Stability of n-particle pseudorelativistic systems

For a system Z(n) of n identical pseudorelativistic particles, we show that under some restrictions on the pair interaction potentials, there is an infinite sequence of numbers n(s), s = 1, 2,..., such that the system Z(n) is stable for (n) = n(s), and the inequality sup (s)n(s)+1n (-1)(s)< +infinity holds. Furthermore, we show that if the system Z(n) is stable, then the discrete spectrum of the energy operator for the relative motion of the system Z(n) is nonempty for some values of the total momentum of the particles in the system. The stability of n-particle systems was previously studied only for nonrelativistic particles.