NEW APPROACH IN THE MICROSCOPIC FERMI SYSTEMS-THEORY

A new version of the microscopic theory of non-relativistic Fermi systems based on functional relations between the ground state energy of a system and its linear response function is presented. A closed functional equation linking the effective interaction between particles in uniform matter with the two-particle interaction potential in vacuum is derived. This functional equation is free from any adjustable parameters. Having it in hand one can calculate the main properties of the system: the ground state energy, the collective spectrum, etc. Methods for approximate solution of this equation, viz., the gas and the local approximations, are analyzed. The capability of the approach is demonstrated on a number of model examples by comparing the calculated ground state energies with those of the solvable Hamiltonians or obtained with the help of the Monte Carlo simulation. The extension of the formalism to non-uniform and finite systems such as multi-electron atoms allowing for a new treatment of the density functional theory is performed. An analytical expression for the effective electron-electron interaction is derived. This interaction is of finite radius and density dependent. The microscopic theory of single-particle excitation spectra of homogeneous Fermi systems is developed. The new phenomenon of fermion condensation in systems with strongly repulsive interaction is considered. This phenomenon is shown to occur when the necessary stability condition of the normal ground-state quasi-particle distribution n(F)(p) = theta(p(F) - p) is violated and this distribution is rearranged. The presence of the fermion condensate is found to result in an essential enhancement of the density of states similar to that of a Bose liquid just below the lambda-point, Various properties of systems with fermion condensate are studied within simple solvable models. The possibility of superfluid correlations in such systems is also investigated. The exponential BCS-smallness of the gap Delta in the single-particle excitation spectra of such systems is found to disappear,which yields a drastic elevation of the superfluid phase transition temperature T-c.