190 Appendix A: Nuclear Geometry Figure A.1: An illustration of an A + A heavy ion collision at impact parameter b . The soft medium particles tend to be distributed similarly to the participant density, ρ$_{part}$ while the hard collisions scale like the binary density, ρ$_{coll}$ . Figure adapted from [443]. rameter of a collision. Theoretically it is found from the inelastic cross section as a function of impact parameter, The impact parameter b$_{cent}$ for a given centrality of C % is defined by Then the impact parameter for a given centrality class C$_{1}$ − C$_{2}$ % is found from dσ db = 2 πb$^{(}$ 1 − ( 1 − N$_{part}$ ( b ) 2 A ) A ) , (A.2) σ$_{tot}$ = ∫ db dσ db . (A.3) ∫ b$_{cent}$ 0 db dσ db = Cσ$_{tot}$. (A.4)