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In the first part of this paper, we present a study of the symmetry energy($a_s$) and its slope parameter ($L$) for nuclear matter in the framework ofthe Fermi liquid theory of Landau and Migdal. We derive an exact relationbetween $a_s$ and $L$, which involves the nucleon effective masses andthree-particle Landau-Migdal parameters. We present simple estimates whichsuggest that there are two main mechanisms to explain the empirical values of$L$: The proton-neutron effective mass difference in isospin asymmetric matterand the $\ell=0$ moment of the isovector in-medium three-particle scatteringamplitude. In the second part of this paper, we discuss the general structureof three-particle interactions in nuclear matter in the framework of the Fermiliquid theory. The connections to the Bethe-Brueckner-Goldstone theory andother approaches are also discussed. We show explicitly how the first few termsin the Faddeev series, together with medium induced three-particleinteractions, emerge naturally in the Fermi liquid theory.

Slope parameter of the symmetry energy and the structure of three-particle interactions in nuclear matter