In previous years, the acceptance for Bhabha scattering events depended only upon the stability of the energy calibration of the forward calorimeters. In 1993, however, the presence of the SiW calorimeters in front of the FD imposed a sharp angular cut at both ends, so that the cross section was dependent on the position and dimensions of the interaction region. These estimates were made using a simple Monte Carlo model which assumed that the acceptance of the FD changes from one to zero at the boundary of the SiW. Figure shows the mean positions of the beam spot for the different OPAL data-taking periods in 1993. Because of the variation of the beam spot position, the absolute value of the accepted Bhabha cross section was time-dependent. During the scan, the mean beam spot positions for the different energy points were highly correlated, so although the absolute values of the cross sections changed with time, the relative values of cross sections at different energies remained nearly constant.
Table lists the luminosity weighted mean beam spot positions for the different energy points.
Also listed are the estimated systematic errors arising from the differences in mean interaction points. The only significant error arises for the pre-scan data, due to a large shift in the position of the beam spot. However, the relative luminosity measurement for this data set has hardly any impact on the results quoted in section . Fluctuations in the calibration of the forward calorimeter also affected the absolute values of the Bhabha cross sections. Using the observed energy spectra, the dependence of the cross section on changes in the energy calibration was determined to be where is the cross section for accepted events.