Polishing the lens: I. Pionic final state interactions and HBT correlations: distorted wave emission-function (DWEF) formalism and examples

The emission of pions produced within a dense, strongly interacting system of matter in the presence of strong radial flow and absorption is described using a relativistic optical model formalism, replacing the attenuated or unattenuated plane waves of earlier emission-function approaches with 'distorted wave' solutions to a relativistic wave equation including a complex optical potential. The resulting distorted wave emission-function model (DWEF) is used in numerical calculations to fit HBT correlations and the resonance-corrected pion spectrum from central-collision STAR Au+Au pion data at \sqrt{s}= 200\ GeV . Excellent agreement with the STAR data is obtained. The applications are extended by applying linear participant scaling to the spacetime parameters of the model while keeping all other parameters fixed. This allows us to predict HBT radii over a range of centralities for both Au+Au and Cu+Cu collisions. Good agreement is found with STAR HBT data for all but the most peripheral collisions. The squares of pionic distorted wavefunctions, 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.