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The equation of state and the quasiparticle mass in the degenerate Fermi system with an effective interaction

General formulas are derived for the quasiparticle effective mass and the equation of state of the Fermi system with account of the interparticle attraction at long distances and repulsion at short distances. Calculations are carried out of the equation of state and the effective mass of the Fermi system at zero temperature with the use of the modified Morse potential. It is shown that the pair repulsive forces promote a decrease of the effective mass, and the attractive forces promote its increase. With a certain choice of the parameters of the potential the dependence of the pressure on the density has a nonmonotonic character, which enables to describe the coexistence of the liquid and gaseous phases. The influence of three-body interactions on the equation of state and the effective mass is considered. The calculation results are compared with experimental data concerning the quasiparticle effective mass in the liquid $^3$He. Key words: normal Fermi liquid, effective mass, quasiparticle, equation of state, interaction potential