Many-Body Theoretical Approach to the Fire-Ball Model in Multiple Production of Particles

The "fire-ball" observed in the multiple production of particles is interpreted and analysed in terms of a correlated assembly of produced particles like a superfluid. It is shown that the momentum spectrum of produced mesons is proportional to the form of dkfk2, by assuming J.¢4 for the meson-meson interaction Hamiltonian in the final state. A possibility of the many fire-balls is briefly discussed. Before going into these discussions a possible reduction of the S-matrix element or the cross section of the overall process is presented, where its final-state interaction part may be separated from the high energy interaction part in a short collision time.