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Study on Hartree-Fock Equation for a Non-Neutral Plasma of Spin Zero Ions in a Paul Trap

Non-neutral plasma in a Paul trap is an quantum system composed of identical ions confined in the trap whose properties can be studied by the quantum theory of fields. The imperceptible identical particle systems such as electron gas in metals have been the concern of experimental and theoretical studies mostly aiming to understand the properties of these systems. Focusing on theoretical description, Hartree-Fock equation of electron gas, a fermion quantum plasma, has been established by the method of “equation of motion” and by using Dirac field. In this respect, the goal of this paper is to establish the Hartree-Fock equation for a non-neutral plasma of identical ions of spin zero at high density and low temperature in a Paul trap while using the complex scalar field.