Calibration of the ATLAS electromagnetic calorimeter using calibration hits

In the present note a method to determine the electron energy from the energies measured in an electron cluster is discussed. The method is based on a detailed Monte-Carlo simulation (labeled \textit{Calibration Hits}) of electrons in the ATLAS detector in which also the energies deposited in the passive and dead materials are recorded. It allows also to compute the different contributions (energy deposited in front, in and behind the Accordion) to the total electron energy. To better understand the various contributions to the energy reconstruction three rounds of simulations have been performed: electrons hitting the middle cell centre, electrons spread uniformly over a cell in absence of magnetic field and electrons spread uniformly over a cell in presence of magnetic field. The method is applied to the Barrel calorimeter and to electrons. Its extension to the End Caps and to photons does not pose problems. In the operative ATLAS conditions an energy resolution sampling term varying from 9.9$\%$ at $\eta$=0.3 and 16.8$\%$ at $\eta$=1.2 is obtained. The linearity varies between 0.1$\%$ and 0.4$\%$ in the energy interval 10-100GeV over the same $\eta$ range.