  Irradiation with Pb ions was used to study the effect of disorder on the
in-plane London penetration depth, $\lambda(T)$, in single crystals of
Ba(Fe$_{1-x}$T$_x$)$_2$As$_2$ (T=Co, Ni). An increase of the irradiation dose
results in a monotonic decrease of the superconducting transition temperature,
$T_c$, without affecting much the transition width. In both Co and Ni doped
systems we find a power-law behavior, $\Delta\lambda(T) \propto T^n$, with the
exponent $n$ systematically decreasing with the increase of disorder. This
observation, supported by the theoretical analysis, conclusively points to a
nodeless $s^\pm$ state with pairbreaking impurity scattering (interband) with
strength being intermediate between Born and unitary limits.
