Experiment on Fission Transients in Highly Fissile Spherical Nuclei produced Download full-text
by Fragmentation of Radioactive Beams
C. Schmitt1,#, P. Nadtochy1, A. Heinz2, B. Jurado1, A. Kelić1 and K.-H. Schmidt1
1GSI, Darmstadt, Germany; 2Yale University, CT 06520, U.S.A.
While transferring energy between the collective and
intrinsic degrees of freedom of the system, viscosity intri-
cately influences nuclear dynamics. Fission of highly ex-
cited spherical nuclei provides optimal conditions for
probing this dissipation phenomenon. In nuclei, when the
system is initially well-localized around its spherical
ground-state minimum, any shape evolution is exclusively
initiated by dissipative forces. A finite time, referred as
the transient time τtrans, is then required for populating the
states at the fission barrier . Information on the
strength β of nuclear viscosity at small deformation can
be directly inferred from τtrans. Most direct probes of fis-
sion times are pre-scission multiplicities of light particles
and γ-rays as they can be associated with a clock (see 
and therein). Yet, they give access to the total reaction
time encompassing, in addition to τtrans, the compound
nucleus formation time, the statistical decay time and the
saddle-to-scission time. Hence, experiment is not able to
isolate the various stages of the process, and the analysis
relies on the interplay of complex influences caused by
the poorly known dependences of dissipation on deforma-
tion, temperature, angular momentum and fissility. This
difficulty explains the still vivid debate on both the origin
and magnitude of nuclear viscosity. We presently report
on the first realization of experimental conditions which
are ideal for isolating the early τtrans contribution. Highly
fissile nuclei characterized by well-defined initial condi-
tions - in excitation energy, angular momentum and de-
formation - have been produced by fragmentation of ra-
dioactive beams. In addition, the width of the fission-
fragment charge distribution σZ, which is sensitive to the
limited region inside the fission saddle , has been accu-
rately measured, yielding a chronometer at the saddle.
The above ideal scenario was successfully realized by
an intense experimental effort invested at GSI . Frag-
mentation of a primary stable 238U beam at 1 A GeV in a
beryllium target produces a large variety of nuclei among
which 45 radioactive highly fissile spherical astatine up to
thorium isotopes. The latter, separated and identified with
the Fragment Separator, acted as secondary relativistic
beams. Fragmentation of these projectiles in a secondary
lead target yields pre-fragments with high excitation en-
ergies , small angular momenta  and still nearly
spherical shapes . The pre-fragment finally de-excites
by a competition between fission and evaporation. Both
fission fragments were detected simultaneously and accu-
rately identified in atomic number thanks to the use of a
double-ionisation chamber (ΔZ1,2 = 0.4 for FWHM).
The measurement of the sum Z1+Z2 of the charges of
the two fragments allows judiciously classifying the data,
since Z1+Z2 is correlated to the initial excitation energy
Eprf of the pre-fragment  – the lower the Z1+Z2, the
higher the Eprf. In Fig. 1. the experimental σZ is seen to
increase with decreasing Z1+Z2, i.e. increasing tempera-
ture. To investigate the slope of this rise, we use the reac-
tion code ABRABLA which reliability has been widely
assessed for the present purpose . As seen in Fig. 1. a
good agreement is achieved with β=(4.5±0.5).1021s-1 in-
dependent on Z1+Z2 i.e. independent on Eprf . That cor-
responds to a transient time of <τtrans> = (3.3±0.7).10-21s.
Also displayed, are the predictions of Bohr-and-Wheeler
transition state model  and Kramers diffusion picture
: Both overestimate the experimental σZ due to the
absence of the transient delay.
The control of the initial conditions achieved in our ex-
periment constitutes a step further as compared to previ-
ous works, and the result points out the undeniable mani-
festation of transient effects at high excitation energy. The
magnitude extracted for the dissipation strength at small
deformation is an information of importance for our mi-
croscopic understanding of nuclear viscosity.
Figure 1: Width σZ as a function of Z1+Z2 for a sample of
spherical beams as indicated. The data (dots) are com-
pared with Bohr-and-Wheeler- (dotted lines), Kramers-
(dashed lines) and ABRABLA Γf(t)- (full lines) predic-
tions. In the two latter cases, β is set to 4.5.1021s-1.
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 P.N. Nadtochy, in preparation.
 www w2k.gsi.de/charms/Publications/publica.htm.
 C. Schmitt et al., to be submitted to PRL.
 N. Bohr et al., Phys. Rev. 56, 1939, p. 426.
 H.A. Kramers, Physica VII 4 , 1940, p. 284.