189 Appendix A Nuclear Geometry For a given nuclear density distribution ρ ( ⃗ r , normalized such that ∫ d $^{3}$xρ = A , one defines the nuclear thickness function T$_{A}$ ( ⃗ x = { x, y } ) = ∫ dzρ ( ⃗ r ); see Fig. A.1 for an illustration of the heavy ion collision geometry. Then the nuclear overlap as a function of impact parameter b is T$_{AA}$ ( ⃗ x ; b ) = σ$_{NN}$T$_{A}$ ( x + b/ 2 , y ) T$_{A}$ ( x − b/ 2 , y ); σ$_{NN}$ is the nucleon-nucleon inelastic cross section, taken here as 42 mb = 4.2 fm $^{2}$. This gives the density of binary collisions in the reaction plane given b . The participant density is given by the probability that there is at least one interaction between a nucleon from nucleus A and the entire stack of nucleons it passes through in nucleus B , The total number of participants is N$_{part}$ = ∫ d $^{2}$xρ$_{part}$ . Centrality is an experimental measurement associated with the impact pa- ρ$_{part}$ ( ⃗ x ; b ) = T$_{A}$ ( x − b/ 2 , y ) $^{(}$1 − e − σ$_{NN}$T$_{A}$ ( x + b/ 2 ,y ) ) + T$_{A}$ ( x + b/ 2 , y ) $^{(}$1 − e − σ$_{NN}$T$_{A}$ ( x − b/ 2 ,y ) $^{)}$. (A.1)