The Influence of High Multiplicities at RHIC on the Gamov Factor

The corrections for two-pion correlations due to electromagnetic final-state interactions at high secondary multiplicities are investigated. The analysis is performed by solving the Schrödinger equation with a potential which is dictated by the multi-particle environment. Two different post-freeze-out scenarios are examined. First, for a uniformly spread environment of secondary particles, a screened Coulomb potential is exploited. It is shown that the presence of a static and uniform post-freeze-out medium results in a noticeable deviation from the standard Gamov factor. However, after going to a more realistic model of an expanding pion system, this conclusion changes drastically. We argue that the density of the secondary pions n_\pi(t,R), where R is a distance from the fireball, is bounded from above by n_\pi(t,R)\le const/R^2 for all times t. Then, a two-particle scalar potential which is found as a solution of the Maxwell equation for non-uniform medium replaces the screened one. Even this upper limit does not result in an essential deviation from the Gamov correction. The second critical parameter determining the value of the correction is found to be the ratio of the relative velocity of detected pions to the centre of mass pair velocity (in the fireball rest frame). In particular, when this parameter is much less than unity, the pion pair promptly escapes the initial high-density region and the distortion of the mutual Coulomb potential is weak.