  We compute the exact 4-spinon contribution to the zero-temperature dynamical
structure factor of the spin-1/2 Heisenberg isotropic antiferromagnet in zero
magnetic field, directly in the thermodynamic limit. We make use of the
expressions for matrix elements of local spin operators obtained by Jimbo and
Miwa using the quantum affine symmetry of the model, and of their adaptation to
the isotropic case by Abada, Bougourzi and Si-Lakhal (correcting some overall
factors). The 4-spinon contribution to the first frequency moment sum rule at
fixed momentum is calculated. This shows, as expected, that most of the
remaining correlation weight above the known 2-spinon part is carried by
4-spinon states. Our results therefore provide an extremely accurate
description of the exact structure factor.
