  We construct the model of a quantum spherically symmetric plasma structure
based on radial oscillations of ions. We suppose that ions are involved in
ion-acoustic plasma oscillations. We find the exact solution of the
Schr\"{o}dinger equation for an ion moving in the self-consistent oscillatory
potential of an ion-acoustic wave. The system of ions is secondly quantized and
its ground state is constructed. Then we consider the interaction between ions
by the exchange of an acoustic wave. It is shown that this interaction can be
attractive. We describe the formation of pairs of ions inside a plasma
structure and demonstrate that such a plasmoid can exist in a dense
astrophysical medium corresponding to the outer core of a neutron star.
