Low-temperature specific heat (SH) and resistivity were measured on Ba(Fe_{1-x}Co_x)2As_2 single crystals in wide doping region. A sizeable residual specific heat coefficient \gamma_0 was observed in the low temperature limit of all samples. The specific heat jump near T_c, i.e. \Delta C/T|{T_c} and the upper critical field H_{c2}^c (H||c) were also determined. It is found that -\gamma_0, \Delta C/T|{T_c}, \sqrt{H{c2}^c} and T_c all shared a similar evolution with doping. All these can be well understood within the model of S pairing symmetry when accounting the Co-dopants as unitary scattering centers in the FeAs planes. Our results give a direct evidence for the violation of the Anderson theorem in FeAs-based superconductors.

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