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Analyzing Correlation Functions with Tesseral and Cartesian Spherical Harmonics

Pawel Danielewicz·Scott Pratt
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Abstract

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.

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Pawel Danielewicz, Scott Pratt. 2007-01-27. Analyzing Correlation Functions with Tesseral and Cartesian Spherical Harmonics. https://doi.org/10.1103/physrevc.75.034907

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