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 cm −3 and the electron temperature is moderately higher than the Fermi energy. The ion acoustic wave, a longitudinal collective mode in plasmas, plays a crucial role in a range of applications, such as the Thomson scattering [1,2] and the Brillouin scattering [3]. Understanding the dynamics of the wave in dense plasmas or warm dense matter is important in various context, including the inertial confinement fusion [4,5] and the compression of x-rays [6][7][8][9].The decay rate of the ion acoustic waves in plasmas is often modeled by the prevalent Landau damping theory. However, this theory is inadequate for dense plasmas, as the Umklapp process, which is not accounted for, becomes pronounced in high densities. It was shown that the Umklapp process dominates the Landau damping for low-k plasmons [10][11][12]. Even though the detailed underlying physical mechanisms of the plasmons are different from those of the ion acoustic waves, it is expected that the Umklapp process is also important to the ion acoustic waves. The goal of this paper is to estimate the effect of this process. Starting from the plasmon damping theory in dense plasmas [11], a new theory predicting the ion acoustic wave sampling is proposed and a regime where the decay rate is larger than the prediction by the Landau damping theory is identified. This result would have implications on the Brillouin scattering of dense plasmas, the x-ray Thomson scattering, and the reflection problem in the inertial confinement fusion.First we provide a brief review on the Landau damping theory for the ion-acoustic wave. Only a neutral plasma of single ion-species ions is considered for simplicity. We denote the electron (ion) temperature by T e (T i ), the corresponding density by n e (n i ), the mass by m e (m i ), and the charge by Z e = 1 (Z i = Z), where the charge neutrality condition reads n e = Zn i . The longitudinal dielectric function is ǫ(k, ω) = 1 + χ e + χ i , whereω 2 i,e = 4πn i,e Z i,e e 2 /m i,e is the ion (electron) plasmon † Current Address: 28 Benjamin Rush Ln. Princeton, NJ 08540 * Electronic address: seunghyeonson@gmail.com frequency, and f i,e is normalized as f i,e = 1d 3 v. We assume v ti < ω/k ≪ v te , where v ti,te = T i,e /m i,e . This is a necessary condition for a moderate Landau damping. Under this assumption, χ e and χ i can be estimated to be χ e ∼ = 1/(kλ de ) 2 and χ i ∼ = −(ω i /ω) 2 , where λ de = T e /4πn e e 2 is the Debye screening length. The condition ǫ = 0 yields the dispersion relation for the ion acoustic wave,where V = ZT e /m i . The ion acoustic wave decay rate from the Landau damping theory is given to bewhereand S = ω iaw /kv te,ti . According to the Landau damping theory for the ion acoustic wave, there are many elec...