Properties of binary fission and multifragmentation in the transition regime

Nuclear Physics A499 (1989) 392-412 North-Holland, Amsterdam

PROPERTIES

OF BINARY THE

G. KLOTZ-ENGMANN,

FISSION AND ~ULTIFRAGME~ATION TRANSITION REGIME H. OESCHLER,

J. STROTH

IN

and E. KANKELEIT

Insritut fiir Kernphysik, Technische H~~hs~~ule Darm~t~dt, D-6100 Darmsiadt, Fed. Rep. Germany Y. CASSAGNOU, M. CONJEAUD, R. DAYRAS, S. HARAR’, R. LEGRAIN, E.C. POLLACCO and C. VOLANT D. Ph. N./ B.E., CEN Saclay, F-91 191 Gif-sur- Yvette Cedex, France Received (Revised

28 December 1988 20 February 1989)

Abstract: Correlations between target fragments were measured in o- and “N-induced reactions at 70, 250 and 800 MeV/u incident energies. ‘The reaction mechanism is characterized by the linear momentum transfer and the excitation energy which were deduced from the kinematics and the mass distribution of the fission fragments. By selecting targets lighter than Th (Au and Ho) the yield from peripheral collisions is reduced by the increase in the fission barrier thus allowing events with the highest linear momentum transfer and excitation energy to be favoured. The results show that up to an incident energy of 800 MeV/u hot nuclei are formed which decay via normal binary fission. The linear momentum transfer is essentially constant over the covered energy range, but the excitation energy increases until the total incident energy is greater than 3 GeV. At this energy, independent of the projectile mass the fission probability of the heavy nuclei drops below 50%, while the emission of intermediate-mass fragments increases. The relative velocities between two intermediate-mass fragments exceed strongly the values of binary fission. Monte Carlo calculations show that the relative velocities between these fragments exclude a sequential emission from the recoil nucleus and support a simultaneous breakup mechanism.

E

NUCLEAR REACTIONS “‘Th(u, F) (‘“N, F), E ~250, 800 MeV/nucleon; rb’Ho(a, F), E = 70, 250, 800 MeV/nucleon; E = 70, 250, 800 MeV/nucleon; E = 800 MeV/nucleon; “‘Au(“N, F), E = 250 MeV/nucleon; measured (fragment)(fragment)~, fragment velocities, fragment energy E,.

“.“Ag(n, fission

F), c,

1. Introduction In the medium-energy regime the linear momentum transfer (LMT) from the projectile to the target residue is a sensitive parameter to characterize the reaction of energies up to mechanism. In earlier works ‘*‘) using p-, d- and a-projectiles 1 GeV on Th, binary fission is shown to dominate the decay channels. The observed trends of the mean LMT led us to propose a classification of the reaction mechanism according to incident velocities. In this work we present a study focussed on possible limits in the LMT and excitation energy in the fission channel and the transition to a multiple breakup of the nucleus. Present

address:

GANIL,

B.P.5027.F-14021

Caen Cedex,

0375s9474/89/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V

France.

G. Klof~-Eng~lufln

Bombarding

fissile targets

er al. / Binary jissicm and m~~tigragme~tatio~

with cu-particles,

the range in LMT is narrow

393

and does

not allow a separation between peripheral and central-collision events directly from the angular correlations. Hence, we selected the high LMT domain by bombarding medium-mass nuclei, where due to the higher fission barrier only the more violent collisions lead to fission. The measurements with lighter targets could be considered as selecting subgroups of the cross section measured by bombarding the Th target and being sensitive to upper limits of the distribution of the LMT and excitation energies. At high incident energies a break-up of the target nucleus into several fragments occurs. E.g. in cc- and ~“Ne-induced reactions at incident energies from 5-42 GeV, where binary hssion was still observed in the peripheral collisions, central reactions lead to multifragmentation processes “). As we have shown in ref. 4), bombarding medium-mass targets with cw-projectiles at incident energies between 1 and 3 GeV, the transition from binary fission to multifragmentation occurs. In this work, emphasis is placed on determining the properties and the production mechanism of the intermediate-mass fragments (IMF). It is still an open question, whether they are emitted sequentially from a heavy residue as proposed by refs. ‘-‘) or whether they orginate from a simultaneous breakup of the nucleus [refs. 3,‘“-‘5)]. In performing Monte Carlo calculations to study the distribution of relative velocities between two IMF, we suggest that within the limits of our hypotheses the IMP production mechanism is strongly dominated by a simultaneous breakup of the nucleus.

2. Experimental

set-up

The measurements were performed at the Saturne II synchrotron facility at Saclay with beam energies between 70 and 800 MeV/u. The intensities for LY-and 14Nprojectiles were a few 10”’ and 10’ particles per second, respectively and were determined by a calibrated energy-loss detector in the beam line behind the target. Self-supporting targets of 220 pg/cm’ Ag, 440 kg/cm2 Ho, 1080 and 1440 kg/cm’ Au and 1200 @g/cm’ Th were used. The experimental time-of-flight telescope (TOF) to determine velocity, -1 and a position sensitive parallel-plate avalanche the angular correlation and velocity of the coincident

set-up (fig. 1) consisted of a energy and mass of fragment counter (PPAC) to measure fragment 2.

The TOF detector consisted of a channel-plate assembly with a 30 kg/cm’ carbon transmission foil at 15.3 cm from the target and a 6 cm2 surface-barrier detector which provided the stop and energy signals. The flight path used was 40.3 cm and the TOF was mounted at 70” and 90” to the beam direction. Corrections were made for the energy loss in the transmission foil and the efficiency of the TOF. The latter depends on the energy loss in the foil and hence mainly on the atomic number of the fragments. The qualitative behaviour of the efficiency was deduced from ref. Ih) and quantitatively adjusted by the energy correlated efficiency measured with the surface-barrier detector. The correction procedure used is illustrated in fig. 2, showing

394

G. Klnfz-Engmann

et al. / Binary fission

I

and

multifragmentation

-

f Faraday

Cup

PPAC

TOF

~35°GL~1050)

(8,=70°,900)

L

:

Surface

“ff

--__ --_

:

Barrier

:

:

0

: I’

:

32

:

/

~

Target

Channel PLates

10 cm Beam

1 Fig. 1. Experimental

set-up consisting

7 of a time-of-flight telescope counter (PPAC).

I,

(

20

LO

I,

I,,

60

fragment Fig. 2. Raw (hatched

,

80

(TOF) and a parallel-plate

avalanche

,?+y

100

120

mass

A,

110

area) and efficiency corrected mass spectra measured in the TOF at 90” in coincidence with PPAC. The insert shows the efficiency curve used.

that for fragments of mass A, > 40 full efficiency was achieved. The time resolution of 500 ps led to a resolution of 1.5% on the mean fission velocity. The 20 x 30 cm’ parallel-plate avalanche counter (PPAC) “) was mounted 22 cm from the target. The detector covered angles from 35 to 105” with respect to the beam and out-of-plane angles of *25” relative to the plane defined by the beam and the TOF axis. The position resolution of 4 mm led to an angular resolution of

G. Khtz-Engmann -

1”. The threshold

The detection

et al. / Binary

fission and mult$-agmentation

of the PPAC was adjusted

energy

threshold

for heavy

to suppress

fragments

395

fragments

below Z, = 5.

(2, < 60) due to the 1.5 km

mylar window foil was 5 MeV. The atomic numbers of the detected fragments were estimated by the energy-loss signal and velocity using a parametrized energy-loss formula lx) with a resolution of LIZ/Z =35X. Multiple hits in the PPAC were recognized by the double read-out technique of the position delay-line chain “). Position, velocity and energy calibration were performed using a ‘%f source deposited on a thin Ni backing. The pulse-height defect in the surface-barrier detector was corrected using the calibration procedure of Kaufman et al. I’)). Angles, energies, velocities and masses of the fragments were analyzed event by event. This experimental arrangement combines three advantages: (i) It allows a high coincidence probability, giving the whole in-plane and out-of-plane angular correlation in one setting. (ii) The velocities of both fragments are measured. (iii) The mass of one is determined with a resolution of 5% and an estimate is obtained for the atomic number of the other. 3. Reaction 3.1. SEPARATION

Using cy- and of the residual to the system fragment-mass

OF

mechanism

BINARY

in the medium-

FISSION

FROM

and high-energy

regime

MULTIFRAGMENTATION

“N-projectiles the coexistence ofbinary fission and multiple breakup nucleus at high incident energies has been reported “). Analogous N +Au in ref. “), fig. 3a exhibits the evolution of the coincident spectrum in the system LY+ Ho as a function of incident energy.

fragment

mass

A,

v ff

(cm/f-d

Fig. 3. (a) Fragment-mass spectra and (b) relative velocities ~1,~between two fragments of a-induced reactions on Ho at 70, 250 and 800 MeV/u incident energy. At the lower energies typical fission-fragment mass distributions are observed with relative velocities corresponding to Viola’s systematics. At the highest energy additionally intermediate-mass fragments occur.

396

G. Klotz-Engmann

et al. / Binnry.fission

and mult$ragmenfation

Whereas at the two lower incident energies only binary fission is observed, at 800 MeV/u incident energy the fragment-mass spectrum shows the growth of a low-mass component. In fig. 3a both, fission fragments with A, = 50-60 and IMF with A, (40, are observed at the highest energy. As known from Viola’s systematics ‘“) binary fission of an equilibrated nucleus leads to a small range of relative velocities between the fragments nearly independent of the mass of the fissioning nucleus. In the present measurement this quantity is directly deduced from the velocity vectors of the fragments event by event, using the relation z),r= Iu, - u7( (see fig. 1). At all incident energies a distribution centered around 2.3 cm/ns was observed for the Ho fragments (fig. 3b) which is in agreement with Viola’s systematics. However, the light fragments seen at 800 MeV/u exhibit higher relative velocities as evidenced by fig. 4. 51

I

1

800 MeV/u

I

I

50

100

fragment Fig. 4. The relative

velocity

1 a+Ho

150

mass

as a function of the fragment mass shows that IMF are correlated relative velocities than fission fragments.

to higher

For the event-by-event analysis of the LMT the following criteria were used: binary fission events were selected by considering only fragment masses larger than A, = 40 and relative velocities below 2.5 cm/ns (Au target) and 2.4 cm/ns (Ho target). These values correspond to the upper limits of the fission velocities at the low incident energies. This separation prefers symmetric-mass splits, as asymmetric fission in the tails of the mass distribution tends to somewhat higher relative velocities. 3.2. ANGULAR

CORRELATIONS

In binary fission the opening angle between the two fragments (in-plane angle) is related to the recoil velocity of the fissioning nucleus and yields the LMT [ref. “)I. The out-of-plane angular distribution reflects mainly the momentum distribution of the fragments caused by particle evaporation. A perpendicular momentum transfer

G. Klotz-Engmann

broadens

the out-of-plane

et

a/./

correlation

Rinarv

fixrim and mult~~ugmmtation

further, but using light projectiles

397

this influence

is negligible”). Hence, the width is governed mainly by the excitation energy of the fissioning nucleus. The fission plane is defined by the beam and the TOF axis. Fig. 5 shows the inversus out-of-plane correlation of the fragments obtained by bombarding Ho targets with cu-projectiles of 70, 250 and 800 MeV/u. At the lowest energy the distribution exhibits concentric rings centered around 90% of the beam momentum. The presence of concentric rings indicates that the transferred momenta are limited to a narrow range and that the broadening is essentially due to evaporation. In the case of the highly fissile Th nucleus at the same incident energy the correlation diagrams show elliptic shapes and indicate an extended momentum distribution I,‘). The present result evidences that at 70 MeV/u incident energy which corresponds to twice the Fermi energy the ru-projectile can be stopped in the Ho nucleus. The observed fission fragments exhibit all the characteristics of a low-energy fission process, e.g. the relative velocities correspond to Viola’s systematics “‘) and the mass spectra show gaussian distributions (fig. 3). These are characteristics of an equilibrated nucleus and indicate a compound-

70 MeV/u

800

120

in-plane Fig. 5. In- and out-of-plane 800 MeV/u incident

1

MeV/u

l.LO

angle

I

I

160

180

0

I

(deg.)

angular distributions (linear scale) of Ho fission fragments at 70, 250 and energy. The fission events are selected by the P,, criterion (see text).

G. Ki[i~z-~ngm~~r7

398

nucleus

like process.

et af. / 6inar~~ssi~~ff and ~~ir~~rffgmenfffi~r~n

The fraction

of fission events corresponds

of the reaction cross section; nevertheless the incident energy of 70 MeV/u is probably

to a low percentage

it represents an interesting result since the highest, where a compound-nucleus

fission process is observed. Increasing the incident energy to 250 and 800 MeV/u the mean value of the angular correlation remains nearly constant, i.e. on average the same linear momentum is transferred to the target. But the contour plots change to elliptic shapes showing that an extended range of momentum transfers contributes to the fission channel. Additionally, the increasing width for the out-of-plane angle indicates an increasing excitation energy. These trends will be discussed in the next chapters in more detail, where both quantities are deduced directly from the measured parameters.

3.3. LINEAR

MOMENTUM

TRANSFER

In contrast to heavy-ion induced fission the recoil momenta of the fissioning nuclei in a-induced reactions are low and the broadening of the kinematic by particle evaporation smears out peripheraland central-collision components. On the other hand cu-projectiles do not transfer much angular momentum ‘) and hence the fission probability of the target nucleus is mainly governed by its excitation energy. Choosing medium-mass targets with higher fission barriers the peripheral reactions with low excitation energies are suppressed and only a small subgroup of violent collisions is observed in the fission channel. Hence, by decreasing the target mass one selects the more central reactions and one is sensitive to the upper limits of the energy and momentum transfer. The linear momentum transfer is determined by converting the fragment angles and velocities into the velocity of the recoiling nucleus (fig. l), assuming that the component perpendicular to the beam is negligible “). Approximating the mass of the recoiling nucleus by the target mass A, (see appendix A) one can calculate the LMT (pii) event by event from the component along the beam direction of the recoil velocity by pii = A, x q where v,z),sin(@,+@,) VII= v, sin 0, + v? sin (*? ’ The LMT distributions of a-induced reactions at 70, 250 and 800 MeV/u incident energy are shown in fig. 6. At 70 MeV/u incident energy the Au and Ho targets lead to narrow symmetric distributions of the LMT. They are centered around 70 and 90% of the beam momentum with cross sections of about 15% and 0.4% of the one obtained with the Th target, respectively. With the increase of the incident energy the spectra show tails towards higher LMT, which are partly caused by increasing particle evaporation. But the most probable values decrease slighly and both trends together lead to a small reduction

399

lo3 102 10' loo 10-l 2

to3

I

E, = 250 MeV/u

S d t g G

lo2

Th ,i.

'0' 100

? g

10-l 103

E, =

800

3

L

MeV/u]

lo2 10' loo 10-l -1

0

1

2 pII

5

6

(GeV/c)

Fig. 6. Distributions of the linear momentum transfer in [u-induced fission at 70, 250 and 800 MeV!u target mabb incident energy. The tission events are selected hy the q, criterion (bee text). Decreasing evidences the ielectibity of huh-group\ with high LMT.

or a leveling off of the mean value of the LMT with increasing incident energy as summarized in fig. 7. We stress that the excitation energy (table l), on the other hand, continues to increase and therefore the limitation seen in the LMT is not due to a limitation in the excitation energy. For example in the case of Ho, in the mean LMT could arise by peripheral reactions becoming more the fission channel. Generally, the saturation can be interpreted by mechanism via nucleon-nucleon collisions, as will be discussed in

the constancy important in the stopping the next sub-

section.

The highest LMT of 1.33 GeV/c is reached 250 MeV/u incident energy. This corresponds

in the central to a transfer

collisions (Ho) at of 330 MeV/c per

et al. /

G. Klotz-Engmann

400

Binary fission

and mult~fragmentation

Fig. 7. Mean momentum transfer per projectile nucleon in a-induced binary fission process as a function of the total incident energy. The fission events are selected by the art criterion (see text). Open symbols are from refs. ‘2,23). (The dashed lines are drawn to guide the eye.)

Table Measured mean fission-fragment (u,,). Errors of 13% are assigned after preequilibrium emission of appendix A using F = 15 MeV/u excitation energies are calculated

1

masses (A,) and linear component of the recoil velocities to both values. The average mass (A,) of the recoil nucleus the fast nucleons (n,,,, ) is calculated in the framework of and @,= 18”. The average linear momentum transfer and by (pII) = (A,)( L’,) and (E,) = ((A, > - 2(A,)) E, respectively

(4

system

(cm/m)

(4)

(4.d

(PI,) (MeV/c)

(EJ (MeV)

‘He+Th

250 800

110 101

0.083 0.076

230.6 228.6

5.4 7.4

594 539

I59 399

“He+Au

70 250 800

94 86 81

0.176 0.167 0.145

199.7 196.1 194.4

1.3 4.9 6.6

1091 1017 875

175 362 486

‘He+Ho

70 250 800

16 63 58

0.237 0.257 0.239

167.4 163.5 162.7

I .6 5.5 6.3

1232 1304 1208

231 562 701

“NfTh

250 800

98 97

0.096 0.066

220.7 219.1

25.3 26.9

658 449

371 376

“N+Au

250

78

0.224

188.5

22.5

1311

487

projectile

per nucleon

nucleon and shows can be transferred

3.4. INTRA-NUCLEAR-CASCADE

that with cu-projectiles nearly the same momentum as with a single proton (3.50 MeV/c, ref. I)).

CALCULATlONS

Intra-nuclear-cascade calculations (I NC) performed with the Yariv and Fraenkel code “) illustrate the relation between impact parameter and LMT. In the calculation events with excitation energies below 2.5 MeV are suppressed to take into account

et al. / Binary,fission

G. Klotz-Engmann

their low fission parameter

probability.

for the reaction

ctnd

In fig. 8 the LMT is given cr +Th

at 800 MeV/u.

401

mult~fragmentation

Although

as a function the correlation

of impact between

impact parameters and LMT is rather broad, the trend of the mean values indicates that high LMT and small impact parameters are well related. Calculations were also performed to study the typical trends of nucleon-nucleon collisions for the investigated observables. Using cy- and ‘“C-projectiles the LMT per projectile nucleon was calculated for incident energies from 2.50 MeV/u up to 2.1 GeV/u (fig. 9). To avoid effects caused by geometrical properties, we have chosen to compare only central collisions, i.e. the impact parameters range from zero to

4

800 MeV/u

t

I

I

0

a+Th

I

I

I

2

L

6

impact

I

i

I

I

8

10

parameter

(fm)

Fig. 8. Linear momentum transfer as a function of impact parameter calculated that central collisions are correlated to high LMT. The contour lines represent spacing.

0’

’

0.2

’

1

Fig. 9. Mean

LMT from

n and

I

I1111’ 0.5 1

E/A

by the INC code shows the yield in logarithmic

2

(GeV/u)

“C projectiles on a Th target calculations).

as a function

of incident

energy

(INC

G. Khtz-Engmann

402

r,,(A,“3 - A;‘)

which corresponds

et al. / Binary fission

to complete

and multifragmentation

overlap

between

projectile

(A,,) and

target (A,). The following behaviour is seen: (i) The LMT per projectile nucleon does not depend on the projectile size. Each nucleon acts independently and is not influenced by the others arriving simultaneously. (ii) The LMT per projectile nucleon does not vary much with incident energy in the range from 200 MeV/u to 2 GeV/u. These results are in reasonable agreement with the experimental data obtained from the Ho target which represent the central collisions (fig. 7). The predicted scaling with the projectile mass is also in agreement with other experiments, since for central collisions the LMT per projectile nucleon is rather constant, ranging from 160 to 200 MeV/c for projectiles up to X4Kr [refs.Z4m27)]. More straightforward calculations applicable for lower incident energies “) lead to similar conclusions: The momentum transfer mechanism can be understood in terms of individual nucleon-nucleon collisions

3.5.

EXCITATION

ENERGY

The transferred energy is mainly converted into excitation energy of the fissioning nuclei. The mean value of the excitation energy can be deduced from the mean fission-fragment mass. The difference 3A between the recoil nucleus A, and twice the mean fragment mass (A,.) reflects the number of evaporated nucleons, each carrying away an excitation energy of 12-15 MeV [ref.“)]. Hence, the initial excitation energy of the equilibrated recoil nucleus is proportional to the mass difference (AA)=(2(AJ. The Q-value of the fission process is neglected, because it corresponds roughly to the total kinetic energy of the fragments. The recoil mass A, depends on the preequilibrium emission of fast nucleons, being removed from the target nucleus in the initial stage of the reaction. The number of these nucleons is estimated from the data (see appendix A) and corresponds for light projectiles roughly to the number of projectile nucleons. Therefore, the recoil mass is approximated

by the target mass.

Comparing the fragment-mass spectra of the Ho target from 70 to 800 MeV/u incident energy (fig. 3a) the mean value of the fission component decreases continuously. This trend reflects an increasing excitation energy of the fissioning nucleus. In fig. 10 the coincident fragment mass spectra of u- and ‘jN-induced reactions on Th are presented. Using cu-projectiles from 250 to 800 MeV/u incident energy the average fission mass decreases and reflects again an increase of the excitation energy. In contrast, using ‘“N projectiles at the same velocities corresponding to 3.5 and 11.2 GeV total incident energy the mean values of the fission-mass spectra are nearly the same and indicate that here the excitation energies are equal. If the number of fast preequilibrium nucleons would be higher with increasing incident energy the number of evaporated nucleons and hence the excitation energy would even be lower. This constancy is also seen when comparing the systems 3.2 GeV

G. Klotz-Engmann

et ul. /

t?inury./ission

0 0

100

50

fragment Fig. 10. Coincidence

fragment-mass

spectra

and

multjfragmentation

403

150

mass

A,

of cy- and ‘“N-induced incident energy.

reactions

on Th at 250 and 800 MeV/u

CY+ Th and 11.5 GeV proton + U [ref. “‘)I. These observations led us to the conclusion that above 3 GeV total incident energy the mean excitation energy remains constant in the fission channel. Our results are summarized in fig. 11, where the average mass differences (JA) for N- and 14N-induced fission are shown as a function of the total incident energy. The mass of the recoiling nucleus has been approximated by the target mass A,, the values of table 1 result from the calculation in the appendix A. Up to 3 GeV incident energy (AA) increases continuously. With decreasing target mass (LA) is larger and reflects subgroups of collisions with higher excitation energies selected by higher fission barriers as already discussed in the linear momentum transfer study. Bombarding

the Ho nucleus

with 3.2 GeV cu-projectiles

I

I

63 p+u A

A

40 - ;

_0 5

0

I

i

a+Ho :a;; “N+Au “N+Th

only the most violent

4 ;

3

b0‘

20 b l

+

I

I

LII

0.1

1

10

E, (GeV) Fig. 11. Average mass difference (AA) = A, ~ 2(A,) deduced from the fission-mass spectra as a function of incident energy for LY-and 14N-induced reactions. The p+ U data are from ref. “‘1. (Lines are drawn to guide the eye.)

G. Klotz-Engmann

404

collisions

lead to fission

700 MeV is deduced 6 MeV. The constancy

and

(table

of (AA)

energy is accompanied

fission and multjfragmentation

et al. / Binary

from

the mass

difference

l), corresponding in the fission

by a decreasing

to a nuclear

channel

observed

fission cross section

an excitation temperature above

energy

of

of about

3 GeV incident

as evidenced

in fig. 12.

The ratio of the fission cross section to the total reaction cross section calculated using the soft-sphere model of ref. ‘I) is shown for (Y-, 14N- and “‘Ne-induced reactions on U and Th nuclei as a function of the total incident energy.

YLLO 4 G20

i

n 0 0 0

a+Th a+U “N+Th 20Ne+U I

1

E, Fig. 12 Fission

(GeV)

cross-sections normalized to the reaction cross sections, calculated with the model ref. ‘I). The U data are from ref. “). (Lines are drawn to guide the eye.) Table 2 Measured fission cross-sections vfil, the reaction cross sections, calculated with the soft-sphere model of ref. “) and the ratio of both. The error of vii, is estimated to 120% mainly due to the unknown angular distribution

System

E, (MeViu)

Cfl‘ (mb)

C,CX (mb)

( “/o)

p,

4He+Th

70 250 800

1960” 1720 1060

2700 2330 2480

72.6 73.6 42.7

“He+Au

70 250 800

290 160 100

2490 2130 2270

11.6 7.5 4.4

“He+Ho

70 250 800

7 27 48

2280 1930 2070

0.3 1.4 2.3

14N+Th

250 800

1830 760

3600 3760

50.8 20.2

“N+Au

250

340

3320

10.2

“) From ref. *).

of

rf al. / Rinury.fis.sion

G. Klotz-Engmann

and

multifkigmentation

40s

With increasing incident energy three observations are obtained around 3 GeV (see also tables 1 and 2): (i) The fission cross-sections decrease. (ii) The deposited energy in the fissioning nuclei ceases to increase. (iii) IMF are observed. We conclude that the violent central collisions no longer lead to a fission process resulting in a constant mean value of the excitation energy in the fission channel. They lead to a multiple break up as observed at higher incident energies ‘) where only the gentle peripheral collisions lead to fission and the more central reactions end by multifragmentation. 4. Properties 4.1.

ONSET

OF

of multifragmentation

MULTIFRAGMENTATION

As shown in sect. 3.1 in o-induced

reactions

between

2.50 and 800 MeV/u

incident

energy, the binary fission is no longer the only decay channel seen in coincidences and multifragmentation starts to compete severely. IMF appear in the coincident mass spectrum (fig. 3a) accompanied by a fall in fission cross-sections (fig. 12 and table 2). The non-binary character of the IMF was evidenced by the isotropic out-of-plane angular correlation “). It is confirmed in fig. 13, where the correlation between the fragments masses in the TOF and the atomic number of the coincident

F

800 MeV/u

60

fragment Fig.

13. Correlation

L’,,< 2.5 cm/ns

(b).

between Normal

coincident velocities

a+Au

a) vtt<2 5 cm/w

fragments exhibit

fission

between

mass

in the TOF fragment two

IMF.

1

A, and the PPAC correlations,

for qf< high

2.5 cm/ns

velocities

(a) and

correlations

406

G. Klotz-Engmann

fragments

in the PPAC

et al. / Binar~~,fission and multifragmentation

is presented.

Separating

the events

due to their

relative

velocity into two classes one finds that for u,r < 2.5 cm/ns two heavy fragments detected in coincidence, reflecting normal binary fission. In contrast, selecting

were high

uti a correlation mainly between two light fragments is observed. Coincidences between light and heavy fragments do not represent asymmetric fission, because their total mass lies significantly below the value seen in fig. 13a. The onset of multifragmentation occurs when the mean excitation energy in the fission channel does no longer increase (sect 3.5 and ref. “)). A similar conclusion has been drawn in ref. “), where (Y- and “‘Ne-induced reactions from 4.2-8.4 GeV incident energy were studied. The multiplicity of light particles was correlated to the total incident energy of the projectile and indicated its important role in the mechanism of relativistic nucleus collisions. The underlying parameter could be the energy deposited in the decaying nucleus where the highest excitation energy of 700 MeV observed in binary fission might constitute the range where fission competes strongly with multifragmentation. This could explain, that for central collisions in 40Ar- and ‘“Ni-induced reactions between 20 and 44 MeV/u incident energy, the fission process decreases strongly. There, the excitation energies range from 650 to 950 MeV [refs. ‘5,26)].

4.2. PRODUCTION

PROBABILITY

OF

INTERMEDIATE-MASS

FRAGMENTS

Comparing the fragment-mass spectra of the Au, Ho and Ag targets at 800 MeV/u o-induced reactions an interesting trend is observed (fig. 14): As expected the higher fission barrier of the lighter targets reduces the contribution of fission fragments in the spectrum. In contrast, the contribution of IMF remains nearly constant for the three targets. Bombarding the Ag target the spectrum is dominated by IMF and the fission component is hardly separable. The production process of the IMF is independent of the fission barrier and this rules out fission-type processes including asymmetric

or sequential

fission.

-i?J YE 5

0.4

2 7-J %_

0.2

3 z z m u Fig.

14. Coincident fission

component

0.0

40

60

80

fragment

fragment-mass decreases

20

spectrum with

increasing

of a-induced fission

100

120

mass reactions

harrier,

140

A, on an Au,

the contribution

Ho and

Ag target:

of IMF

is constant.

The

G. Khz-Engmann

Since the experimental

C’I

al. / Binar~~.fitsion

set-up is limited

407

and mu/~~~ragnwn/ation

in solid angle only a fraction

of the IMF

is detected in coincidence. But the differential cross section of the IMF emission can be deduced from the inclusive mass spectrum, which is dominated by I MF and fission fragments play only a minor role. At 800 MeV/u a-induced reactions a differential cross-section of about 50+ 20 mb/sr at 90” for IMF (10 < A < 40) is obtained independent of the target nucleus.

4.3. PRODUCTION

MECHANISM

OF

INTERMEDIATE-MASS

FRAGMENTS

Concerning the production mechanism of the light fragments the question arises whether they are produced in a simultaneous breakup of the nucleus. In a recent experiment “) bombarding a Au target with 84 MeV/u “0 projectiles, excitation energies around 600 MeV were obtained and IMF have been observed. From the suppression of low relative velocities, which provide information about the Coulomb repulsion between the IMF, a time scale of the emission process was deduced showing that the IMF are emitted sequentially from a heavy residue. The same analysis cannot be applied to our data, because in our set-up small correlation angles and hence small relative velocities are not measured. Assuming sequential emission of the IMF from a heavy recoil, due to momentum conservation the light fragments receive nearly the total Coulomb energy and their single velocity corresponds approximately to Viola’s value of 2.4cm/ns. Taking into account that our set-up accepts only fragments emitted in opposite hemispheres their single velocities sum up to a relative velocity around 4-5 cm/ns. To verify this argument quantitatively we performed Monte Carlo calculations (see appendix B) for the sequential emission of two IMF from a heavy recoil nucleus taking into account the detector acceptance of our set-up. The resulting distribution is centered distribution

around 4.5 cm/ns (fig. 15, dotted of relative velocities between

I

I

line) and disagrees IMF (lo< A, (40

I

U-J I-

I

I

800 MeV/u

with the measured and 5
a+Au

IMF-IMF iA,cLO,

2 1151

x

5 E , 1

1

2 vff

Fig. 15. The measured The full curve shows curve represents

3

“L+_

L

5

6

(cm/ns)

relative velocity between two I MF (A, < 40, 2, c 15 1 is centered around 3.8 cm/n% the results of a Monte <‘arIo simulation for simultaneous breakup. The dotted the distribution assuming sequential emission from a heavy recoil nucleus.

408

Sequential

G. K/HZ-Engmann

emission

et al. / Binar_v,fission

can be excluded

and multifragmentation

in a-induced

reactions

at 3-4 GeV incident

energy. In contrast to a sequential emission a simultaneous breakup of the target nucleus leads to lower relative velocities. In the simulation the fragment masses were chosen randomly using a power-law distribution A-’ with T = 2 and a lower mass limit of A = 10. Assuming a start configuration, where the fragments are positioned randomly inside a sphere, a freeze-out radius of R = 18 fm reproduces the experimental velocity distribution. This radius is slightly larger than in the case of a binary fission process (14 fm) and suggests a decay of a dilute system. However, this value is only a rough estimate since it depends on the chosen start configuration and the lower limit in the mass distribution.

5. Summary The present study of binary fission shows that in bombarding medium-mass nuclei a selection of the high LMT domain is possible. We observed 90% momentum transfer at 70 MeV/u incident energy leading to an equilibrated nucleus which decays by normal fission (a + Ho). In medium- and high-energy induced fission two independent trends in the LMT and in the excitation energy are observed: - Between 70 and 250 MeV/u incident energy the mean LMT of a-projectiles saturates, while the excitation energy continues to increase. The highest observed transfer is about 330 MeV/c per projectile nucleon in central collisions. This constancy can be understood in terms of nucleon-nucleon collisions. - Up to 3 GeV incident energy the excitation energies of the fissioning nuclei increase, while above 3 GeV incident energy they remain constant. The highest excitation energy observed in medium heavy fissioning nuclei is around 700 MeV and corresponds to a temperature of about 6 MeV. Above 3 GeV incident energy with (Y- and 14N-induced reactions this change in the trend is accompanied by a strong decrease of the fission cross-section and the emission of IMF is observed. They stem from non-binary processes and their production probability is independent of the target mass. The parameter provoking the transition from binary fission to multifragmentation is likely to be the energy deposited. A critical value might constitute the highest excitation energy of 700 MeV observed in binary fission events. The relative velocities between two IMF are a key quantity in understanding the breakup mechanism. The measured values exceed those of binary fission, but they are lower than expected for a sequential emission process and suggest a simultaneous breakup of a dilute system. We would like to acknowledge the staff of Saturne for the very good beams and especially G. Milleret for his help in the beam transport. We thank H. Stelzer for

G. Klotz-Engmann

making available

et al. / Binary jission

the PPAC and H. Folger and the GSI target laboratory

most of the targets. This work was partially supported by the Bundesministerium Technologie under contract 06 DA 453.

Appendix PREEQUILIBRIUM

409

and mult~fmgmentation

for preparing

fur Forschung

und

A

EMISSION

In high-energy collisions during the preequilibrium stage fast particles can be emitted as clusters or single nucleons in the forward hemisphere. From the mass balance between target mass A, and projectile mass A,, and the number n of fast nucleons the mass of the fissioning target residue can be calculated by A,= A,+ A,- n. The number n of the fast nucleons can be estimated applying momentum and energy conservation; the projectile momentum p. is transferred into the linear momentum

pll of the target residue

and into the linear

momenta

of the n fast nucleons

p,,(i) by

(2)

Po=Pll+ i P,,(i) ,=I

The incident energy E,, is converted into excitation energy E,, recoil energy E, of the target residue, the kinetic energy &,,,(i) and binding energy E,,(i) of the fast nucleons: (3) with E,=(A,.-~(A,.))F

(recoil

velocity

E,.=~A,xq’

(~=12-15MeV),

approximated

by the measured

linear

component)

Eh( i) - 8 MeV.

The sum of the kinetic energies of the fast nucleons is calculated from the mean value, which is deduced from their mean momentum. This approximation is justified, when the momenta of the fast nucleons do not vary too much yielding f Ekin( i) = n&,,,(i) I-1

= n(J(p(

i)c)‘+

(m,,c’)‘~

m,,c’)

.

(4)

If the angular distribution of the fast nucleons is known, their average momentum p(i) can be determined from the average linear component. The angular distribution of the preequilibrium nucleons was measured in ref. j2). Using (Y- and “‘Ne-projectiles at 1.05-2.1 GeV/u incident energy in coincidence with fission fragments an exponential distribution d W/dR( 0) - e~“““l~’ with a slope parameter @,, between

G. ~l~t~-~?I~~~~rl~rf

410

15” and 20” was observed. and integrating

al. / ni~[ir~,~ssi~~

Weighing

mufr!tluRmenraticrrr

the linear component

over the whole solid angle, one obtains

of the fast nucleons

as a function

PII = Using eq.(5) with dW/d@

Eq. (2) provides

and

of their total momentum ii j?(i) cos @swdO. .

= sin@ d W/d0

the average

linear

by the angular

distribution

the average linear momentum as

it results

component

of the fast nucleons

by

Comparing eq. (6) and eq. (7) one can calculate the mean momentum of the fast nucleons and hence their total energy (eq. (4)). As unknown parameter only their number n remains, which can be determined iteratively via eq. (3) using the measured fission fragment masses (A,-) and recoil velocities u, . The result is summarized in table 1 showing that the number of fast nucleons does not exceed twice the projectile mass number. Appendix MONTE

CARLO

SIMULATION

B

OF MULTIFRAGMENTATION

To study the sensitivity of relative velocities between the IMF on their production mechanism, Monte Carlo calculations were performed for the system 800 MeVfu N i- Au. To simulate the distintegration of the recoiling nuclei, their initial mass, atomic number and recoil velocities after the primary reaction were determined from INC calculations. Selecting central collisions (b < 5 fm) the resulting mean values were centered at {A,} = 182, (Z,) = 74 and (v,-) = 0.3 cm/ns. These values are rather uncritical for this study. The IMF were emitted isotropically in the center-ofmass system. Their mass distribution was chosen proportional to A-’ with ~=2 and a lower limit of A = 10. The atomic number of the fragments was deduced from their mass number assuming the N/Z ratio of the recoil nucleus. To determine their final velocity vectors Coulomb trajectories of the many-body system were calculated using the Lagrange formalism and treating the interacting fragments as point charges. Without prescission energies they were accelerated due to their mutual Coulomb repulsion. The iteration was performed up to l= 3000 fm/c where about 98% of the final velocities were obtained. After the transformation into the laboratory system only the fragments in the angular range of the detectors were accepted (see sect. 2) and events with multiple hits in one detector suppressed. In both detectors a general energy threshold of E,,,i,, = 10 MeV was used. Two processes were simulated, the sequential emission of IMF and the spontaneous breakup of the nucleus.

G. Klotz-Engmanrt

et al. J Rinar~~,fi.ssion and mu/tjfra~mPntntion

411

(i) Sequential emission of IMF. Two IMF were emitted sequentially from the heavy recoil in evaporation-like binary processes. The scission distance of R = (1.225 x ( A,,,.“3 +A:‘>) + 2) fm was determined from the kinetic energies of IMF with A < 20 in ref. “). Varying the time interval between the emission processes 67 from 0 to 2000 fm/c the relative velocities This is due to the fact, that the Coulomb opposite hemispheres is low in comparison

of opposite

IMF remained

rather constant.

interaction between two IMF emitted in to the IMF-recoil interaction. In contrast,

the relative velocity depends on the multiplicity of the fragments. This results from the reduced Coulomb repulsion from the lighter recoil nucleus after the first emission processes. If one increases the multiplicity of the emitted IMF from 2 to 4, the mean relative velocities are reduced by about 10%. (ii) Simultaneous break up. The simultaneous break up was simulated by dividing the recoil nucleus completely into fragments. Corresponding to the chosen mass distribution (see above) on average 5 fragments were produced, which were positioned without overlap randomly inside a spherical freeze-out configuration. The radius adjusted to fragments radius was chosen to 1.4A’, ’ and the freeze-out reproduce the measured mean relative velocity between IMF. The final velocities were calculated from the Coulomb trajectories taking into account the experimental detector acceptance as discussed above.

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