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Auger decay of molecular double core-hole state

We report on theoretical Auger electron kinetic energy distribution originated from sequential two-step Auger decays of molecular double core-hole (DCH) state, using CH4, NH3 and H2CO molecules as representative examples. For CH4 and NH3 molecules, the DCH state has an empty 1s inner-shell orbital and its Auger spectrum has two well separated components. One is originated from the 1st Auger transition from the DCH state to the triply ionized states with one core hole and two valence holes (CVV states) and the other is originated from the 2nd Auger transition from the CVV states to quadruply valence ionized (VVVV) states. Our result on the NH3 Auger spectrum is consistent with the experimental spectrum of the DCH Auger decay observed recently [Phys. Rev. Lett. 105, 213005 (2010)]. In contrast to CH4 and NH3 molecules, H2CO has four different DCH states with C1s^{-2}, O1s^{-2} and C1s^{-1}O1s^{-1} (singlet and triplet) configurations, and its Auger spectrum has more complicated structure compared to the Auger spectra of CH4 and NH3 molecules. In the H2CO Auger spectra, the C1s^{-1}O1s^{-1} DCH -> CVV Auger spectrum and the CVV -> VVVV Auger spectrum overlap each other, which suggests that isolation of these Auger components may be difficult in experiment. The C1s^{-2} and O1s^{-2} DCH -> CVV Auger components are separated from the other components in the H2CO Auger spectra, and can be observed in experiment. Two-dimensional Auger spectrum, representing a probability of finding two Auger electrons at specific pair of energies, may be obtained by four-electron coincidence detection technique in experiment. Our calculation shows that this two-dimensional spectrum is useful in understanding contributions of CVV and VVVV states to the Auger decay of molecular DCH states.