Thank you very much for your answer.  It is much more clear now.

Unfortunately I cannot understand German, but I will try to have a look in your book anyway.

Thank you,

Just to simplify it, - participant is a nucleon who has undergone at least one collision so in general (nucleus-nucleus collisions) number of participants is lower than number of collisions. But in case of a nucleon -  nucleus collisions Npart = Ncoll+1 as the projectile nucleon can interact many times while each target nucleon participates in a collision only once.  For Pb - Pb central collisions each nucleon may participate in up to about several collisions which means a large amount of deposited energy leading to  creation of quark - gluon plasma, at sufficiently high energy of course.

The numbers of participants is the number of nucleons that undergo at least one collision during the interaction between two ions, instead the number of binary collisions, represent the number of times in which, during a collision between two ions, any two parts of the two ions involved in the collision, collide

Usually in heavy ion papers, "Number of binary collisions" refers to parton-parton collisions, and "Number of participants" - to the number of participating nucleons. Thus, it is a huge difference between these two observables, because parton=quark, and roughly speaking each nucleon has 3 quarks in it, therefore one get so high number of Ncoll - up to 2000 for central collisions. Indeed, at ultra-relativistic energies, one can distinguish partons (quarks) that collide from the whole nuclei.

I am thinking of non-relativistic collisions. Here each nucleon which undergoes a collision excites a nucleon from below the Fermi level of the target nucleus, creating

a two particle-one hole set in the process of sharing the energy per nucleon (plus Fermi

coupling energy). So the one N-N collision has resulted in 3 carriers of excitation energy-the initial nucleon,now downscattered in energy, the struck nucleon, now boosted in energy above the Fermi energy, and the hole below the Fermi energy. Each of these

carriers may in principle have another collision with the same result, so  the excitation

carriers,including holes,should be 2N+1 where N is the number of collisions. This is for simple elastic scattering characteristic of reactions below the threshold of particle

(e.g. pion,muon...)production. If above this threshold, the number of excitation carriers

per collision may be greater (that is, if the collisions are other than elastic binary N-N). Just to

complicate the simplified discussion, note that an incoming nuucleon (either singly or

carried as part of a cluster/heavy ion) might undergo other than simple 2 body N-N

collisions,e.g. some collective excitation mode in target nucleus.