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Especially, for the case that K = 1 we obtain δ1 (Jf = 0) = 3 . 147) Thus, δ1 (Jf = 0) is generally a positive number. Applying the monotonicity theorems of analysis one can show that δ1 is monotonic decreasing as a function of increasing initial total angular momentum J . 0 for the case that J = 1/2, a lower limit can be given for the case that J → ∞. 148) as general limits for the parameter δ1 . 5. 149) ξK = K(K + 1) A(000) where the anisotropy coefficient A(K11) is solely real for K = odd and fully imaginary for K = even.

Carrying out the partial wave expansion of the incoming electron p0 ms0 (−) and of the outgoing electron p ms , respectively, and applying the same standard methods of angular momentum algebra as in the previous sections, also see Sect. 1, the summation over the magnetic quantum numbers can be carried out and the anisotropy parameter may be expressed as Bscat (K kq) = (2k + 1)(2K + 1) 2J0 + 1 ΔE 4π|p0 |2 j i 0− 0 e j i(σ 0 −σ 0 ) 0 0 0 0 j0 j0 j J1 J1 b × (−1)J +J1 +J1 +J0 +j −j0 + 0 −1−K +q × (Jj )J1 V (J0 j0 )J1 (Jj )J1 V (J0 j0 )J1 × (2 0 + 1)(2 × (2b + 1) × j 0 j0 K J1 J1 J0 0 + 1)(2j0 + 1)(2j0 + 1)(2J1 + 1)(2J1 + 1) b k K 0 −q q ⎧ ⎫ ⎨ 0 b 0 ⎬ J J K 1/2 k 1/2 .

The neutral initial atomic state is excited via photoabsorption. This has been particularly used in the investigation of Auger emission from excited rare gases; the so-called resonant Auger transitions. This type of Auger transitions will be discussed in more detail in Sect. 6. 54) Γγ and the anisotropy parameter of photoexcitation as √ (2K + 1)(2Γ + 1) Bexci (K Q , Γ γ ) = 2J0 + 1 (−1)J −M+1−λ MM M0 λλ × J M|Ti |J0 M0 ωnλ J M |Ti+ |J0 M0 ωnλ × 1 1 Γ λ −λ −γ J J K M −M −Q . 55) Applying the dipole approximation and using standard methods of angular momentum algebra we are able to eliminate the summation over all magnetic quantum numbers.

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