Freeze-out Configuration in Multifragmentation

The excitation energy and the nuclear density at the time of breakup are extracted for the $\alpha + ^{197}Au$ reaction at beam energies of 1 and 3.6 GeV/nucleon. These quantities are calculated from the average relative velocity of intermediate mass fragments (IMF) at large correlation angles as a function of the multiplicity of IMFs using a statistical model coupled with many-body Coulomb trajectory calculations. The Coulomb component $\vec{v}_{c}$ and thermal component $\vec{v}_{0}$ are found to depend oppositely on the excitation energy, IMFs multiplicity, and freeze-out density. These dependencies allow the determination of both the volume and the mean excitation energy at the time of breakup. It is found that the volume remained constant as the beam energy was increased, with a breakup density of about $\rho_{0}/7$, but that the excitation energy increased $25\%$ to about 5.5 MeV/nucleon.