By Kahn S.M., Sunyaev R.A.

After 3 many years of severe learn in X-ray and gamma-ray astronomy, the time used to be ripe to summarize simple wisdom on X-ray and gamma-ray spectroscopy for scholars and researchers able to get involved in new high-energy missions. This quantity exposes either the medical fundamentals and smooth equipment of high-energy spectroscopic astrophysics. The emphasis is on actual rules and watching equipment instead of a dialogue of specific periods of high-energy items, yet many examples and new effects are incorporated within the 3 chapters in addition.

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Because the atomic electrons form a system of identical particles and because they are fermions, the total wave-function must be anti-symmetric with respect to particle interchange. We can construct such an anti-symmetric wave-function by forming the following linear combination of product wavefunctions: 1 ψ({r j }) = √ N! (−1)P ψ1 (r j1 )ψ2 (r j2 ) . . ψN (j N ) . (143) P Here, in each term in the sum, the set of single-electron wave-functions is arranged in the same order, but the electron coordinates, r j1 , r j2 , .

That is the distorted wave approach. Usually distorted wave radial wave-functions are calculated in a partial wave expansion, summing over states of definite orbital angular momentum l. Close to threshold, the energy of the outgoing electron is low and only a small number of terms in the partial wave expansion need be kept. The maximum l required can be roughly estimated from classical considerations: L ≈ pf a ⇒ l ≈ kf a (172) where a is the characteristic dimension of the atom. At high impact energies, many partial waves are required and the plane-wave Born approach provides a much simpler alternative.

One couples their product together to yield states of definite J 2 and Jz . This is called an LS coupling scheme or sometimes Russell-Saunders coupling. The anti-symmetrization of the wave-function involves a superposition over permutations of the electron coordinates. Coupling involves a super(i) (i) position over different values of ml and ms . In principle, one can antisymmetrize first and couple afterwards or couple first and anti-symmetrize afterwards. In practice, the latter is usually easier.

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