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Electron collisions for a two dimensional Fermi liquid (FL) are shown to givea quasiparticle damping with interesting frequency and temperature variationsin the BCS superconducting state. The spin susceptibility which determines thestructure of the damping is analyzed in the normal state for a Hubbard modelwith a constant on--site Coulomb repulsion. This is then generalized to thesuperconducting state by including coherence factors and self energy and vertexcorrections. Calculations of the NMR relaxation rate reveal that the FL dampingstructure can reduce the Hebel--Slichter peak, in agreement with data on theorganic superconductor (MDT-TTF)$_2$AuI$_2$. However, the strongly suppressedFL damping in the superconducting state does not eliminate the Hebel-Slichterpeak, and thus suggests that other mechanisms are needed to explain the NMRdata on (TMTSF)$_2$ClO$_4$, the BEDT organic compounds, and cupratesuperconductors. Predictions of the temperature variation of the damping andthe spin response are given over a wide frequency range as a guide toexperimental probes of the symmetry of the superconducting pairs.Comment: 10 pages, RevTeX 3.0, 9 figures in uuencoded postscrip

Fermi-liquid damping and NMR relaxation in superconductors