  Irradiation of superconductors with different particles is one of many ways
to investigate effects of disorder. Here we study the disorder-induced
transition between $s_\pm$ and $s_{++}$ states in two-band model for Fe-based
superconductors with nonmagnetic impurities. Specifically, the important
question of whether the superconducting gaps during the transition change
smoothly or steeply? We show that the behavior can be of either type and is
controlled by the ratio of intra- and interband impurity scattering and a
parameter $\sigma$ that represents a scattering strength and changes from zero
(Born approximation) to one (unitary limit). For the pure interband scattering
potential and $\sigma \lesssim 0.11$, the $s_\pm \to s_{++}$ transition is
accompanied by the steep behavior of gaps, while for larger values of $\sigma$,
gaps change smoothly. The steep behavior of the gaps occurs at low
temperatures, $T < 0.1 T_{c0}$, otherwise it is smooth. The critical
temperature $T_c$ is always a smooth function of the scattering rate in spite
of the steep changes in the behavior of the gaps.
