Abstract:
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 $n_s$, $s=1,2,\dots$, such that the system $Z_n$
is stable for $n=n_s$, and the inequality $\sup_sn_{s+1}n_s^{-1}<+\infty$
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.
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