Analyses of Third Order Bose-Einstein Correlation by Means of Coulomb Wave Function

Abstract

Abstract. 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 3π − BEC becomes simpler than that of our previous work. We re-analyze the raw data of 3π − BEC by NA44 and STAR Collaborations by this formula. Results are compared with the previous ones.

Three-pion correlations

“…3: Therein A(3) = A 12 , A(4) = A 123 , A(5) = A 132 and A(6) = A 13 . In the plane wave approx., we have the correct expression, where A(3) ∼ A(6) are skipped [5,7],…”

“…where E 2 2B = exp(−R 2 Q 2 ) (Gaussian form) and/or E 2 2B = exp(−R Q 2 ) (exponential form), and E 3 3B = exp(−R 2 Q 2 3 ) and so on. Third we explain the formulae by Coulomb wave function including the degree of coherence λ and the interaction range R [4,5,6,7]. The two-body Coulomb wave function is well known as,…”

“…Combining A(1) ∼ A(6) in Fig. 3, we obtain F 1 as: (The other formulae F 12 ∼ F 123 and F 132 are given in [6,7]. )…”

“…Using two formulae in the core-halo approach (with Gaussian source function, the fraction of core part f c and the degree of coherent p c in [5,6,7]) we obtain Fig. 7.…”