  The ground state of a spin-1/2 Heisenberg chain with both frustration and
long-range interactions is studied using Lanczos exact diagonalization. The
evolution of the well known dimerization transition of the system with
short-range frustrated interactions (the J1-J2 chain) is investigated in the
presence of additional unfrustrated interactions decaying with distance as
1/r^a. It is shown that the continuous (infinite-order) dimerization transition
develops into a first-order transition between a long-range ordered
antiferromagnetic state and a state with coexisting dimerization and critical
spin correlations at wave-number k=\pi/2. The relevance of the model to real
systems is discussed.
