  A theory for laser ion acceleration is presented to evaluate the maximum ion
energy in the interaction of ultrahigh contrast (UHC) intense laser with a
nanometer-scale foil. In this regime the energy of ions may be directly related
to the laser intensity and subsequent electron dynamics. This leads to a simple
analytical expression for the ion energy gain under the laser irradiation of
thin targets. Significantly, higher energies for thin targets than for thicker
targets are predicted. Theory is concretized to the details of recent
experiments which may find its way to compare with these results.
