Volume 150B, number 6 PHYSICS LETTERS 24 January 1985
SHORTENING OF THE NUCLEON'S MEAN FREE PATH IN HEAVY ION COLLISIONS
H. TOKI 1 and H. STOCKER
Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University,
East Lansing, MI 48824, USA
Received 18 October 1983
Revised manuscript received 22 October 1984
The mean free path of nucleons in heavy ion collisions is most essential for the development of nuclear collective phe-
nomena. We discuss the effect of the nucleon Fermi motion in nuclei for shortening the mean free path. This Fermi motion
together with the prior Pauli effect makes nuclei nontransparent for heavy ions in the medium energy domain.
When the bombarding energy of heavy ion projec-
tiles incident on heavy target nuclei well exceeds the
Coulomb barrier (E/A > 20 MeV), the nuclei interpen-
etrate each other. The simplest picture for the dynam-
ics of such heavy ion collisions is based on the
assumption of independent nucleon-nucleon scatter-
ing taking place in the collisions, which finds its mani-
festation in the nuclear cascade model [1,2] used to
describe the time development of the process. Here,
the mean free path 3` of the nucleons plays an essen-
tial role : if 3. >> d o (the internucleon spacing or the
range of the nuclear force), the quasi-free scattering
model should be valid. On the other hand, if 3` ~ d O
and 3`'~ R, where R is the nuclear radius, nuclear
matter behaves like a quantum liquid and a hydrody-
namical description [3,4] may be applicable. Of par-
ticular importance is the mean free path of nucleons
in nuclear matter at zero temperature. For low energy
nucleon-nucleon scattering. This is the reasoning of-
cause of the Pauli blocking effect, which forbids the
nucleon-nucleon scattering. This is the ro'~oning of-
ten used to argue that nuclei should be transparent to
medium energy heavy ions (E/A ~ 20-100 MeV/A).
What do the experimental data tell us? Fig. 1
shows the total reaction cross section [5] for 12C +
12C and the inclusive cross section [6] of protons
1 Present address: Department of Physics, Tokyo Metropolitan
University, Setagaya, Tokyo 158, Japan.
412
produced in asymmetric heavy ion collisions (e.g. Ne
+ Au) as a function of the bombarding energy. The
total reaction cross section closely reflects the energy
dependence of the nucleon-nucleon cross section.
The dip at medium energy has been attributed to the
expected rather large transparency on nuclei at this
energy. We want to argue that the dip is solely caused
by the peripheral collisions. On the other hand, the
cross section of the emitted protons does not exhibit
this dip but in fact increases monotonically as a func-
tion OfEla b. This finding indicates that nuclei are
not transparent to each other in the energy range of
E/A ~ 20-300 MeV/A. The smooth increase of the
proton cross section, however, is not the only indica-
tion of nontransparency at E/A ~ 300 MeV/A. A re-
cent analysis [7] of high multiplicity triggered data
[8], i.e. central collisions, also indicates the absence
of transparency for large nuclear overlaps. A typical
data sample [7,8] is shown in fig. 2: the energy distri-
bution of the emitted fragments is plotted as a func-
tion of the kinetic energy per nucleon of the ejectile
in the laboratory frame for 12C(70-80 MeV/A) + Ag
and Br. The spectrum shows no sign of a projectile
remnant peak; i.e. uninteracted nucleons. However,
the mean free path of a nucleon calculated with the
Pauli blocking effect included in this regime is around
5 fm. Hence a large fraction of the protons should be
able to interpenetrate the target nucleus without col-
lision. In fact, cascade model calculations [ 1 ] using
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