Asymmetry parameter of peaked Fano line shapes

The spectroscopic line shape of electronic and vibrational excitations is ubiquitously described by a Fano profile. In the case of nearly symmetric and peaked Fano line shapes, the fit of the conventional Fano function to experimental data leads to difficulties in unambiguously extracting the asymmetry parameter, which may vary over orders of magnitude without degrading the quality of the fit. Moreover, the extracted asymmetry parameter depends on initially guessed values. Using the spectroscopic signature of the single-Co Kondo effect on Au(110) the ambiguity of the extracted asymmetry parameter is traced to the highly symmetric resonance profile combined with the inevitable scattering of experimental data. An improved parameterization of the conventional Fano function is suggested that enables the nonlinear optimization in a reduced parameter space. In addition, the presence of a global minimum in the sum of squared residuals and thus the independence of start parameters may conveniently be identified in a two-dimensional plot. An angular representation of the asymmetry parameter is suggested in order to reliably determine uncertainty margins via linear error propagation.