid curve is the fusion prediction of eq. (1). The dot-dashed curves represent predictions from Swiatecki’s model. The dashed curve corresponds to the critical-distance model (see text) and at high energy to the saturation limit of 1, predicted by Bass 24) considering rolling motion.

conditional saddle point due to angular momentum, a correction was introduced by Swiatecki by adding the ratio of centrifugal to surface force to (2),

2. Zheng et al. / Fast fission

454

where 1 is the angular

momentum

and AyA:qA~

+

A$)

(4) JlqTTTT’

In (4), e is the unit of charge, m is the nuclear mass (931 MeV/c’), r. the nuclear constant and f’ the fraction of the total angular momentum responsible for the radial centrifugal force. This approximation represents a simple trade of centrifugal for electrostatic forces. The form predicted for the “extra push” is given by Swiatecki as

AE =

q(z214‘ftot -

(z2/4rrthr12~

where K = 7.60 x 1O-4

Af&(Af $- AB2 a2 A,+‘42 .

The constant “a” has to be determined either empirically or from theoretical considerations. When the value (Z2/A)erf ,0, exceeds some critical threshold value the extra radial injection energy AE is required to push the contact (Z2/A),ffthr configuration inside the conditional saddle point; otherwise AE is equal to zero. In ref. i2) empirical values for (Z2/A)efrthr, “a” and “7 were found to be 33, 12 and 2, respectively; these values were obtained from a set of fusion excitation with targets ranging from 24Mg to functions for reactions of 208Pb projectiles 64Ni [ref. ““)I. The comparison between the experimental data and the calculations from different models is displayed in fig. 3. For the simple assumption represented by (1) 6 and R were calculated from the interaction potential of ref. 23); very similar results are also obtained with the proximity potentia126). Large disagreement between the experimental data and Swiatecki’s model was found if we use the set of parameters of ref. i2). This is not surprising as the cross sections measured here are substantially larger than those obtained in ref. 25) [on the contrary, they are in good agreelnent with recent measurements from other authors27)]. However, a rather good fit to the data could be obtained for our three systems by choosing a value off in between those for sticking and rolling (see fig. 3). An alternative would be to use a new set of parameters (a = 10, (Z2/A)eflthr = 34, rolling motion,

i.e. f = $).

3.2. MASS DISTRIBUTIONS

The mass distribution of the symmetric fragmentation component was obtained at each bombarding energy for several detection angles. The choice of angle appeared to have no influence on the mass distributions (see table 1). The mean value of the

Z. Zheng ef al. / Fast jission

455

mass distribution was always found to correspond to half the total mass of the system minus the average number of neutrons evaporated by one fragment (within the uncertainty of two or three mass units). The full width at half-maximum (FWHM) of the experimental mass distribution was corrected for neutron evaporation by assuming that the excitation energy was shared between the fragments proportional to their masses. The results are summarized in table 1. The most striking feature is the difference between the behavior of the FWHM for the reaction Ar + U compared to that for the two others. A large increase of FWHM with bombarding energy is observed for the lighter systems [as in ref. “)] whereas no significant change appears for Ar + U, Such behavior, for the Ar + U system, can be explained as fohows. Recall that the fission barrier 16) of the compound nucleus is very small (- 0.2 MeV with shell effects included) and that, consequently, fast fission should occur even at bombarding energies close to the fusion barrier. Fig. 4 shows the dependence of the corrected FWHM (averaged over the different detection angles) on the critical angular momentum. When large l-values are involved (I,, > 80), the values of FWHM are very close for the three systems. By contrast, for low values of I,, a large difference is observed for the values of FWHM obtained for the reaction Ar+ U compared to the others. Clearly the large increase of FWHM cannot be attributed to an increase of angular momentum alone as predicted in ref. 14). We consider now the limiting I-value (rrr=,) for stabihty for the various nuclei4) (due to the centrifugal force). These limits give the threshold region for fast fission. For the reactions Ar +Au and Ar + Bi, as was observed for Ar +Ho [ref. “)I, a large increase for the FWHM is observed when I,, > Is, = s (arrows in fig. 4). For the heaviest composite system (from Ar +U) the situation is quite different: a large width is observed even for the lowest energy and I,, (i.e. below

too

;

4- f+-

75

+I+-+--

~

B LL

+-t

50

teBf=O e A

,r+U

f

Ar+Bi

f

25 IO

50

!.._Ar+Au

q

Ar+Au Ar+Bi Ar+U

I 100 R,,

(exp.)

Fig. 4. Evolution of the width (FWHM) of the symmetric component with critical angular momentum. The arrows indicate the limit of stability of the compound nucleus within the rotating liquid~rop model 9.

456

Z. Zheng et al. / Fast fission

Indeed the fission barrier for that compound system is so low (see table 2) that it appears difficult to give a meaningful value to 1, = Q Therefore even at the fusion threshold, the composite system from Ar+U may well behave as if it had no fission barrier. A second explanation could be the occurence of fast fission for I-values below I,‘= e as predicted for the systems which require an “extra-extra push” in order to- overcome the inconditional saddle point “). Finally, the last point to stress is the evolution, with incident energy, of the width of the mass distribution for the fast-fission process alone. For Ar+U, it can be considered that fast fission is the main mechanism responsible for symmetric fragmentation over the whole energy range studied. Within the experimental uncertainties, one can say that the width of the mass distributions either remains constant, or slightly increases with incident energy. Similar conclusions were derived from the study of the Ar +HQ system as far as the fast-fission component was concerned 33). For fission after compound-nucleus formation the evolution of the mass distribution with incident energy is well reproduced by statistical fluctuations at the saddle point 8, or by dynamics of fluctuations (transport equation) from saddle to scission point 15*34), In the fast-fission process, the characteristics of the symmetric fragmentation are determined at the turning point in the potential-energy landscape 9, and should depend much more on the incident energy; the larger the energy the deeper the penetration and the larger the mass as~metry stiffness coefficient. But centrifugal forces play an important rofe when the incident energy increases and counteract an expected large penetration (compact turning point). Consequently the position of the turning points would not depend largely on incident energy and the width of the mass distributions would be rather constant as observed experimentally. Such behavior shows that the understanding of the evolution of the mass-distribution width is quite different from that for fission after compound-nucleus formation. I,( = a).

3.3. TOTAL

KINETIC-ENERGY

DISTRIBUTIONS

Another interesting piece of information concerning the symmetric fragmentation component can be obtained by studying the evolution of the total kinetic-energy distribution (average value and width) with the incident energy. This study was performed on the Ar -i-Au system only : to prevent systematic errors due to straggling effects and energy losses a thin (200 pg/cm’) self-supported gold target was used. For this study a narrow band in the mass distribution was selected (30 u centered at the average mass); such a selection reduces the influence of the mass asymmetry on the widths (- 3 “/,) and the average value of the total kinetic energy thus deduced does not differ largely from that corresponding to fission into two fragments of equal masses. The total kinetic-energy distributions in the c.m. system (TKE) are presented in fig. 5. The average total kinetic energies ((TKE)) and widths (FWHM) were corrected for peutron evaporation 35). The results, summarized in table 3, are

et al. / Fast fission

2. Zheng

100 +

I

I

I

*Ai

457

‘“‘au ..-

E=X)OMeV .. * . .: . .. .* . .

50 u) E % a, “0 +0 2

*.

.:

E=250MeV .’

.*

100

.: ’

-1

..

.*

.

:*

50

0 E=215MeV

.

‘ . .* .a_

100

50

0 120

160

_

200

240

TKE (MeV) Fig. 5. Total

kinetic-energy

distributions at the different bombarding energies. mass ratio in the range l-l.3 were selected.

Fission

fragments

with a

compared with predictions for fission after compound-nucleus formation from refs. 36, 37). For the reaction Ar + Au, we can infer from the study of the mass distribution that, at 215 MeV, fission occurs only after compound-nucleus formation, whereas at larger energies such “slow fission” is mixed with fast fission. When the incident energy is increased, as was observed in ref. 38), the experimental values of (TKE) are constant and in good agreement with the calculations 36). Clearly (TKE) for

Z. Zheng et al. / Fast fission

458

Total kinetic-energy distributions for the Ar+Au system


E lab (MeV)

215 250 300

TABLE 3 -_ (average values (TKE) and widths FWHM) compared with predictions (the temperature 7 of the compound nucleus is also indicated)

measured

corrected

181 rfrs 176&S 181+.5

185_+5 1s2+5 190f5

FWHM calculated [ref. 3_6)]

(&I LI= &A

1.52 18515

1.77 2.09

(MeV)

measured

corrected

calculated [ref. 37)]

36+2 44+2 48i2

35+2 44+2 48+2

23 24 25

fast fission does not differ significantly from that for fission after compound-nucleus formation. This result is understandable in the context of the qualitative picture of fission. The differences between the two processes (fast and slow fission) reflect different starting positions in the fission valley. This prescission contribution to the TKE is estimated to be about 50 MeV [ref. ““)I for our system if a true compound nucleus is formed. The experimental uncertainty of +5 MeV, if attributed fully to prescission TKE, corresponds to a difference of 5 fm between the starting positions in the fission valley 36); this difference is larger than what can be expected for the distance between the turning and saddle points ( 5 2 fm). Therefore it does not seem possible to observe experimentally the small variations expected in TKE between fission after compound-nucleus formation and fast fission, as it would require experimental uncertainties smaller than 1 MeV. The situation is different when considering the width of TKE distributions and a large difference is observed, even at the lowest bombarding energy, between experimental results and predictions. The calculated variances of the fission-fragment kinetic-energy distribution 37) take into account the effect of vibrations in the stretching degree of freedom but neglect dissipation and fluctuations in the fission degree of freedom (elongation). More recently it was shown that the contribution of such diffusion effects is not negligible 39*40) and it will be very interesting to compare our results with the predictions of these newer models of fission. In fig. 6 we compare the evolution of the widths of the mass and TKE distributions with predictions obtained by assuming statisticaf fluctuations for harmonic oscillations ‘341). The solid curve was normalized at the lower bombarding energy and represents an evolution of FWHM proportional to the square root of the temperature r (i.e. to E*l14). T o calculate the excitation energy, E*, we have subtracted the average rotational energy of a rigidly rotating sphere. It has been shown that the width of the fission mass distributions (after compound-nucleus formation) does indeed increase as E*1’4 [ref. s)]. From fig. 6 we see that the FWHM of the TKE distribution also increases faster than expected from such a law, but not as rapidly as the FWHM of the mass distributions. This observation may provide a good test for more detailed models of fast fission.

Z. Zheng et al. / Fast jksion

459

Fig. 6. Evolution of the mass widths (0 left scale) and TKE distributions (0 right scale) as a function of the excitation energy. The solid curve gives the expectation for statistical fluctuations-(see text).

4. Conclusions

By studying three reactions (Ar + Au, Ar + Bi, and Ar + U) we have shown that cross sections measured for fusion (symmetric fragmentation component) can be parametrized by a critical distance parameter rcr of 1.05 fm. In the context of the dynamical model of Swiatecki the friction can be characterized by a situation between that for sticking and rolling. Alternatively, a good fit to our data can also be obtained for all three reactions if we choose a new set of parameters for “a”, (Z2/Afeffthr and $ A strong correlation has been found between the observed widths of the mass distribution and the expectation for dominance of fast over “slow” fission. Large widths are found for reaction systems with I,, > 1, I c rather than for large t,, values alone. This result gives a strong argument for assigning to fast hssion that part observed to have a very wide mass distribution. New characteristics for this mechanism are also presented in measuring the evolution of the total kinetic-energy distribution with incident energy (Ar + Au system). The average total kinetic energy was found to be independent of the fast-fission contribution as estimated from the width of the mass distribution. By contrast, the width of TKE distributions increases with this contribution. These observations should provide good tests for theoretical models of fast fission. We thank J. M. Alexander for a critical reading of the manuscript.

460

Z. Zheng et al. / Fast

fission

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