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By Bernd Lohmann

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1. Predictions for the spin polarization vector of the Auger electron Polarization of projectiles unpol. e, γ , trans. pol. e, trans. pol. e, long. pol. e, circ. pol. γ , lin. pol. γ , lin. pol. γ , P=0 Px = 0 Py = 0 Pz = 0 η2 = 0 η3 = 0 η1 = 0 Auger electrons px py pz 0 =0 0 =0 0 =0 0 =0 0 =0 0 =0 =0 0 =0 0 =0 0 =0 0 0 oscillations the direction of the E vector is physically unimportant and only its axis is physically defined. Thus, for a fully linearly polarized photon beam it is sufficient to consider the two cases of an in-plane and a perpendicular to the plane linearly polarized beam.

4 Wigner–Eckart Theorem An important tool in angular momentum theory is the Wigner–Eckart theorem. It allows for decoupling those quantities which depend explicitly on the dynamics of the interaction from those which are purely geometrical. 27) where J TK J denotes the corresponding reduced matrix element. 28) J TK J = 2K + 1. 27), we see that the tensor operators T (J J )KQ are purely geometrical quantities. e. the creation of an inner shell hole. Particularly, we consider the ionization and excitation process with arbitrarily polarized photons and electrons, respectively.

68) For describing the initial and final states we adopt the notation of the previous sections. The initial electron is characterized as p0(+) ms0 where p0(+) denotes, in the sense of scattering theory, an incoming electron with impact p0 and outgoing boundary conditions (cf. Starace 1982), and ms0 denotes its magnetic spin quantum number. Inserting complete basis sets and expressing the tensors in terms of 3j -symbols yields √ (2k + 1)(2K + 1) Bscat (K Q , kq) = (−1)J −M+1/2−ms0 dp 2J0 + 1 MM ms ms0 ms M0 0 × × × J Mp ms |V |J0 M0 p0(+) ms0 ∗ (+) J M p(−) ms |V |J0 M0 p0 ms0 (−) 1/2 1/2 k ms0 −ms0 −q J J K M −M −Q .