COHERENT AND INCOHERENT DYNAMIC STRUCTURE FUNCTIONS OF THE FREE FERMIGAS

A detailed calculation of the coherent and incoherent dynamic structur e functions of the free Fermi gas, starting from their expressions in terms of the one- and semi-diagonal two-body density matrices, is deri ved and discussed. Their behavior and evolution with the momentum tran sfer is analyzed, and particular attention is devoted to the contribut ions that both functions present at negative energies. Finally, an ana lysis of the energy weighted sum rules satisfied by both responses is also performed. Despite the simplicity of the model, some of the concl usions can be extended to realistic systems.