Dear Tao Zeng,

there is an empirical parameter description of the energy/wave-length dependence of the x-ray absorption (mass-attenuation coefficient µ/rho) from the early 1900 given by Victoreen.

µ/rho = C*lambda3 - D*lambda4+ sigmaK-N*N*Z/A

with µ/rho as the mass-attenuation coefficient,

lambda as the x-ray wave-length,

N as the Avogadro number;

Z as the atomic number and

A as the atomic weight.

C and D are the empirical parameters; they change when crossing the absorption edge...

The term 'sigmaK-N*N*Z/A' is the contribution of the Compton scattering to the x-ray attenuation and its energy dependence is given by the Klein-Nishina (K-N) cross-section.

You can find a detailed description in the International Tables for X-ray Crystallography, Vol. III.

I will send you an excerpt of the relevant pages therein by RG messenger...

(just done...)

Unfortunatlely the parameters C and D are based on the wave-length description of µ/rho in the tables.

Conversion between wave-length lambda and photon energy E is done by:

E * lambda = h*c

numbers entered according to h and c:

E[eV] * lambda[A] = 12398[eV*A]

Final remark:

When using the formula above, there is a lot of calculation to do. Especially when going the very hard X-ray regime, where the Compton scatter cannot be neglected.

A way to get an easy access to the energy dependence of the x-ray attenuation is the use of the NIST/XCOM database:

https://physics.nist.gov/PhysRefData/Xcom/html/xcom1.html

Here you can put in the energies by hand or by data file. There is no need to have a look at the absorption edges or whether the photon energy might be too high...

Hints on some obstacles*) in using the XCOM program are given in:

Presentation How to use XCOM

*) e.g. units and data format

Good luck and

best regards

G.M.

Dear Tao Zeng ,

additional remark:

I have found one of my Victoreen calculations done many years ago.

Please see the attachment: the red curve is the Victoreen calculation according to the Victoreen formula without the Klein-Nishina contribution.

The parameters C and D were taken from the International Tables For X-Ray Crystallography, Vol III, as mentioned above.

The data of the blue curve were taken from the Veigele tables (CRC Handbook of Spectroscopy Vol. I); at that time XCOM was not born yet...

You see, that both curves perfectly match above*) Ge-K-edge energy without the use of any relative scaling factor and that the K-N contribution is very small and thus it is not necessary to be taken into account here.

*) only here the used parameters C1 (=238) and D1 (=81,1) are valid...

Best regards

G.M.