  The effect of correlation on Peierls transition, which is accompanied by a
dimerization, t_d, of a bond alternation for transfer energy, has been examined
for a half-filled one-dimensional electron system with on-site repulsive
interaction (U). By applying the renormalization group method to the
interaction of the bosonized Hamiltonian, the dimerization has been calculated
variationally and self-consistently with a fixed electron-phonon coupling
constant (\lambda) and it is shown that t_d takes a maximum as a function of U.
The result is examined in terms of charge gap and spin gap and is compared with
that of the numerical simulation by Hirsch [Phys. Rev. Lett 51 (1983) 296].
Relevance to the spin Peierls transition in organic conductors is discussed.
