Abstract
Green’s function techniques are used to formulate the long-wavelength limit for the dispersion relation for collective excitation frequencies of a many-fermion system ground state in the random-phase approximation. Explicit account of spin and isospin degrees of freedom lead to four longitudinal modes: a spatial density fluctuation (which is essentially «zero sound»), a spin density variation, an isospin density one (the Goldhaber-Teller mode) and a coupled spin-isospin density mode. Their stability (reality of frequency) is studied for nuclear and neutron matter using several realistic \(\mathcal{N}--\bar {\mathcal{N}}\) potentials including the Reid soft-core potential, for which all modes turn out to be stable. Counter examples are given which prove instability where RPA predicts stability.
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