By invoking the existence of the zero-sound mode we have succeeded in generalizing the Bohm-Pines method, for the collective description of the interparticle interactions in a dense electron gas, to calculate the binding energy per nucleon in the ground state of a nuclear matter. The present calculation gives rise to a saturation Fermi wave vector kFO=1.74 fm−1, which is larger than the mostly accepted value of 1.43 fm−1. Our calculated result for the velocity of the zero-sound mode is found to be well-agreeable with those of other theories. It is further seen that there is an instability in the nuclear matter, with respect to long wavelength density fluctuations, in the low density region n≤0.78n0, n0 being the saturation nuclear density. From the present theory, we obtain a compression modulus K=116.7 MeV at the saturation density, which is smaller than the well-known result (210±30) MeV. However, by adjusting the value of the effective mass, M*, of the nucleon, we are able to reproduce the correct result for the compression modulus. Such a value of M* is found to be greater than the bare nucleon mass M. From the present theory, we obtain the energy of the monopole resonance Eph=32.38 MeV, which agrees reasonably well with the experimental data for heavy nuclei. By lowering the value of the saturation Fermi wave vector, we observe a decrease in the value of the compression modulus, which is just the opposite to the results of other theoretical calculations.
What Determines the Fermi Wave Vector of Composite Fermions?