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

London penetration depth in Ba(Fe$_{1-x}$T$_x$)$_2$As$_2$ (T=Co, Ni) superconductors irradiated with heavy ions