Recalculation of 4${\mathit{k}}_{\mathit{F}}$ correlations in one-dimensional systems

The 4${\mathit{k}}_{\mathit{F}}$ response function is recalculated for the one-dimensional electron system in the presence of the umklapp matrix element ${\mathit{g}}_3$. It is shown that the 1/${\mathrm{\omega }}_{\mathit{c}}^{2\mathrm{-}4\gamma }$ singularity is replaced by a finite value below the energy gap set by ${\mathit{g}}_3$.