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Experiments on Fission Dynamics with Relativistic Heavy-ion Beams
K.-H. Schmidt,∗,a P. Armbruster,a J. Benlliure,b C. Böckstiegel,c A. Botvina,†,a H.-G. Clerc,cT. Enqvist,d A. Grewe,c A. Heinz,‡,a A. R. Junghans,§,a B. Jurado,a J. Müller,c M. V. Ricciardi,aF. Rejmund,e S. Steinhäuser,c and B. Vossaa
GSI, Planckstr. 1, 64291 Darmstadt, Germanyb
University of Santiago de Compostela, 15706 Santiago de Compostela, Spainc
IKDA, TU Darmstadt, Schloßgartenstr. 9, 64289 Darmstadt, GermanydUniversity of Jyväskylä, 40351 Jyväskylä, Finlande
IPN Orsay, IN2P3, 91406 Orsay, France
Received: November 25, 2001; In Final Form: February 21, 2002
At GSI, Darmstadt, an experimental program on fission with relativistic heavy-ion beams is in progress. A large
range of excitation energies, combined with low angular momentum and small shape distortion is accessible. Full
nuclide identification of the reaction residues is achieved by applying inverse kinematics. The nuclide production
and the kinematics of fission fragments from a variety of primordial and radioactive projectiles reveal new insight
into the influence of shell effects and dissipation on the fission process. The present contribution gives an overview
on the experimental methods, the experimental results, and the prospects for future progress.

1. Introduction
Nuclear fission as a prototype of a non-equilibrium dynamical process of a mesoscopic system of fermions is not yet fully
understood. To most part, this is due to the lack of experimental
knowledge obtained so far in conventional experiments. Theseexperiments were restricted in the choice of the system, in thecontrol of the relevant parameters like excitation energy, angularmomentum, and shape, and in the measurable quantities.
Low-energy fission could only be studied using primordial or
long-lived target materials. With the exception of some spontaneously fissioning nuclei, this limited the investigations to a few
species in the vicinity of the available target nuclides.
Fission from high excitation energies, mostly studied inheavy-ion reactions at beam energies around 5 to 20A MeV, suffered from two problems: Firstly, high excitation energies wereaccompanied with broad angular-momentum distribution. Secondly, the reaction dynamics started with large shape distortions.
Generally, the full identification of the fission fragments innuclear charge and mass is a difficult task, due to the low fissionfragment velocities. This goal has only been reached in a few
thermal-neutron-induced fission reactions for nuclei in the lightgroup of the fission fragments. In fission from high excitationenergies, the full nuclide identification in-flight has never beenachieved.
This contribution gives an overview on the results of first experiments performed at GSI, using relativistic beams of primordial and radioactive fissile nuclei, in which several of the previous restrictions could be overcome.
2. Experiment2.1. Accelerator and Spectrometer. Two installations of
GSI, Darmstadt, are most essential for the experiments we report on in the present contribution: The heavy-ion synchrotron
SIS18 accelerates heavy ions up to uranium to energies of atleast 1A GeV, and the fragment separator,1 shown in Figure 1,
allows determining the magnetic rigidity of the reaction prod∗Corresponding author. E-mail: k.h.schmidt@gsi.de. FAX: +496159 71 2785.
†Permanent address: Inst. for Nuclear Research, Russian Academyof Sciences, 117312 Moscow, Russia‡Present address: Argonne Nat. Lab., Physics Div., 9700 South Cass
Avenue, Argonne, IL 60439, U.S.A.
§Present address: Nucl. Phys. Lab., BOX 354290, University ofWashington, Seattle, WA 98195, U.S.A.

ucts emerging from a target mounted at its entrance with highresolution.
2.2. Full Identification of One Fission Fragment. Using
relativistic beams of primordial nuclides, one product emerging
from the reaction can be analyzed with the fragment separator
used as a high-resolution spectrometer.2–4 The magnetic rigidity, combined with the energy loss and time-of-flight,5 measured
with dedicated detectors, allows fully identifying this reaction
product in nuclear charge and mass. In addition, its longitudinal momentum is measured with high precision. It is essentialthat the ions are fully stripped at the relativistic energies. Thus,
their nuclear charge can be deduced from the measured energy
loss in an ionization chamber with high resolution.6 Figure 2
demonstrates the resolution in mass number and nuclear charge
in a typical example.
2.3. Simultaneous Measurement of Both Fission Fragments. In another full-acceptance experiment, both fission
fragments are simultaneously registered in a large double ionization chamber and a time-of-flight section,7 and their nuclear
charges and velocity vectors were determined. The experimental
setup is shown in Figure 3. Beams of primordial and radioactive
nuclei from the fragment separator have been used. As important information to distinguish between different reaction mechanisms, i.e. electromagnetic- or nuclear-induced fission, the nuclear charge of the fissioning system could be determined fromthe nuclear charges of the fission fragments, which were again
measured with high precision. A two-dimensional cluster plotof the energy loss recorded in the two parts of the double ionization chamber is depicted in Figure 4.
2.4. Reaction Mechanisms Used to Induce Fission.
Heavy-ion collisions at relativistic energies can be classified into
different groups. Very peripheral collisions without nuclear contact are governed by electromagnetic forces.9 Mostly, the giant
dipole resonance is excited.7 The excitation-energy distribution

Figure 1. Schematic presentation of the fragment separator and themain detectors.

c 2002 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 6/30/2002

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Figure 4. Cluster plot of fission fragments recorded by the double
ionization chamber in the reaction 238 U + (CH2 )n .

Figure 2. Example for the resolution in nuclear charge and mass for reaction products of the system 1 H + 208 Pb at 1A GeV (from Reference 8).
The spectra measured with a few different settings of the spectrometerare overlaid.

Figure 3. Experimental setup to simultaneously measure both fission
fragments produced in inverse kinematics (from Reference 7).

of heavy fissile nuclei peaks at about 11 MeV and has a width ofa few MeV. Peripheral collisions with nuclear contact lead to theabrasion of a number of nucleons and induce appreciably higher
excitation energies, which amount to 27 MeV on the average per
nucleon abraded.10 With increasing mass loss, the excitation energy of the spectator reaches to very high values, even making it
a suitable tool to investigate thermal multifragmentation.11 For aheavy nucleus, excitation energies of several hundred MeV canbe reached with a relative mass loss of only a few percent. Thus,
shape distortions after the abrasion phase are small. Due to thelack of momentum transfer to the spectator, the angular momentum induced is rather small, too, in the order of 10 to 20h̄ on the
average, as deduced from theoretical estimations,12 which areconfirmed by experimental results.13 Thus, the characteristics
searched for in anti-proton-induced reactions14 are even better
realized in peripheral heavy-ion collisions.
3. Results and Discussion
3.1. Multi-modal Fission. Multi-modal fission of radioactive nuclei was investigated in a dedicated experiment.7 Relativistic secondary projectiles were produced by fragmentationof a 1A GeV 238 U primary beam in a beryllium target and identified in nuclear charge and mass number by the fragment separator. According to the impact parameter, some of these secondary projectiles were excited by electromagnetic interactions
in a secondary lead target, inducing fission from excitation en-

Figure 5. Upper part: Measured nuclear-charge distributions in thetransition zone from symmetric to asymmetric fission around 227 Th.
Lower part: Result of a model calculation as described in the text (fromReference 7).

ergies around 11 MeV. The fission fragments were identified innuclear charge, and their velocity vectors were determined. Elemental yields and total kinetic energies of 70 short-lived nuclear
species have been obtained, almost all of them for the first time.
In particular, the transition from symmetric to asymmetric fission around 227 Th has been covered systematically.
The most important experimental achievements of thissecondary-beam experiment were the rather free choice of thenucleus to be investigated, independently of its chemical properties and independently of its radioactive decay characteristics,
down to half-lives in the order of 100 ns, the excellent nuclearcharge resolution for all fission fragments, and the remarkably
good determination of the mean total kinetic energies with uncertainties in the order of 10−5 of the laboratory energies.
The data were analyzed in terms of fission channels.15 The
weights of the three predominant channels, standard I, standard
II, and superlong, were found to be consistent with the trends ofprevious results found for heavier actinides.16 Calculations witha semi-empirical fission model17 were performed, assuming (i)that the population of the fission channels is determined by thelevel density above the mass-asymmetry-dependent fission barrier, (ii) that the dynamics from saddle to scission is describedby the fission-channel concept,18, 19 and (iii) that the mean values
and the widths of charge distribution and total kinetic energy ofthe fission fragments are finally determined at the scission configuration. The results are compared to the experimental data inExperiments on Fission Dynamics

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Figure 6. Element yields (upper part) and deduced local even-odd effect as defined in Reference 22 (lower part) for electromagnetic-induced fissionof 220 Ac and 226 Th.

Figure 7. Total nuclear-induced fission cross section of different secondary projectiles of 430A MeV in a lead target compared to model calculations
with different options.

Figure 5. This analysis corroborates the fission-channel concept
and reveals the strong influence of phase space on the fission
process.7
3.2. Dissipation. Fission is a unique tool to investigate nuclear dissipation. Our experiments are sensitive to the following
features: At low excitation energies, dissipation manifests itself
in the breaking of pairs. At high excitation energies, it reduces
the flux over the fission barrier.
3.2.1. Onset of Dissipation in a Super-fluid Nuclear System.
The excellent Z resolution achieved in the secondary-beam experiment7 described in the previous section, allowed investigating pair breaking in fission in a systematic way.20 Strong
even-odd effects in the element yields were found in symmetriccharge splits for the first time. A general tendency of the evenodd effects to increase in very asymmetric charge splits was established, even for odd-Z fissioning nuclei. Two representative
cases are shown in Figure 6. A new theoretical description,21
based on the statistical model, is able to explain these findings
and to deduce the energy dissipation in the fission process, starting from a cold, superfluid system at the barrier down to thescission configuration.
3.2.2. Dissipation in Hot Nuclei. The properties of the projectile fragments produced in peripheral nuclear collisions are
best suited for investigating the influence of dissipation on thefission process. These particular properties allow analyzing thedata with the theoretical framework developed by Grangé andWeidenmüller,23 avoiding disturbing influences of high angularmomenta or large shape distortions. Besides the total fission
cross section (Figure 7), the excellent Z resolution of the experiment allows to introduce two new experimental signatures
which are sensitive to dissipation; the width of the element distributions (Figure 8) and the “partial” fission cross sections (Figure 9), both available for specific elements produced as projectile fragments with different initial projectiles. By use of secondary beams, the influence of fissility and excitation energiesof the fissioning systems could independently be investigated.24

Figure 8. Measured width of the charge distribution of fission fragments from the reaction 238 U + (CH2 )n at 1A GeV for given values of
Z1 + Z2 in comparison with model calculations with different parameters.

Figure 9.
Partial fission cross sections measured in the reaction
238
U + (CH2 )n at 1A GeV for given values of Z1 + Z2 in comparison withmodel calculations with different parameters.

The different experimental signatures are sensitive to different
things: While the total fission cross sections integrate over allprocesses, the width of the element distributions particularly
measures the mean excitation energy at fission. The partial fission cross sections probe the excitation-energy dependence ofthe fission probability. All three signatures are rather consistently described by the model calculation with a reduced dissi-

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Figure 10. Average N-over-Z of the projectile fragments from the reaction 238 U (1A GeV) + Pb4 compared to SMM32, 33 calculations with different
initial excitation energies. The β stability and the prediction of EPAX30 for 197 Au + p are also given.

Figure 11. Velocity distribution of detected reaction products from a 238 U beam (1A GeV) in titanium (full histogram) and hydrogen (hatchedhistogram). The counts have been normalized to the same number of projectiles. Due to technical reasons, the spectrum is truncated at +2 cm/ns.

pation coefficient β = 2 ×1021 s−1 , which is close to the critical
damping.
The interpretation of these data is still in progress. A major goal is to incorporate a realistic in-grow function, representing the solution of the Fokker-Planck equation, for the timedependent fission width in the statistical deexcitation code, sincepreviously used approximations25, 26 were found to lead to erroneous results.27, 28
3.2.3. Temperature Limit for Sequential Decay. The excitation energy induced in the abrasion process as a function ofmass loss has been established experimentally10 : An excitationenergy of 27 MeV has been found to be induced by the abrasionof one nucleon. Thus, very high excitation energies can be induced. It is known that very high excitation energies lead to a simultaneous breakup of the system, before the excited fragments
decay sequentially.11 For the analysis of nuclear dissipation, described in the preceding section, one needs to know the initialconditions at the beginning of the statistical deexcitation cascade (the sequential decay) in which fission is part of the competing processes. That means, if there is a breakup phase, weneed to know the excitation energy after that phase. Recently,
we could deduce the freeze-out temperature Tf after the breakup
stage from the isospin thermometer,29 that is, by the variationof the N-over-Z ratio in the evaporation cascade. We found avalue of about Tf = 5 MeV, corresponding to E ∗ = 2.5 MeV/u in
the SMM32, 33 calculations shown in Figure 10, independently
from the projectile and from the size of the fragment. Lower
values preserve the neutron excess of the projectile to a larger
extent, while higher values tend to approach the EPAX30 prediction which assumes a universal “evaporation-residue corridor”31
where the competition between evaporation of protons and neutrons goes into saturation.
The assumed breakup density, another important parameter of
the SMM calculation, was assumed to be 6 times normal nuclear
density. However, it does not have a sizeable influence on theneutron-to-proton ratio of the fragments.
Besides other very interesting consequences, this finding is
an important ingredient to deduce the influence of dissipationon the fission process, as described in the preceding section. In
addition, it means that fission is prohibited above a temperatureof 5 MeV by other than dissipative phenomena, namely by thermal instabilities.
3.3. Extremely Asymmetric Mass Splits. The highresolution spectrometer is a sensitive tool to investigate fission
leading to extremely asymmetric mass splits. We investigated
the fission following the spallation of 238 U by 1 GeV protons ininverse kinematics.34 Fission fragments as light as neon could
be observed. Their cross sections and their isotopic distributions
contain valuable information on the dynamics of fission, e.g. on
the charge polarization in extreme mass splits. Figure 11 shows
the velocity distributions of sodium, chlorine, and vanadium isotopes produced in the titanium windows and in the hydrogentarget itself. While the fragmentation products at mid-velocity
are produced in the windows, fission appearing at a velocity of
2 cm/ns in forward and backward direction is mostly producedin the hydrogen target. Note that sideward-emitted fission fragments are not transmitted by the fragment separator due to its
limited angular acceptance.
In addition, this finding shows for the first time that light nu-

Figure 12.
Yields of potassium isotopes measured at ISOLDE35
in comparison with the isotopic distribution measured in the inversekinematics reaction 238 U on proton.34

Experiments on Fission Dynamics
clides produced at ISOLDE35 by spallation of uranium-carbide
targets by 600 MeV protons, previously considered as “fragmentation” products, result from extremely asymmetric fission ofhighly excited, heavy spallation products. Indeed, as Figure 12
shows, the measured isotopic distribution of potassium isotopes,
identified as fission products in 238 U (1A GeV) on proton, perfectly fits to the ISOLDE yields.
4. Prospects
In spite the considerable progress achieved in fission experiments by applying inverse kinematics, including the use of secondary beams, several improvements of the experimental technique are desirable. Actually, a new super-conducting analysis
magnet is being designed,36 which will allow determining themasses of the fission fragments. When the charged particles are
deflected, one can also apply the large-area neutron detector37
to register the neutrons emitted from the fragments to determine
the number of neutrons emitted prior to scission and to deduce
the excitation energies of the fragments.
Another goal is a better knowledge of the initial excitationenergy of the system, in particular in electromagnetic-induced
fission. The excitation by inelastic electron scattering in an electron - heavy-ion - collider ring, which is actually part of theplans for the new GSI facility, would improve the situation considerably.
5. Summary
Experiments in inverse kinematics using relativistic beams ofprimordial and radioactive species have opened up new possibilities for experimental investigations of nuclear fission by extending the choice of systems to be investigated, by better controlling some relevant parameters like angular momentum andinitial shape, and by fully identifying the fission fragments. First
results allowed improving our understanding of dissipation fromvery low to very high excitation energies, the characteristics ofmulti-modal fission and the occurrence of extremely asymmetric mass splits. Other characteristics of the new experimental
technique, however, have not yet reached the standard, occasionally achieved in conventional experiments. In particular itis the goal of new experimental installations actually planned toprovide a better definition of the initial excitation energy and tosimultaneously detect the emitted light particles.
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