Effect of electron irradiation on resistivity and London penetration depth of (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$

The effect of electron irradiation on the in-plane resistivity and London penetration depth was studied in single crystals of (Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ (x = 0.19, 0.24, and 0.34). The irradiation fluence varied between $8.7\times10^{18}$ and $5.2\times10^{19}$ electrons per cm$^{2}$. We found a profound decrease of the critical temperature, $T_c$, by 3 - 10 K depending on doping and the irradiation dose. Expectedly, the residual resistivity increases. The analysis of low-temperature part of London penetration depth shows that the superconducting gap becomes more anisotropic in under-doped (x = 0.19 and 0.24) crystals. Interestingly, however, the full - gap at the optimal doping (x = 0.34) remained at the same $\Delta(0)/T_c$ ratio after $5.2\times10^{19}$ e/cm$^2$ irradiation even though $T_c$ has decreased by almost 10 K (1/4 of the original value). The results will be discussed in a framework of s$_\pm$ pairing with a complex interplay between intra - and inter - band interactions and scattering.