191 Appendix A: Nuclear Geometry the average centrality: ∫ b$_{cent}$ 0 db dσ db = 1 2 ( C$_{1}$ + C$_{2}$ ) σ$_{tot}$. (A.5) (a) (b) Figure A.2: (a) Plot of dσ/db as a function of b for the Woods-Saxon $^{197}$Au nucleus. The shaded region corresponds to 20 − 30% centrality with endpoints at b = 6 . 6 and 8.1 fm; the single representative impact parameter for this centrality class, found by properly weighting from Eq. (A.5), is b = 7 . 4 fm. (b) Plot of the nuclear density as a function of radius separately for protons and neutrons in $^{208}$P b [444]. The nuclear density profile can take many forms. The simplest numerically is the hard cylinder geometry, which is constant in density over the reaction plane: This of course leads to participant and binary densities that are also constant ρ$_{HC}$ ( x, y ) = ρ$_{0}$θ ( $^{√}$x 2 + y 2 − R$_{HC}$ ) . (A.6)