Possible formulations for three-charged particles correlations in terms of Coulomb wave functions

Abstract

The recent data for Bose-Einstein Correlations (BEC) of three-charged particles obtained by NA44 Collaboration have been analysed using theoretical formula with Coulomb wave functions. It has been recently proposed by Alt et al. It turns out that there are discrepancies between these data and the respective theoretical values. To resolve this problem we seek a possibly modified theoretical formulation of this problem by introducing the degree of coherence for the exchange effect due to the BEC between two-identical bosons. As a result we obtain a modified formulation for the BEC of three-charged particles showing good agreement with the data. Moreover, we investigate physical connection between our modified formulation and the core-halo model proposed by Csörgő et al. Our study indicates that the interaction region estimated by the BEC of three-charged particles in the S + Pb collisions at 200 GeV/c per nucleon is equal to about 1.5 fm∼1.8 fm.

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

“…From the comparison of the results on 2π − BEC [6,7] with those on 3π − BEC, we have a relation, R 2nd ≃ 1.5R 3rd .…”

“…2. For comparison, the results in the previous work [6] are also shown in the lower part of Table 1. Parameters f c and p are almost the same with the previous calculations.…”

“…In the previous work [6], we introduced the Coulomb wave function to the core-halo model [11], where following parameters are used; the fraction of multiplicity from the core part, f c = n core / n tot , and the fraction of coherently produced particles from the core part, p c = n co / n core . In the quantum optical approach, chaoticity parameter is defined as p = n chao / n core , where p = 1 − p c .…”

“…In Ref. [5], the 3π − BEC is calculated by the use of the Coulomb wave function with fixed source radius R. We have analyzed the BEC without assuming the size of source radius using the Coulomb wave function [6,7]. In this paper, we would like to refine the formula for the 3π − BEC using the diagrammatic representation for BEC in the quantum optical (QO) approach [8,9,10].…”

Three-pion correlations

“…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,…”