By Bernd Lohmann

Attitude and spin resolved Auger emission physics bargains with the theoretical and numerical description, research and interpretation of such different types of experiments on unfastened atoms and molecules. This monograph derives the overall thought utilising the density matrix formalism and, by way of irreducible tensorial units, so known as nation multipoles and order parameters, for parameterizing the atomic and molecular platforms, respectively. it's the first ebook on attitude and spin-resolved Auger emission.

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67) kq where the anisotropy parameter Bscat is defined as Bscat (K Q , kq) = 1 tr V tkq V T (J )+ KQ . 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 .

E. the definition of the reaction plane, the two sets of state multipoles can be simply transformed by us(K) ing the reduced rotation matrices dQ Q (θ ). They are real numbers and solely depend on the polar angle θ . The reduced rotation matrices show some useful symmetries which are explicitly discussed in Appendix B. 115) we eventually get + = I (θ ) tkQ A(KkQ) T (J )+ KQ dQ (K) Q (θ ). 4 The Auger Emission 41 Carrying out the summation over all magnetic quantum numbers the generalized anisotropy parameter A(KkQ) can be expressed as (Lohmann 1990) √ j j (2K + 1)(2k + 1) i(σ −σ ) + i e (−1)Jf +J +j A(KkQ) = 4π|p|2 jj b × Jf V (j J )Jf Jf V (j J )Jf × (2b + 1) (2 + 1)(2 + 1)(2j + 1)(2j + 1) ⎧ ⎫ ⎨K b k ⎬ j j K K b k b 1/2 .

The reaction plane a most simple coordinate system occurs. This is because the polarization density matrix cannot be diagonalized for an arbitrarily polarized beam. We discussed this problem for electron impact ionization (Lohmann 1984), and for the case of photoionization with an arbitrarily polarized synchrotron beam (Kleiman et al. 1999a). We will choose the coordinate system shown in Fig. 3. The laboratory frame is denoted by XY Z, the Z-axis is parallel to the incident beam direction. The reaction plane is spanned by the axis of the incoming projectiles and the direction of the observed Auger electrons.