The collective excitation of nuclear matter in a bosonized Landau Fermi liquid model

The collective excitation of nuclear matter is analyzed in a bosonized Landau Fermi liquid model. When the nonlinear self-interacting terms of scalar mesons are included in Walecka model, the collective excitation energy of nuclear matter can be obtained self-consistently, and the calculation results are consistent with the corresponding experimental data of the nucleus ${}^{208}Pb$ when the quantum number of the orientation of the total spin $m$ is zero. The cases with the nonzero $m$ values are also studied, and it is found that the collective excitation energy of nuclear matter decreases with the absolute value of $m$ increasing when the total spin is conserved. Moreover, four kinds of collective excitation modes of nuclear matter are discussed when the isospin and spin of nucleons are taken into account. The direct interaction between two nucleons near Fermi surface only changes the effective nucleon mass and Fermi velocity, while the exchange interaction plays an critical role in the collective excitation of nuclear matter.