The discrete spectrum of a many-particle pseudorelativistic Hamiltonian (Q1281517)

The properties of the discrete spectrum are investigated for the pseudorelativistic Hamiltonians of systems like an atom or an atomic ion with infinite mass of the nucleus. For atoms and positive ions, the asymptotics of the number of eigenvalues is obtained near the boundary of the essential spectrum. It is proved that the asymptotics of the discrete spectrum in the pseudorelativistic case is similar to the asymptotic for nonrelativistic Hamiltonians in spite of the influence of relativistic effects on the localization of the essential spectrum.