NEW APPROACH IN THE MICROSCOPIC FERMI SYSTEMS-THEORY

A new version of the microscopic theory of non-relativistic Fermi syst ems based on functional relations between the ground state energy of a system and its linear response function is presented. A closed functi onal equation linking the effective interaction between particles in u niform matter with the two-particle interaction potential in vacuum is derived. This functional equation is free from any adjustable paramet ers. Having it in hand one can calculate the main properties of the sy stem: the ground state energy, the collective spectrum, etc. Methods f or approximate solution of this equation, viz., the gas and the local approximations, are analyzed. The capability of the approach is demons trated on a number of model examples by comparing the calculated groun d state energies with those of the solvable Hamiltonians or obtained w ith the help of the Monte Carlo simulation. The extension of the forma lism to non-uniform and finite systems such as multi-electron atoms al lowing for a new treatment of the density functional theory is perform ed. An analytical expression for the effective electron-electron inter action is derived. This interaction is of finite radius and density de pendent. The microscopic theory of single-particle excitation spectra of homogeneous Fermi systems is developed. The new phenomenon of fermi on condensation in systems with strongly repulsive interaction is cons idered. 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 essen tial enhancement of the density of states similar to that of a Bose li quid just below the lambda-point, Various properties of systems with f ermion condensate are studied within simple solvable models. The possi bility of superfluid correlations in such systems is also investigated . The exponential BCS-smallness of the gap Delta in the single-particl e excitation spectra of such systems is found to disappear,which yield s a drastic elevation of the superfluid phase transition temperature T -c.