  Steady-state pair correlations between inelastic granular beads in a
vertically shaken, quasi two-dimensional cell can be mapped onto the particle
correlations in a truly two-dimensional reference fluid in thermodynamic
equilibrium. Using Granular Dynamics simulations and Iterative
Ornstein--Zernike Inversion, we demonstrate that this mapping applies in a wide
range of particle packing fractions and restitution coefficients, and that the
conservative reference particle interactions are simpler than it has been
reported earlier. The effective potential appears to be a smooth, concave
function of the particle distance $r$. At low packing fraction, the shape of
the effective potential is compatible with a one-parametric fit function
proportional to $r^{-2}$.
