Dear Chinedu Onyeke ,

please have for example a look at page 4&5 (F4.3 & F4.4 ('2 Some X-ray Basics')).

https://juser.fz-juelich.de/record/134957/files/F4_Baumgarten.pdf

Here you see for the case of Cu*) the overall energy dependence of the x-ray absorption coefficient/cross section. The absorption coeffient does not only change 'far away' from the edge but also close to the edge(s).

The overall wavelength/energy dependence can be approximated by a Victoreen function:

µ(lambda) = a*lambda3 - b*lambda4

or µ(E) = a'*E-3 - b'*E-4

This approximation is valid between the absorption edges and up to some keV above K-edge energy.

The coefficients a (a') and b (b') change when crossing an absorption edge.

For a logarithmic presentation of µ(E) please see for example:

https://physics.nist.gov/PhysRefData/XrayMassCoef/ElemTab/z29.html

Here you see that close to the edge and 'far away' there is the same type of energy dependence.

*) Cu ist just an example; such Victoreen function are also valid for other elements; but having other individual coefficients a (a') and b (b').

Best regards

G.M.

Dear Chinedu Onyeke ,

this is simply a matter of quantum mechanics: Below the edge, the absorption related to this particular edge is zero - simply because the electron cannot be excited.

Above the edge, due to the transition matrix element (see Fermi's Golden rule), the probability to excite the electron into unoccupied states decreases, the larger the difference between the energy of the exciting photon and the binding energy of the photon is.

You may find a calculus e.g. in the book of Alford, Feldman & Mayer

Fundamentals of Nanoscale Film Analysis,

Article Fundamentals of Nanoscale Film Analysis

page 181 to 184.

Hope this helps, Dirk

Thank you all