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 0370-2693/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)