Calculation of the transverse nuclear relaxation rate for YBa_{2}Cu_{3}O_{7} in the superconducting state

The importance of the electronic spin fluctuations in the ${\mathrm{CuO}}_2$ planes in the theory of the transverse nuclear relaxation for ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ has been demonstrated by Pennington and Slichter. We present the predictions of a RPA-like theory for the transverse nuclear relaxation time, τ, in the superconducting state. s- and d-wave gap symmetries yield distinctively different results for ${\mathrm{\tau }}^{\mathrm{-}1}$; for an s-wave gap ${\mathrm{\tau }}^{\mathrm{-}1}$ decays rapidly below ${\mathit{T}}_{\mathit{c}}$, while for a d-wave gap it remains nearly constant. Measurements of ${\mathrm{\tau }}^{\mathrm{-}1}$ below ${\mathit{T}}_{\mathit{c}}$ could provide valuable information about the symmetry of the superconducting state. Results for the temperature dependence of ${\mathrm{\tau }}^{\mathrm{-}1}$ in the normal state are also given.