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The gap function $\Delta(\omega)$ carries essential information on both, thepairing glue as well as the pair-breaking processes in a superconductor.Unfortunately, in nearly localized superconductors with a non-constant densityof states in the normal state, the standard procedure for extraction of$\Delta(\omega)$ cannot be applied. Here, we introduce a model-independentmethod that makes it possible to extract $\Delta(\omega)$ also in this case.The feasibility of the procedure is demonstrated on the tunneling data for thedisordered thin films of TiN. We find an unconventional feature of$\Delta(\omega)$ which suggests that the electrons in TiN are coupled to a verysoft pair-breaking mode.

Model-independent determination of the gap function of nearly localized superconductors