SMM Volumes with Au + C input

Figure 1 below shows three plots concerning the various volumes associated for SMM. The plots reflect the behavior of the SMM volumes based on input energy, E_i, and system size, A₀ from the EOS Au + C data.

Figure 1:

• Figure 1a: The decrease in A₀ with an increase in E_i. This is an approximate parametrization based on the relation between A₀ and the EOS experimental cold total charged particle multiplicity, m^cold, in the Au + C data (A₀ = 199 - 1.6m^cold, see Figure 27a of the statistical paper) and the relation between E_i and m^cold (E_i = 0.13m^cold + 0.9, see Figure 4b of the SMM draft).

• Figure 1b: The hot and cold multiplicites as a function of E_i. Here it is approximated that m^hot = m^cold / 2. Also m^hot is assumed to be approximately the same as the total hot fragment multiplicity in keeping with SMM.

• Figure 1c: The various volumes that can be considered in SMM with the above inputs:
  • The volume of system at normal nuclear density: V₀ = (4/3) pi r₀³ A₀. The decreasing V₀ is a result of the decreasing A₀ input as a function of increasing E_i.
  • The total volume of system at breakup from SMM: V = (1+kappa) V₀. The decrease in V is a result of the decrease in V₀.
  • The free volume from SMM: V_f = chi V₀, with chi from: chi = [ 1 + (d/r₀) (m^hot1/3 - 1) ]³ - 1 . The change in V_f is due to the increase in chi and decrease in V₀ as E_i increases.
  • The free volume from SMM added to the volume of the system at normal nuclear density: V_f + V₀.

• Constants are:
  • pi = 3.1415
  • r₀ = 1.17
  • kappa = 2
  • d = 1.4