In order to include a correction by the Coulomb interaction in Bose-Einstein correlations (BEC), the wave function for the Coulomb scattering were introduced in the quantum optical approach to BEC in the previous work. If we formulate the amplitude written by Coulomb wave functions according to the diagram for BEC in the plane wave formulation, the formula for $3pi^-$BEC becomes simpler than that of our previous work. We re-analyze the raw data of $3pi^-$BEC by NA44 and STAR Collaborations by this formula. Results are compared with the previous ones.
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