One-body Langevin dynamics in heavy-ion collisions at intermediate energies

We present a new framework to treat the dissipation and fluctuation dynamics associated with nucleon-nucleon scattering in heavy-ion collisions. The two-body collision processes are effectively described in terms of the diffusion of nucleons in viscous nuclear media, governed by a set of Langevin equations in momentum space. The new framework combined with the usual mean-field dynamics can be used to simulate heavy-ion collisions at intermediate energies. As a proof of principle, we simulate Au + Au reactions and obtain results consistent with other existing codes under the same constrained conditions. We also study the formation of fragments in Sn + Sn reactions at 50 MeV/nucleon, and results are discussed and compared to two other models commonly employed for collisions.

Figure 1

Density profiles of stable nuclei ${}^{58}\mathrm{Ni}$ and ${}^{197}\mathrm{Au}$ obtained from solutions of the Thomas-Fermi equations.

Figure 2

Time evolution of radial density profiles for single nuclei ${}^{58}\mathrm{Ni}$ and ${}^{197}\mathrm{Au}$ in steps of 40 fm/c.

Figure 3

Final rapidity distributions as a function of reduced rapidity for ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ at beam energies of 100 MeV/nucleon (upper panel) and 400 MeV/nucleon (lower panel) at an impact parameter $b=7$ fm. Solid curves, dashed curves and the dashed-dot curve correspond to the Brownian model, BUU-type models, and QMD-type models [26], respectively.

Figure 4

Final average in-plane flow as a function of reduced rapidity for ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at beam energies of 100 MeV/nucleon (upper panel) and 400 MeV/nucleon (lower panel) and an impact parameter $b=7$ fm. Solid curves, dashed curves and the dashed-dot curve represent the Brownian model, BUU-type models, and QMD-type models [26], respectively.

Figure 5

Flow slope parameter for different transport models [26] for ${}^{197}\mathrm{Au}+{}^{197}\mathrm{Au}$ collisions at beam energies of 100 MeV/nucleon (blue squares) and 400 MeV/nucleon (red triangles) at an impact parameter $b=7$ fm. The error bars represent the fitting uncertainties. These become invisible when they are smaller than the symbols. The colored bands correspond to roughly 52% confidence intervals from the statistics of calculations from both the BUU-type and the QMD-type models. (See text for a more detailed explanation.)

Figure 6

Density contours for nucleons projected onto the reaction plane in the reaction ${}^{112}\mathrm{Sn}+{}^{112}\mathrm{Sn}$ at 50 MeV/nucleon at an impact parameter of $b=0.5$ fm, at different times during the reaction. Results calculated with the Brownian motion model are displayed in the first row of the panels. The bottom two rows show results from SMF and AMD calculations [32]. The densities for the projected contours start at 0.07 ${\mathrm{fm}}^{-2}$ and consecutively increase by 0.1 ${\mathrm{fm}}^{-2}$.

Figure 7

Distribution of IMF multiplicity obtained from different models for the reaction ${}^{124}\mathrm{Sn}+{}^{124}\mathrm{Sn}$ at 50 MeV/nucleon at an impact parameter $b=0.5$ fm. The upper panel shows the multiplicity distribution of IMFs with charge $Z>2$ and the lower panel with $Z>6$ [32].