Strong field tunnel ionization of an atom is considered from the point of view of semiclassical initial value representation methods which are based on real-valued classical trajectories alone. While the straightforward application of such propagators fails to give an accurate description of tunnel ionization in one dimension, incorporating the semiclassical propagator into S-matrix techniques standard in strong field physics leads to a more accurate method which recovers the tunneling dynamics. From the point of view of strong field physics, this procedure offers a method of incorporating core effects into the standard strong field approximation. In two dimensions, both the standard and the new semiclassical propagators are shown to give equally accurate results at sufficiently short times, but the new method exhibits much better scaling of the convergence rate with increasing dimensionality.
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