Prospects for the Top Pair Production Cross-section at $\sqrt{s}$ = 10 TeV in the Single Lepton Channel in ATLAS

The measurement of the top quark pair production cross-section at the LHC is considered for a center of mass collision energy of 10 TeV and an assumed 200 pb^-1 of integrated luminosity. We present a detailed study of the prospects for measuring the cross-section with the ATLAS detector using final states consisting of a single lepton ($e$ or $mu$) plus jets. We describe methods for obtaining the cross-section based on two simple but different event selections, neither of which require the ability to tag jets originating from a $b$-quark and one of which does not require the use of a missing energy cut. These event selections can be used to clearly demonstrate the existence of top quarks in the early data. A method to measure the dominant W+jets background from the data is developed and shown to significantly reduce the systematic uncertainties of the ttbar cross-section measurements. Assuming the Standard Model scenario, we expect a measurement of the cross-section with a relative uncertainty of less than 20% (excluding the luminosity uncertainty).