Analyzing Correlation Functions with Tesseral and Cartesian Spherical Harmonics

The dependence of inter-particle correlations on the orientation of particle relative-momentum can yield unique information on the space-time features of emission in reactions with multiparticle final states. In the present paper, the benefits of a representation and analysis of the three-dimensional correlation information in terms of surface spherical harmonics is presented. The harmonics include the standard complex tesseral harmonics and the real cartesian harmonics. Mathematical properties of the lesser-known cartesian harmonics are illuminated. The physical content of different angular harmonic components in a correlation is described. The resolving power of different final-state effects with regarding to determining angular features of emission regions is investigated. The considered final-state effects include identity interference and strong and Coulomb interactions. The correlation analysis in terms of spherical harmonics is illustrated with the cases of gaussian and blast-wave sources for proton-charged meson and baryon-baryon pairs.