General formulation for photon-induced two-electron emission

According to equs. (1.48a) and (1.48b), integration over the spectrometer function can be done in either kin or pass. One obtains for the area over Gsp( kin, pass) the value Tkx A sp, and for the area over Gsp( kin, pass) the value fcj A sp, where A sp is the fwhm of the spectrometer function, and the constant kx = 1.06 is often set to unity (see footnote concerning equ. (2.39a)). (iv) In addition to the given energy distributions one has also to consider the relations which follow from energy conservation  

In these expressions, the energies refer to the actual values (the mean values are characterized by a superscript 0). 

After these preliminaries, one can introduce the intensity distribution function /s( kjni, kin2) for electron pairs created in the source volume (subscript s ) with kinetic energies kinl and kin2. For direct double photoionization one obtains 

X S(Eph - kinl - kin2 - ,+ +) d ph, (10.52a) where the deferential cross section which is a smooth function of the kinetic energies can be taken out of the integral as an on-the-energy-shell value. Integration over the photon energies then leads to 

For photon-induced two-step double ionization the treatment is slightly different. As expressed in equ. (4.62c), the Lorentzian function Lr(E, ,+ ), which arises from the decay of the intermediate state, appears and energy conservation holds separately for each of the two steps (see equ. 10.51b)). Since the Lorentzian function is not smooth it has to be taken into account explicitly in the evaluation of the energy integrals. Hence, one gets 

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