Interplay of anisotropies of momentum distribution and mean field in heavy-ion collisions

Two important parametrizations of momentum-dependent nucleonic fields, proposed for the simulations of central heavy-ion collisions, one by Gale et al. and the other by Welke et al., suffer from practical limitations. The first gives rise to mean fields isotropic in momentum, even when underlying momentum distributions are anisotropic, making descriptions of early nonequilibrium stages of collisions unrealistic. The second parametrization gives rise to anisotropic mean fields, but is computationally expensive, because the mean field has to be computed separately for every location of a nucleon in phase space, through folding. Here we construct a parametrization of the nucleonic mean field that yields an anisotropic mean field for an anisotropic momentum distribution and is inexpensive computationally. To demonstrate the versatility of our parametrization, we take the case of results from the parametrization by Welke et al. and attempt to approximate them. In arriving at a suitable anisotropic mean-field potential, we draw, on one hand, from the idea behind the parametrization of Gale et al., of a separable expansion of the potential energy, and, on the other, from the idea of a parallel expansion of the energy and mean field in anisotropy. We show that using our novel parametrization we can qualitatively and partially quantitatively reproduce the features of the mean-field parametrization of Welke et al.. This opens up the possibility of exploring the effects of mean-field anisotropy in collisions, without the penalty of computational cost behind the folding parametrization.