  A theory for the ion acoustic wave damping in dense plasmas and warm dense
matter, accounting for the Umklapp process, is presented. A higher decay rate
compared to the prediction from the Landau damping theory is predicted for
high-Z dense plasmas where the electron density ranges from $10^{21}$ to $
10^{24} \mathrm{cm^{-3}}$ and the electron temperature is moderately higher
than the Fermi energy.
