Shapes and Sizes from Non-Identical-Particle Correlations.pdf

a r X i v : n u c l - t h / 0 6 1 2 0 0 6 v 1 2 D e c 2 0 0 6 S. Pratt 1 Shapes and Sizes from Non-Identical-Particle Correlations Scott Pratt Dept. of Physics and Astronomy, Michigan State University East Lansing, MI 48824 USA I review the prospects for measuring source characteristics from correlations other than those involving iden- tical pions. Correlations generated from Coulomb and strong interactions are shown to provide remarkable resolving power for determining three-dimensional information, in some cases accessing more detail than can be represented by Gaussian fits. Keywords: correlation,interferometry,imaging I. INTRODUCTION AND THEORY As is well-known to the participants of this conference, identical-particle correlations provide insight into the space- time structure of the asymptotic phase-space density [1]. The experimentally measured two-particle correlation func- tion C(P,q) is related to the source function S (P,r) through a simple Fourier transform, RP(q) ≡CP(q)?1 = Z d 3 rSP(r)cos(q · r). (1) Here, P is the total momentum and q = (p1 ? p2)/2 is the relative momentum of the pair. The source function is defined by the outgoing phase space density, SP(r) = R d 3 r1d 3 r2δ(r1 ? r2 ? r) f (P/2,r1, t) f (P/2,r2,t)R d 3 r1d 3 r2 f (P/2,r1, t) f (P/2,r2, t) , (2) where all quantities are calculated in the rest frame of the pair, where P = 0. As long as the time t is beyond any time for which particles are emitted, S is independent of t since both particles are moving with identical velocity, which is zero in this frame. The source function physically represents the nor- malized probability for two particles of the same velocity to be separated by a distance r in their asymptotic state. Although the source function only measures a distribution of relative distances, it still provides invaluable insight into the dynam- ics of a collision. For instance, long lived sources will lead to large separations along the direction of the pair’s velocity. Det