Sequential Decay Distortion of Goldhaber Model Widths for Spectator Fragments

The primary fragment momentum distributions from AMD-V can be described by a Gaussian shape characterized by a width σ. Figure 1: The three momentum widths, σ , σ , σ , as a removed from a nucleus that originally has A0 nucleons, a nucleus consisting of K nucleons will emerge. For this fragment of K nucleons, Goldhaber [1] showed that the momentum width, σ, could be expressed as: σ = σ0 sqrt [K(A0 K)/(A0 – 1)], where σ0, the reduced momentum width, is related to the intrinsic Fermi motion of a single nucleon, i.e.,: σ0 = sqrt (1/5)PF. Based upon electron scattering ments of Fermi momenta, σ is expected to be ≈ 112-116 MeV/c. However, σ ≈ MeV/c [2]. Some theoretical works [3] have attempted to explain this difference. However, the answers were still absent. In this work, we studied peripheral collisions of 200 MeV/nucleon Ar + Al with AMD-V model [4] and followed with the afterbuner (GEMINI) [5]. In the AMD-V model, initial width of the nucleon momentum distribution is ~ 105 MeV/c for Ar and ~ 101 MeV/c for Al. These values are less than expected from electron scattering measurements, but are still in a reasonable range. The fragment mass numbers and the three momentum widths, σPx, σPy, σPz, are plotted