Two theorems on the kernel of Faddeev equations for the scattering of three charged particles and some applications

The operator TcG0, which represents the singular part of the kernel of the Faddeev equations for the scattering of charged particles above breakup threshold, is studied. The operator is considered in two classes of functions. The functions from the first class have an on-shell limit and the functions from the second class have an on-shell singularity of a type (z−P 2)iτ, τ∈R. In both classes the most singular part of TcG0 is found to be proportional to a delta function. In order for Faddeev equations to have a solution in the second class, τ is shown to be equal to the sum of the Sommerfeld parameters of all two-body subsystems.

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