Spectral properties of a pseudorelativistic system of two particles with finite masses

The discrete spectrum of the Hamiltonian of a pseudorelativistic system of two particles with finite masses is investigated for a fixed total system momentum $p$ and interaction potentials having the form $Z|r_{12}|^{-\gamma}$ for large $|r_{12}|$, where $Z<0$ and $0<\gamma\leq2$. The leading spectral asymptotic term is derived for $\gamma<2$. For $\gamma=2$, conditions are found for the finiteness and infiniteness of the discrete spectrum that depend (for some $Z$) on the fixed momentum $p$, which radically distinguishes the situation in question from the nonrelativistic case.