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

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