The collective excitation of the nuclear matter is analyzed in a bosonizated formula of Landau Fermi liquid theory. When the nonlinear self-interacting terms of the scalar meson are taken into account in the Walecka model, the collective excitation energies of the nuclear matter can be obtained self-consistently. It shows that the calculation results are consistent with the corresponding experimental data of the nucleus
208Pb when the quantum number of the orientation of the orbital angular momentum
m is zero. Moreover, the cases with the nonzero
m values are also studied, it manifests that the collective excitation energy with the fixed nonzero
m value are almost invariant when the quantum number of the orbital angular momentum
l changes. However, the collective excitation energy of the nuclear matter decreases with the absolute value of
m increasing. The direct interaction between two nucleons near the Fermi surface only changes the Fermi velocity, while the exchange interaction causes the collective excitation of the nuclear matter. At this point, it is different from the traditional views in nuclear physics, which announce that the random phase approximation is essential to generate the nuclear collective excitation states.
We treat short-range correlations in nuclear matter, induced by the repulsive core of the nucleon-nucleon potential, within the framework of a self-consistent Green's function theory. The effective in-medium interaction sums the ladder diagrams of both the particle-particle and hole-hole type. The demand of self-consistency results in a set of nonlinear equations which must be solved by iteration. We explore the possibility of approximating the single-particle Green's function by a limited number of poles and residues.
General treatment of nuclear many-body problem will be given in terms of Green functions and the correlation property of nucleus will be exhibited by correlation factor. Effective interaction certifying the independent particle motion is introduced and proved to identify with Brueckner's K-matrix. And on the basis of this point, applying the method of the particle-hole pair to the system, a collective mode will be derived and the effective interaction contributing to collective motion will be studied. It will also be shown that this effective interaction has the property very different from electron plasma case.
We propose a new method to calculate the particle-hole Green's function for an infinite system of fermions in the long-wavelength limit of the random-phase approximation. Contrary to the standard approach the present method does not require approximating the residual particle-hole interaction by a sum of separable terms. The method can also be applied to the Landau theory of Fermi liquids. We illustrate the method by evaluating the response function of nuclear matter in the long-wavelength limit for two different isospin channels.