Theory of near-zero-wave-vector neutron scattering in Haldane-gap antiferromagnets

One-dimensional integer-spin Heisenberg antiferromagnets have disordered ground states and a gap to a triplet magnon near the antiferromagnetic wave vector, k≊π. Near a zero wave vector the lowest energy excitation is a pair of magnons. We calculate the neutron-scattering cross section near k=0, using a Landau-Ginsburg model and exact S-matrix results for the O(3) nonlinear σ model. The cross section is proportional to ${\mathit{k}}^2$. As a function of energy, it shows a rounded peak somewhat above the two-magnon threshold. The effects of anisotropy are also considered.