Precision Luminosity for $Z^{0}$ Lineshape Measurements with a Silicon-Tungsten Calorimeter

The measurement of small-angle Bhabha scattering is used to determine the luminosity at the OPAL interaction point for the LEP I data recorded between 1993 and 1995. The measurement is based on the OPAL Silicon-Tungsten Luminometer which is composed of two calorimeters encircling the LEP beam pipe, on opposite sides of the interaction point. The luminometer detects electrons from small-angle Bhabha scattering at angles between 25 and 58mrad. At LEP center-of-mass energies around the Z0, about half of all Bhabha electrons entering the detector fall within a 79nb fiducial acceptance region. The electromagnetic showers generated in the stack of 1 radiation length tungsten absorber plates are sampled by 608 silicon detectors with 38,912 radial pads of 2.5mm width.The fine segmentation of the detector, combined with the precise knowledge of its physical dimensions, allows the trajectories of incoming 45GeV electrons or photons to be determined with a total systematic error of less than 7microns. We have quantified all significant sources of systematic experimental error in the luminosity determination by direct physical measurement. All measured properites of the luminosity event sample are found to be in agreement with current theoretical expectations. The total systematic measurement uncertainty is 3.4x10^-4, significantly below the theoretical error of 5.4x10^-4 currently assigned to the QED calculation of the Bhabha acceptance, and contributes negligibly to the total uncertainty in the OPAL measurement of Gamma{invisible}/Gamma{l+l-}, a quantity of basic physical interest which depends crucially on the luminosity measurement.