  The X-ray emission from the circumstellar interaction in Type II supernovae
with a dense circumstellar medium is calculated. In Type IIL and Type IIn
supernovae mass loss rates are generally high enough for the region behind the
reverse shock to be radiative, producing strong radiation, particularly in
X-rays. We present a model for the emission from the cooling region in the case
of a radiative reverse shock. Under the assumption of a stationary flow, a
hydrodynamic model is combined with time dependent ionization balance and
multilevel calculations. The applicability of the steady state approximation is
discussed for various values of the ejecta density gradient and different sets
of chemical composition. We show how the emerging spectrum depends strongly on
the reverse shock velocity and the composition of the shocked gas. We discuss
differences between a spectrum produced by this model and a single-temperature
spectrum. Large differences for especially the line emission are found, which
seriously can affect abundance estimates. We also illustrate the effects of
absorption in the cool shocked ejecta. The applicability of our model for
various types of supernovae is discussed.
