Local Fermi liquid theory

Typically, is near to one for Ce systems with the bare f-level well below Ep. Note that the Anderson width A is much smaller than that conduction-band width, so that N (Ep) is indeed large when compared with the bare conduction-band DOS. On the other hand, it should be clear that singlet formation via an indirect exchange coupling cannot transfer much spectral weight from the bare local level up to Ep. Thus, a narrow resonance near the Fermi level of maximum height (jrAY and width k Tp < A arises. It should be emphasized that the local DOS considered here is not the quasiparticle DOS that is used in Fermi-liquid theory to express thermodynamic quantities via free-particle for-... 

The kernel is a well known quantity that appears in several branches of theoretical physics. For example, evaluated for the electron gas, /xc is, up to a factor, the local field correction . To emphasize the correspondence to the effective interaction of Landau s Fermi-liquid theory, to which it reduces in the appropriate limit, /xc plus the bare Coulomb interaction is sometimes called the effective interaction , while in the theory of classical liquids the same quantity is referred to as the Ornstein-Zernicke function. 

For liquid metals, one has to set up density functionals for the electrons and for the particles making up the positive background (ion cores). Since the electrons are to be treated quantum mechanically, their density functional will not be the same as that used for the ions. The simplest quantum statistical theories of electrons, such as the Thomas-Fermi and Thomas-Fermi-Dirac theories, write the electronic energy as the integral of an energy density e(n), a function of the local density n. Then, the actual density is found by minimizing e(n) + vn, where v is the potential energy. Such... 

The DDM is not expected to lead to the "final" theory of the nucleus. (That would probably be closer to the HFB model mentioned above, or the recently developed Relativistic Fermi Liquid model [ANA83], or something very different.) Hence, no effort is made to find the "best" parameters for each nuclear region, as is done in most of the currently popular models. Instead, all model parameters are given fixed strengths and Z-A-dependences. There are no local parameters. This provides a perfect excuse for not obtaining perfect agreement with the experimental data ... 

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