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Nuclear spin-lattice relaxation rate and nonmagnetic pair-breaking effect in electron-doped Pr_{0.91}LaCe_{0.09}CuO_{4-y}: Signature of highly anisotropic s-wave gap

We numerically calculate the nuclear spin-lattice relaxation rate (Rs) in the superconducting state in terms of anisotropic s-wave gaps. By taking into account electron-phonon coupling, our calculated Rs for a conventional s-wave superconductor, indium, is in quantitative agreement with the experimental data with a clear Hebel-Slichter peak. In contrast, by using the highly anisotropic s-wave gaps inferred from the magnetic penetration depth and scanning tunneling microscopy, our calculated Rs curves for electron-doped Pr_{0.91}LaCe_{0.09}CuO_{4-y} show no Hebel-Slichter peak, in agreement with the experimental data. Finally, the observed weak nonmagnetic pair-breaking effect provides unambiguous evidence for a highly anisotropic s-wave gap in this underdoped cuprate.