exotic nuclei structure and reaction noyaux exotiques ... - IPN - IN2P3

for peripheral ones. In experiments radial collective
energy was recognized, in most of the cases, from
comparisons of kinetic properties of fragments with
models/ simulations.The mean relative velocity
between fragments, β rel , independent of the reference
frame, allows to compare radial collective
energy for both types of sources (QF or QP). The
effect of the source size (Coulomb contribution on
fragment velocities) can be removed by using a
simple normalization which takes into account,
event by event, the Coulomb influence, in velocity
space, of the mean fragment charge.
All the quantitative information concerning the evolution
of radial energy, E R , with excitation energy
for both types of sources is presented in figure 1.
At an excitation energy of about 5 AMeV, the β rel
Figure 2: Left and right sides refer respectively to the
mean charge of the heaviest fragment of partitions
, and to the generalized asymmetry in charge of
the fragment partitions without the heaviest one,
Az\{Z1}, (see text) as a function of the reduced fragment
multiplicity, Mfrag/, for different total excitation
per nucleon of the sources. Full squares, open and
full circles stand respectively for QF sources and QP
sources produced at 80 and 100 AMeV incident energies.
values corrected from Coulomb effects and corresponding
to QF and QP sources are similar. We
have also added the E R values published by the
ISIS collaboration [3] corresponding to the π - +Au
reactions which provide sources equivalent to the
QP ones in terms of excitation energy range and
size. The observed evolution of E R for such sources
is almost the same as for QP sources. For hadron-induced
reactions the thermal pressure is the
only origin of radial expansion, which indicates that
it is the same for QP sources. To be fully convincing,
an estimate of the part of the radial collective
energy due to thermal pressure calculated with the
EES model [4] for an excited nucleus identical to
QF sources produced at 50 AMeV incident energy
is also reported (open square) in figure 1.
We have shown that radial collective energy is essentially
produced by thermal pressure in semi-
peripheral heavy-ion collisions as it is in hadroninduced
reactions. For QF sources produced in
central heavy-ion collisions the contribution
from the compression-expansion cycle becomes
more and more important as the incident energy
increases. Those observations show that the radial
collective energy does influence the fragment partitions.
Moreover it is observed that, at fixed total
excitation energy per nucleon, the evolution of the
average fragment multiplicity normalized to the
source charge/size = is fixed by
the value of the radial collective energy: when E R
increases more fragments are produced.
Scalings of partitions
Does the intensity of the radial collective energy
also govern the details of fragment partitions, namely
the relative charge/size of fragments in partitions.
One can first consider the evolution of the
size of the heaviest fragment, for given total excitation
energies, with the reduced fragment multiplicities
M frag /. On the left panel of figure 2 average
values of the heaviest fragment charge for QP
and QF sources are reported: they follow exactly
the same evolution. Finally the division of
the charge among other fragments is investigated
using the generalized asymmetry in charge
of the fragment partitions. One can re-calculate the
generalized asymmetry by removing Z 1 from partitions,
noted A Z \{Z 1 }. The results, displayed in figure
2 (right panel) do not depend on the source type
at a given total excitation energy and a given reduced
fragment multiplicity. Note that the general
asymmetry follows a linear trend except for the
lower reduced fragment mutiplicity which corresponds
to M frag =2; indeed in that case, after removing
Z 1 , only one fragment is available for the
asymmetry calculation and in each event the heavier
Z of the partition below Z equal 5 was taken.
Such a result shows the subtle role played by the
radial collective energy. It influences the overall
degree of fragmentation but it does not affect the
relative size of fragments in partitions for fixed reduced
fragment multiplicities. Those scalings represent
a benchmark against which models describing
fragmentation of finite systems should be tested.
In particular the peculiar role of the freeze-out
volume in reproducing or not those scalings must
be investigated.
References
[1] B. Borderie and M. F. Rivet, Prog. Part. Nucl. Phys. 61, 551,
2008.
[2] E. Bonnet et al. (INDRA and ALADIN Collaborations), Nucl.
Phys. A, 1., 2009.
[3] L. Beaulieu et al., Phys. Rev. C 64, 064604, 2001.
[4] W. A. Friedman, Phys. Rev. C 42, 667, 1990.
[5] E. Bonnet et al. (INDRA and ALADIN Collaborations), submitted
to Phys. Rev. Lett.
107