  To include the bound electron effects in particle-in-cell (PIC) simulation,
we propose a model in which the response of the dipole components of partially
ionized ions to external electromagnetic fields can be included. Instead of
treating the macro-ion particle as a single particle without an internal
structure, the ions are considered to have a structure composed of a central
nucleus and a bounded electron cloud in our model. The two parts experience the
interactions of both the external electromagnetic fields and the internal
Coulomb fields. In this way, the laser scattering effects by a partially
ionized medium can be modeled properly in the PIC simulation. The laser
propagation in a neutral medium and the Bragg scattering of the laser in
crystal structure have been simulated with a PIC code modified based on our
model as the benchmark. Our model may find applications to study some
interesting problems, such as the x-ray laser-driven wakefield acceleration in
crystals, the x-ray laser-driven high energy density physics, and intense laser
propagation in partially ionized nonlinear optical materials, etc.
