  We study the magnetic properties of a frustrated Heisenberg spin chain with a
dynamic spin-phonon interaction. By Lanczos diagonalization, preserving the
full lattice dynamics, we explore the non-adiabatic regime with phonon
frequencies comparable to the exchange coupling energy which is e.g. the
relevant limit for the spin-Peierls compound $CuGeO_3$. When compared to the
static limit of an alternating spin chain the magnetic properties are strongly
renormalized due to the coupled dynamics of spin and lattice degrees of
freedom. The magnitude of the spin triplet excitation gap changes from a strong
to a weak dimerization dependence with increasing phonon frequencies implying
the necessity to include dynamic effects in an attempt for a quantitative
description of the spin-Peierls state.
