  We report calculations of the high-order harmonic spectra of few-atomic
clusters of two noble gases, helium and krypton, subjected to laser pulses of
intensities above $10^{13}$ W/cm\textsuperscript{2}. We employ a fully
\textit{ab intio} framework, namely the real-time time-dependent configuration
interaction singles coupled to a discrete Gaussian basis set. Our model
reproduces the observed higher than quadratic dependence between the high-order
harmonic yield and the number of atoms, and the obtained value of the
enhancement rate is in quantitative agreement with experimental results. We
suggest a mechanism responsible for the high-order harmonic enhancement,
according to which, after the tunneling ionization, the residual ion polarizes
the electron densities of surrounding atoms in the cluster, which leads to
increased electron-electron repulsion during the recollision. The proposed
mechanism is not only fully consistent with both our calculations and the
experimental data, but can also explain the limitations of previous theoretical
studies on high-order harmonic generation in clusters.
