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Electromagnetic Shower Properties in a Lead-Scintillator Sampling Calorimeter

The Collider Detector at Fermilab (CDF) is a general-purpose experimental apparatus with an inner tracking detector for measuring charged particles, surrounded by a calorimeter for measurements of electromagnetic and hadronic showers. We describe a {\sc geant4} simulation and parameterization of the response of the CDF central electromagnetic calorimeter (CEM) to incident electrons and photons. The detector model consists of a detailed description of the CEM geometry and material in the direction of the incident particle's trajectory, and of the passive material between the tracker and the CEM. We use {\sc geant4} to calculate the distributions of: the energy that leaks from the back of the CEM, the energy fraction sampled by the scintillators, and the energy dependence of the response. We parameterize these distributions to accurately model electron and photon response and resolution in a custom simulation for the measurement of the $W$ boson mass.