  We study nano-sized spherically symmetric plasma structures which are radial
nonlinear oscillations of electrons in plasma. The effective interaction of
these plasmoids via quantum exchange forces between ions is described. We
calculate the energy of this interaction for the case of a dense plasma. The
conditions when the exchange interaction is attractive are examined and it is
shown that separate plasmoids can form a single object. The application of our
results to the theoretical description of stable atmospheric plasma structures
is considered.
