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Abstract We reconsider the fermion spectral function in the presence of the Cooper pair condensation and identified the interaction type of complex scalar and fermion, which gives consistent results with the expected s-wave superconductor for the first time. We derive the matrix Riccati equation, which allows the precise calculation of the fermion spectral function. Apart from the gap structure, we studied the effect of the chemical potential and the density and compared it with the BCS theory. We found that two theories give similar results in small chemical potential but very different ones in the high-density case, which we attribute to the correlation effect.