Skyrme Symmetry VDF Coulomb Momentum Dependence

SMASH simulation supports two sets of nuclear potentials:

Skyrme with (optional) Symmetry potentials;
VDF (vector density functional) model potentials, Sorensen:2020ygf [13].

In addition to these nuclear potentials, Coulomb potentials can also be enabled.

Note: Skyrme and Symmetry potentials do not need to be both active, but if one of the two is enabled, then one cannot use VDF potentials.

Skyrme and VDF potentials both describe the behavior of symmetric nuclear matter. The symmetry potential can adjust the Skyrme potential (but not the VDF potential) to include effects due to isospin. The Skyrme and Symmetry potentials are semi-relativistic, while the VDF potential is fully relativistic. A momentum-dependent term can be added to the Skyrme potential. The additional term is not treated in a fully Lorentz-invariant way. Visit the following subpages for more information:

Configuring potentials

The following snippet of the configuration file configures SMASH such that the Skyrme as well as the Symmetry potential are activated for the simulation. There is however no requirement to include both simultaneously. They can be switched on and off individually.

 Potentials:
     Skyrme:
         Skyrme_A: -209.2
         Skyrme_B: 156.4
         Skyrme_Tau: 1.35
     Symmetry:
         S_Pot: 18.0
     Coulomb:
         R_Cut: 5.0

Note that the Coulomb potential requires a Lattice while for the other potentials it can be used as an optimisation.

Configuring VDF Potentials

The following snippets from the configuration file configure SMASH such that the VDF potential is activated for the simulation.

In the first example, VDF potentials are configured to reproduce the default SMASH Skyrme potentials (without the symmetry potential, as it is not described within the VDF model):

 Potentials:
     VDF:
         Sat_rhoB: 0.168
         Powers: [2.0, 2.35]
         Coeffs: [-209.2, 156.5]

In the second example, VDF potentials are configured to describe nuclear matter with saturation density of \(\rho_0 = \mathrm{0.160 fm}^{-3}\), binding energy of \(B_0 = -16.3\) MeV, the critical point of the ordinary nuclear liquid-gas phase transition at \(T_c^{(N)} = 18\) MeV and \(\rho_c^{(N)} = 0.375 \rho_0\), the critical point of the conjectured "QGP-like" phase transition at \(T_c^{(Q)} = 100\) MeV and \(\rho_c^{(Q)} = 3.0\rho_0\), and the boundaries of the spinodal region of the "QGP-like" phase transition at \(\eta_L = 2.50 \rho_0\) and \(\eta_R = 3.315 \rho_0\):

 Potentials:
     VDF:
         Sat_rhoB: 0.160
         Powers: [1.7681391, 3.5293515, 5.4352788, 6.3809822]
         Coeffs: [-8.450948e+01, 3.843139e+01, -7.958557e+00, 1.552594e+00]

Configuring the momentum dependence

The momentum-dependent term can be added to the Skyrme potential. In order to activate it one has to specify the parameters C and Lambda in MeV and 1/fm respectively in the "Momentum_Dependence" section under "Potentials". Note that the parameters from the momentum-dependent term and the Skyrme potential need to be consistent in order to reproduce nuclear ground state properties. An example of parameters corresponding to a medium-stiff (K=290 MeV) equation of state is given in the following.

 Potentials:
  Symmetry:
    S_Pot: 18.0
  Skyrme:
    Skyrme_Tau: 1.76
    Skyrme_B: 57.2
    Skyrme_A: -29.3
  Momentum_Dependence:
    C: -63.5
    Lambda: 2.13

Use_Potentials_Outside_Lattice — bool, optional, default = true

Wether to include the potentials also for particles that have left the lattice. If set to false, the particles will propagate on straight lines once they leave the volume that is covered by the lattice.