Stability and properties of finite Fermi systems of particles with different masses

The dependence of the properties of finite two-component Fermi systems containing two types of oppositely charged particles on the ratio of their masses has been studied. A theoretical model for the quantum-mechanical description of a system containing a finite number of pairs of particles has been proposed on the basis of the Hartree-Fock approximation and the random-phase approximation with exchange. A method that makes it possible to exclude the motion of the center of mass of the system from the spectrum of excited states has been developed in the random-phase approximation with exchange. This method has been used to calculate the binding energies and static dipole polarizabilities of systems containing 8, 20, and 40 pairs of oppositely charged particles at various ratios of their masses.