Stability and properties of finite Fermi systems of particles with different masses
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Stability and Properties of Finite Fermi Systems of Particles with Different Masses A. N. Ipatov and L. G. Gerchikov St. Petersburg State Polytechnic University, St. Petersburg, 195251 Russia email: [email protected] Received August 20, 2013
Abstract—The dependence of the properties of finite twocomponent Fermi systems containing two types of oppositely charged particles on the ratio of their masses has been studied. A theoretical model for the quan tummechanical 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 randomphase 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 randomphase 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. DOI: 10.1134/S106377611401004X
ton droplets with a diameter of about 1 μm [10], we consider nanocomplexes containing no more than 100 pairs of particles with opposite charges. The aim of this work is to analyze the dependence of the physical properties of such a system on the ratio of the masses of the particles, in particular, to determine whether electron–hole nanosystems in their properties are closer to excitonic molecules similar to biexcitons [11] or to macroscopic exciton droplets [10]. The calculations were performed with the methods of nonrelativistic quantum manybody theory: the Hartree–Fock approximation [16, 17] and random phase approximation with exchange [18]. The binding energies and static dipole polarizabilities of Fermi sys tems containing a finite number of pairs of particles at various ratios of their masses are calculated within the proposed model. The properties of objects under investigation are described with a particular attention to the exclusion of the motion of the center of mass of the system from the spectrum of excited states.
1. INTRODUCTION The properties of Fermi nanosystems containing a finite number of particles have been actively studied during last decades [1]. The physical properties, as well as theoretical methods for the description of such systems, depend on the type and, correspondingly, on the ratio of the masses of interacting particles. For individual atoms, molecules, and atomic clusters, in which the ratio of the masses of atomic nuclei (posi tive ions) to the mass of electrons is several orders of magnitude, only the electron subsystem in most cases requires quantummechanical description [2–4], whereas the motion of positive charges can be neglected or molecular dynamics methods can be used [5]. On the contrary, in the case of electron–positron clusters predicted recently [6, 7], both interacting sub systems consisting of particles with the same mass require quantummechanical description. The situa tion
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