Pauli principle sum rule and consistency relations for phenomenologically adjusted fermi liquid parameters

The sum rules for the Landau parameters which follow from the Pauli principle and the consistency relations between those parameters and the compressibility of nuclear matter and the symmetry energy are badly violated by the phenomenologically adjusted parameters used up to now. Here we show that all these relations can be nicely fulfilled if the one-pion-exchange and one-rho-exchange contributions are explicitly added to the l = 0 part (zero range) of the original Landau-Migdal interaction. It is important, however, to choose the particle-hole spectrum and the particle-hole interaction consistently.