Calculation of the electromagnetic penetration depth requires calculation of the imaginary part of the dielectric constant of the system of interest. For simple metals, for this purpose use can be made of the analytic expressions calculated by K. Sturm, the link to the relevant publication I present below.

One important point deserves mentioning here. Considering a periodic crystal, the square of the (complex) refractive index is equal to the reciprocal of the head element of the inverse of the dielectric matrix of the system in the momentum representation (more about this shortly). If the latter dielectric matrix were diagonal (which is the case for uniform ground states), then the square of the refractive index would be equal to the dielectric constant. In crystals, this is not the case due to Umklapp processes, arising from the fact that in periodic crystals momentum is conserved only up to a reciprocal-lattice vector. Therefore, it is important that in practice one calculates the dielectric matrix, inverts it and then takes the reciprocal of the head element of this matrix. Neglecting the inversion, that is just by taking the head element of the dielectric matrix, amounts to neglecting the so-called local-field effects, the fact that light upon entering a crystal undergoes multiple scattering, in each of which it can take up and give up momentum associated with the reciprocal-lattice vectors (the 'local' electromagnetic field configuration inside a crystal is not the same as that of the incident light). 

In the momentum representation, the dielectric matrix ε is a matrix whose indices are those of the underlying reciprocal-lattice vectors; in εl,l' the indices l and l' refer to the reciprocal-lattice vectors Kl and Kl' respectively. The head element of the matrix ε, as well as that of the inverse of the dielectric matrix ε-1, corresponds to Kl = Kl' = 0.

Lastly, the matrix ε depends on the wave vector q and the frequency ω, which in the relevant calculations are to be identified with the wave vector and the frequency of the incident light (here X ray). The above-mentioned Umklapp processes account for the off-diagonal elements of ε to be in general non-vanishing.

For completeness, below I also present a link to a relevant publication (see in particular Eqs. (26) and (27) herein).

http://www.tandfonline.com/doi/abs/10.1080/00018738200101348

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.46.15812

Maybe this website is of some help for you!

http://henke.lbl.gov/optical_constants/atten2.html

Thank you Behnam and Philipp, i got answer my question from your answer. thank you once again

This is also a useful site:

http://11bm.xray.aps.anl.gov/absorb/absorb.php

You can also download the program XOP which can calculate and plot absorption vs energy for any material. It also has a lot of other useful functionality for x-ray optics ray tracing, heat load calculation, x-ray source spectra, etc...

http://www.esrf.eu/Instrumentation/software/data-analysis/xop2.3

Ah, I did my dissertation based in part on that question, precisely :) And the Henke tables, though undoubtedly an excellent reference, do not contain the details of the fine structure in the absorption that depend on the crystal structure of the material in question, and depending on the material and the exact energy (or wavelength if you prefer) of the X-rays, they can enhance or decrease absorption by more than 10% compared to standard tables which usually just give a "background" or general value. I recommend you visit the FEFF project homepage http://www.feffproject.org/

I will not go into theoretical or experimental detail since that is not my intention here, and all of it is much better explained in a more complete (and more lengthy) manner in a few references I am presenting; I am only trying to recommend the FEFF software to do a calculation, as it is rather a fast, real space code that agrees very well (within 1%) with most experimental data I am personally familiar with.

This first reference illustrates my point more clearly --- in the article, it is mentioned how obtaining x-ray images of integrated circuit interconnects made of tungsten is a necessary tool, but also a technological challenge. I should point out, however, the FEFF software used in it was missing an absorption channel (something discovered over the course of research that lead to my dissertation) so it somewhat underestimates the absorption, which has since been corrected, giving results much closer to the experimental values in the same article:

• Levine, Grantham, Tarrio, Patterson, McNulty, Levin, Ankudinov and Rehr, "Mass absorption coefficient of Tungsten and Tantalum, 1450 eV to 2350 eV: Experiment, Theory, and Application", J. Res. Nat. Stand. Technol, Vol. 108, pages 1-10, 2003.

A few other reference articles are:

• Rehr, J.J and R.C. Albers, "Theoretical approaches to the x-ray absorption fine structure", Reviews of Modern Physics, Vol. 72, No. 3, July 2000
• Elam, W.T. and B.D. Ravel, J.R. Sieber, "A new atomic database for X-ray spectroscopic calculations", Radiation Physics and Chemistry, Vol. 63, pages 121-128, 2002
• Rehr, J.J. and A.L. Ankudinov, "Solid state effects on X-ray absorption, emission and scattering processes", Radiation Physics and Chemistry, Vol. 70, pages 453-463, 2004
• M.P. Prange, J.J. Rehr, G. Rivas, J.J. Kas and John W. Lawson, "Real space calculation of optical constants from from optical to x-ray frequencies", Physical Review B, Vol. 80, 155110, 2009

http://www.feffproject.org/