  Dynamical dipole $\gamma$-ray emission in heavy-ion collisions is explored in
the framework of the quantum molecular dynamics model. The studies are focused
on systems of $^{40}$Ca bombarding $^{48}$Ca and its isotopes at different
incident energies and impact parameters. Yields of $\gamma$ rays are calculated
and the centroid energy and dynamical dipole emission width of the $\gamma$
spectra are extracted to investigate the properties of $\gamma$ emission. In
addition, sensitivities of dynamical dipole $\gamma$-ray emission to the
isospin and the symmetry energy coefficient of the equation of state are
studied. The results show that detailed study of dynamical dipole $\gamma$
radiation can provide information on the equation of state and the symmetry
energy around the normal nuclear density.
