A transport theory of relativistic nucleon-nucleon collisions with confinement

Abstract

A transport theory is developed on the quark level to describe nucleon--nucleon collisions. We treat the strong interaction effectively by the Friedberg-Lee model both in its original and in its modified confining version. First we study the stability of the static three-dimensional semiclassical configuration, then we present results of the time evolution given by a Vlasov equation for the quarks coupled to a Klein-Gordon equation for the mean field. We find at higher energies that the nucleons are almost transparent, whereas at lower energies we observe a substantial interaction. At very low energies we see a fusion of our bags, which is due to the purely attractive nature of the mean field and hence is an artifact of our model. We test the confinement mechanism and find that at higher energies the nucleons are restored shortly after the collision.