Exchange boson dynamics in cuprates: optical conductivity of HgBa_2CuO_4+delta.

The electron-boson spectral density function I;{2}chi(Omega) responsible for carrier scattering of the high temperature superconductor HgBa_{2}CuO_{4+delta} (T_{c}=90 K) is calculated from new data on the optical scattering rate. A maximum entropy technique is used. Published data on HgBa_{2}Ca_{2}Cu_{3}O_{8+delta} (T_{c}=130 K) are also inverted and these new results are put in the context of other known cases. All spectra (with two notable exceptions) show a peak at an energy (Omega_{r}) proportional to the superconducting transition temperature Omega_{r} approximately 6.3k_{B}T_{c}. This charge channel relationship follows closely the magnetic resonance seen by polarized neutron scattering, Omega_{r};{neutron} approximately 5.4k_{B}T_{c}. The amplitudes of both peaks decrease strongly with increasing temperature. In some cases, the peak at Omega_{r} is weak and the spectrum can have additional maxima and a background extending up to several hundred meV.