Only the absorption side is considered, and the fine structure of the extended side is not considered
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.
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