Deconvolution of the lifetime broadening from x-ray absorption spectra of atomic and molecular species

An algorithm suitable to deconvolve the entire core-hole lifetime broadening from x-ray absorption spectra is described in detail. The algorithm is based on the convolution theorem in Fourier space and is implemented numerically for the treatment of typical spectra with an arbitrary energy sampling. The adoption of a Gaussian filter to avoid noise blow-up allows one to sharpen a Lorentzian profile of width Γ into a Gaussian with σ ≈ Γ/3. The method is applied to previously published K-edge spectra of isolated atomic and diatomic molecular species such as Kr, Br2 and I2. In the Kr case the main Rydberg resonance is clearly separated from the continuum threshold. The region of the [1s4p] and [1s4s] double-electron excitation resonances is highlighted with an unprecedented resolution and is found to be very similar to the Ar K-edge [1s3p]-[1s3s] resonance region. In the diatomic molecular cases, a complete separation of the main resonance from the rest of the spectrum is achieved in Br2, whereas the corresponding I2 resonance, originally visible as a hump in the K-edge threshold, is highlighted.