The correlation potential, felt by a positron diffusing in some semiconductors and produced by polarisation cloud around the positron, is evaluated in the local density approximation (LDA). The electronic and the positronic structures are obtained using both pseudopotential and LMTO methods. The effects of LDA correlation potential agree well with the calculations beyond LDA by Pennetta and Baldereschi. Finally, the lifetimes are calculated using the annihilation enhancement factors.