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 almost-equal-to pi. Near 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-Ginzburg model and alternatively exact S-matrix results for the O(3) nonlinear sigma-model. The cross section is proportional to k2. As a function of energy, it shows a rounded peak somewhat above the two-magnon threshold. The effects of anisotropy are also considered.