On the discrete spectrum of Hamiltonians for pseudo-relativistic electrons

We consider the Hamiltonian $H$ of a system of $n$ pseudo-relativistic electrons in a Coulomb field of $n_0$ fixed nuclei. Under the assumption that the total charge of electrons and nuclei is non-negative, it is proved that the discrete spectrum of $H$ is infinite, and a spectral asymptotic formula is derived (without taking the Pauli exclusion principle into account). The results are extended to systems of the same type with long-range potentials more general than Coulomb potentials. It is also proved that the discrete spectrum is finite in the short-range case.