  The results of a search for top squark (stop) pair production in final states
with one isolated lepton, jets, and missing transverse momentum are reported.
The analysis is performed with proton--proton collision data at $\sqrt{s} = 8$
TeV collected with the ATLAS detector at the LHC in 2012 corresponding to an
integrated luminosity of $20$ fb$^{-1}$. The lightest supersymmetric particle
(LSP) is taken to be the lightest neutralino which only interacts weakly and is
assumed to be stable. The stop decay modes considered are those to a top quark
and the LSP as well as to a bottom quark and the lightest chargino, where the
chargino decays to the LSP by emitting a $W$ boson. A wide range of scenarios
with different mass splittings between the stop, the lightest neutralino and
the lightest chargino are considered, including cases where the $W$ bosons or
the top quarks are off-shell. Decay modes involving the heavier charginos and
neutralinos are addressed using a set of phenomenological models of
supersymmetry. No significant excess over the Standard Model prediction is
observed. A stop with a mass between $210$ and $640$ GeV decaying directly to a
top quark and a massless LSP is excluded at $95$ % confidence level, and in
models where the mass of the lightest chargino is twice that of the LSP, stops
are excluded at $95$ % confidence level up to a mass of $500$ GeV for an LSP
mass in the range of $100$ to $150$ GeV. Stringent exclusion limits are also
derived for all other stop decay modes considered, and model-independent upper
limits are set on the visible cross-section for processes beyond the Standard
Model.
