Effects of multi-pion correlations on the source distribution in ultra-relativistic heavy-ion collisions

Multi-pion correlation effect on the source distribution is studied. It is shown that multi-pion Bose-Einstein correlation make the average radius of the pion source become smaller. The isospin effect on the pion multiplicity distribution and the source distribution is also discussed. PACS number(s): 11.38 Mh, 11.30 Rd,25.75 Dw Ultrarelativistic hadronic and nuclear collisions provide a unique environment to create dozens, and in some cases hundreds, of pions [1–3]. To study the pion source distributions in these processes, therefore, one must take into account the effects of multi-pion Bose-Einstein (BE) correlations [4–14]. Among others, Lam and Lo [4] suggested that the larger isospin fluctuations were due to the Bose nature of the emitted pions. Pratt [7] suggested that if the number of bosons in a unit value of phase space is large enough, bosons may condense into the same quantum state and a pion laser could be created. Considering isospin effect, Pratt and Zelevinsky [8] used the method in Ref. [7] to explain Centauro events [15,16]. Zajc [6] first used Monte-Carlo method to analyse multi-pion Bose-Einstein correlation effects on two-pion interferometry. Detail derivation of multi-pion Bose-Einstein correlation can be found in Ref. [12]. The bosonic nature and isospin of the pion should affect the single pion spectrum distribution in coordinate space. However, this issue has not yet been discussed in the literature. The purpose of this paper is to analyse the effects of multi-pion correlation and isospin on the source distribution in coordinate space. We begin with write down the definition for the n-pion inclusive source distribution: 1 Pn(x1, · · ·, xn) = 〈j(x1) · · · j∗(xn)j(x1) · · · j(xn)〉, (1) which can be explained as the probability of observing n pions at point {xi, i = 1, n} all in the same n pion event. Here j(x) is the current of pions, which can be expressed as [9,12,13]