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The phase field,which originates from the electronic interaction,plays an important role in describing a strongly correlated system in one dimension.However,in higher dimensions the effect of phase field cannot be obviously understood.With the eigenfunctional theory,we calculate the pair distribution function of the three-dimensional electron gas to study the relationship between the phase field and the electronic correlation effect and show that at zero temperature the correlation effect of the electrons is mainly dominated by the phase fluctuation,which is produced by the electronic interaction.We also discuss the failure of random phase approximation in studying the correlation function when the correlation effect is strong in the view of the phase field.