Factorisation of beams in van der Meer scans and measurements of the $\phi^*_{\eta}$ distribution of $Z\rightarrow e^+e^-$ events in pp collisions at $\sqrt{s}=8$ TeV with the ATLAS detector

Two analyses of data recorded in proton-proton collisions at the ATLAS detector in 2012 are presented in this thesis. The first pertains to the beam separation (van der Meer) scans required to calibrate the absolute luminosity. An estimate is made for the size of the correction needed to the standard van der Meer calibration method, which assumes that the proton bunch density profiles are factorisable. This is done by observing and modelling the evolution of various beam spot phenomena during the separation scans. The second analysis described is a series of measurements of the $Z/\gamma$ cross-section, differential in the $\phi^*_{\eta}$ observable, for different ranges of the boson invariant mass and absolute rapidity. In particular the events in which the boson decays to electron-positron pairs are considered. The $\phi^*_{\eta}$ observable is defined in terms of the well-measured lepton directions and enables a probe of initial state gluon radiation in the non-perturbative regime of QCD.