  In this work, we firstly investigate how to and how well one can reproduce
the Woods-Saxon density distribution of initial nuclei in the framework of the
improved quantum molecular dynamics model. Then, we propose a new treatment on
the initialization of nuclei. The initialization of the nuclei is correlated
with the nucleonic mean-field potential with the same potential energy density
functional, in which the three-body force term is accurately calculated. Based
on the new version of the model, the influences of the width of wave function,
calculations of three-body force, and the slope of symmetry energy on the heavy
ion collision observables, such as the neutron to proton yield ratios for
emitted free nucleons and for coalescence invariant nucleons, for
$^{124}$Sn+$^{112}$Sn at the beam energy of 200 MeV per nucleon are discussed.
Our calculations show that the neutron to proton yield ratios at the high
kinetic energy region can be used to probe the symmetry energy above the
saturation density.
