  An angle-resolved photoemission study of the scattering rate in the
superconducting phase of the high-temperature superconductor \LSCO\ with
$x=0.145$ and $x=0.17$, as a function of binding energy and momentum, is
presented. We observe that the scattering rate scales linearly with binding
energy up to the high-energy scale $E_1\sim0.4$ eV. The scattering rate is
found to be strongly anisotropic, with a minimum along the (0,0)-($\pi,\pi$)
direction. A possible connection to a quantum-critical point is discussed.
