The Model Periodic Coulomb interaction in k-space: modelling the spherically averaged structure factor

Within Quantum Monte Carlo (QMC) calculations the Model Periodic Coulomb (MPC) interaction is a well know method to reduce finite size effects related to the long range nature of the Coulomb interaction. Recently we presented a method based on modelling the continuous-$k$ spherically averaged structure factor (SF) to understand and reduce Coulomb finite size effects. Here we show that our SF based method can be viewed as $k$-resolved MPC. This allows us to analyse the implicit assumptions that underlie MPC and what to do when these assumptions are not justified, i.e. in non-interaction Hartree-Fock systems or even surfaces. While we present data for the homogeneous electron gas the method itself is general.