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29 March 2024
 
  » arxiv » nucl-th/0507004

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Polishing the Lens: I Pionic Final State Interactions and HBT Correlations- Distorted Wave Emission Function (DWEF) Formalism and Examples
Gerald A. Miller ; John G. Cramer ;
Date 3 Jul 2005
Subject nucl-th hep-ph nucl-ex
AbstractThe effects of interactions of pions emitted from a dense system of matter are incorporated using an optical potential formalism. The need for replacing the plane wave pions of earlier approaches by ``distorted waves’’ computed using an optical potential is explained, and the constraining influence of chiral symmetry on the optical potential is discussed. The new HBT formalism, DWEF, which incorporates the distorted waves is derived and implemented in a practical manner suitable for numerical calculations. The STAR Au-Au pionic data (at $sqrt{s}= 200$ GeV) for HBT correlations and the spectrum is studied for three different regions of centrality, with good agreement. Furthermore, the influence of the real part of the optical potential is found to be crucial: this potential is so deeply attractive that the pions can be said to be massless inside the medium. Predictions are made for central Cu-Cu collisions. The squares of pionic distorted wave functions, obtained as exact numerical solutions to the wave equation, are displayed and significant differences with the results of using the familiar eikonal approximation are found. Using the eikonal approximation leads to a qualitative accounting for the effects of the imaginary part of the optical potential, but fails entirely to include the effects of the real part of the optical potential. A simple example is used to illustrate that an attractive optical potential can have large effects on extracting radii and can also lead to oscillations in radii measured at low momenta. We also show that a commonly used smoothness approximation is not valid for pions of low momenta, but works very well if the average pion momentum is greater than about 160 MeV/c.
Source arXiv, nucl-th/0507004
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