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Irradiation with 2.5 MeV electrons at doses up to 5.2 $\times$10$^{19}$electrons/cm$^2$ was used to introduce point-like defects in single crystals ofBa$_{1-x}$K$_x$Fe$_2$As$_2$ with $x=$ 0.19 ($T_c=$ 14 K), $x=$ 0.26 ($T_c=$ 32K) and 0.34 ($T_c=$ 39 K) to study the superconducting gap structure by probingthe effect of non-magnetic scattering on electrical resistivity, $\rho(T)$, andLondon penetration depth, $ \lambda (T)$. For all compositions, the irradiationsuppressed the superconducting transition temperature, $T_c$ and increasedresistivity. The low - temperature behavior of $\lambda (T)$ is best describedby the power - law function, $\Delta \lambda (T) = A(T/T_c)^n$. Whilesubstantial suppression of $T_c$ supports $s_{\pm}$ pairing mechanism, insamples close to the optimal doping, $x=$ 0.26 and 0.34, the exponent $n$remained high ($n \geq 3$) indicating robust full superconducting gaps. For the$x=$ 0.19 composition, exhibiting coexistence of superconductivity and long -range magnetism, the suppression of $T_c$ was much more rapid and the exponent$n$ decreased toward dirty limit of $n$ = 2. In this sample, the irradiationalso suppressed the temperature of structural/magnetic transition, $T_{sm}$,from 103 K to 98 K consistent with the itinerant nature of the magnetic order.Our results suggest that underdoped compositions, especially in the coexistingregime are most susceptible to non-magnetic scattering and imply that inmulti-band Ba$_{1-x}$K$_x$Fe$_2$As$_2$ superconductors, the ratio of theinter-band to intra-band pairing strength, and associated gap anisotropy,increases upon the departure from the optimal doping.

physical review. b, condensed matter and materials physics

Effects of electron irradiation on resistivity and London penetration  depth of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($x \leq$ 0.34) iron - pnictide  superconductor