The many-body problem and quasiparticles

We are, of course, interested in describing a many-body system of interacting particles. We can obtain an improved independent particle model which corresponds to the electrons moving in the unscreened field of the nuclei by describing the averaged interactions among the electrons. We write the Hamiltonian operator, Kq, as 

The independent particles described by the Hartree-Fock Hamiltonian, or indeed by the Hamiltonian associated with any independent particle model other than the non-interacting model (or bare particle model) are different from the original particles, i.e. the electrons. These particles are termed quasiparticles. The interactions between these quasiparticles are weaker than the interaction between the original bare particles. There are important differences between the properties of the quasiparticles and those of the bare particles. In particular, we have seen that 

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