q dependence of the dynamic susceptibility χ’’(q,ω) in superconducting YBa₂Cu₃O_6.6 (T_c=46 K)

q-dependent neutron-scattering measurements of the dynamic susceptibility χ’’(q,ω) in superconducting YBa₂Cu₃O_6.6 are presented. The observed magnetic scattering near the antiferromagnetic zone center has a nontrivial, approximately flat-topped q dependence. A separable model of the susceptibility, χ’’(q,ω)=χ’’(ω)F(q), is found to describe this scattering at all energies in the range 2 meV ≤ħω≤40 meV. Measurements at temperatures above and below T_c=46 K indicate that the q-dependent ‘‘shape’’ function, F(q), is the same in both the superconducting and normal states. A phenomenological expression for F(q) is presented and the physical significance of its parametrization is discussed. These results are compared with current theories in the literature.