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We construct the model of a quantum spherically symmetric plasma structurebased on radial oscillations of ions. We suppose that ions are involved inion-acoustic plasma oscillations. We find the exact solution of theSchr\"{o}dinger equation for an ion moving in the self-consistent oscillatorypotential of an ion-acoustic wave. The system of ions is secondly quantized andits ground state is constructed. Then we consider the interaction between ionsby the exchange of an acoustic wave. It is shown that this interaction can beattractive. We describe the formation of pairs of ions inside a plasmastructure and demonstrate that such a plasmoid can exist in a denseastrophysical medium corresponding to the outer core of a neutron star.

Attractive interaction between ions inside a quantum plasma structure